MANUAL 
 
 HYDRAULIC MINING. 
 
 FOR THE USE Of 
 
 THE PRACTICAL 
 
 T. F. VAX WAGENEN, E.M. 
 
 THIRD EDITION DEVISED. 
 
 NEW YORK: 
 D. VAN NOSTRAND COMPANY, 
 
 23 MURRAY & 27 WARREN STS. 
 1900. 
 
Copyright, 
 
 D. VAN NOSTRAND CO., 
 1897. 
 
PREFACE. 
 
 THE following pages are written solely for 
 the use of the practical and working miner, 
 who, while rarely deficient in common sense, 
 is generally unacquainted with the principles of 
 physics and more or less rusty in arithmetical 
 methods. In the daily discharge of his business 
 he is continually confronted with engineering 
 problems of more or less complexity, and com- 
 pelled to depend for their solution trained en- 
 gineering advice being unobtainable or too ex- 
 pensive upon his own limited experience or 
 upon that of his co-laborers. 
 
 Under these circumstances, errors in con- 
 struction and operation are frequently repeated. 
 The author ventures the hope that the study and 
 use of the following pages will, to some extent 
 at least, obviate the necessity for costly experi- 
 menting, now so common. 
 
 3 
 
 438587 
 
The Manual does not claim to cover the whole 
 subject, nor to answer all questions in hydraulic 
 engineering. Nor will it take the place of an 
 experienced and competent engineer in impor- 
 tant enterprises. On the contrary, no miner 
 who is not himself an expert, and who can af- 
 ford it, should be without such advice and assis- 
 tance as can be afforded by a well-educated 
 and practised hydraulic engineer. 
 
 THEO. R VAN WAGENEN, 
 
CONTENTS. 
 
 PAGE. 
 
 INTRODUCTORY REMARKS, . . .7 
 
 CHAPTER I. 
 
 GENERAL PHYSICAL CONDITIONS, . e .11 
 
 CHAPTER II. 
 GENERAL METHODS OF PLACER-MINING, . . 19 
 
 CHAPTER III. 
 DIRECTIONS FOR THE MINER, . . . .25 
 
 CHAPTER IV. 
 THE PROPERTIES OF WATER, . . .43 
 
 CHAPTER V. 
 CONSTRUCTION OF WATER WAYS, . . .51 
 
 CHAPTER VI. 
 FLOW OF WATER IN FLUMES AND DITCHES, . . 58 
 
 CHAPTER VII. 
 IRON PIPING, . . . . . .04 
 
 CHAPTER VIII. 
 NOZZLES AND DISCHARGE, . . . .79 
 
 CHAPTER IX. 
 
 THE SLUICE, . . . . . .82 
 
INTRODUCTORY REMARKS. 
 
 HYDRAULIC mining is the art of separat- 
 ing gold from gravel, sand, and clay cement, 
 through the medium of moving water and the 
 force of gravity. 
 
 The process is one lying wholly within the do- 
 main of the science of mechanics a branch of 
 human knowledge now so well understood that 
 results may be predicated with extreme accura- 
 cy, if correct premises are obtained. 
 
 Hence", ^hydraulic mining presents fewer risks 
 and more certainties than any other department 
 of mining, other tilings being equal. It is sim- 
 ply a question of moving gravel or soil from one 
 place to another. Given, therefore, in addition 
 to an abundance of water to move and wash the 
 gravel, ample space to deposit it again after it 
 lias been washed, and the problem of obtaining 
 a profit is reduced to a minimum. 
 
8 INTRODUCTORY REMARKS. 
 
 Gold occurs in gravel deposits in a metallic 
 condition. The chemical and mechanical ope- 
 rations required to separate it from the vein 
 substances with which it was originally asso- 
 ciated have all been performed by nature. That 
 wonderful agency has also supplemented her 
 work by again collecting the particles of metal 
 ^wifckifi certain limits, fir-other words,^ cfegrada- 
 tion and erosion of quartz-veins has been fol- 
 lowed by the partial concentration of the mfc 
 apt 90* broken up; and while this operation has 
 
 ^rr^*^i 
 
 not resulted in Jwr enrichment of the gold-bear- 
 ing material ifm^-the contrary, it is much poorer, 
 -%nik "for bulk); the metal is placed in association 
 with substances from which it uiagrbe separated 
 
 e\l 
 
 with extreme ease and very small cost. 
 
 A 
 
 As an example, the gold-bearing veins of the 
 western United States have an average value of 
 about ten dollars per ton of quartz extracted, 
 which ten dollars can be mined, transported to 
 mill, crushed, amalgamated, refined, and sold at 
 a gross cost of about eight dollars per ton, or 
 eighty per cent. The same gold vein, after pass- 
 ing through the laboratory of nature, will consist 
 
IN TROD UCTOR Y REMA RKS. Q 
 
 of a gravel-bed or deposit worth about twenty 
 cents per ton, which twenty cents may be se- 
 cured and marketed at a cost not over five cents, 
 or twenty-five per cent. Other things being 
 equal, therefore, hydraulic mining presents three 
 times the chance for profit that is fountl in 
 gold quartz-mining, and one-third the riskpivith 
 the additional advantage that the extent and 
 richness of ^k^' gravel-beds may be completely 
 studied and ascertained before working Ht, and 
 at a slight cost ; while vein-mining is from 
 first to last more or less of an experiment and 
 '4 chance. \*f) 
 
 The records of mining show that over seventy- 
 five per cent, of all the gold mined within his- 
 toric times has been derived from the working 
 of gravel-beds. It is also a matter of fact that 
 the area of auriferous gravel deposits is vastly 
 greater than that of quartz-veins. This is es- 
 pecially the case on the Pacific coast of both 
 North and South America. The immense chain 
 of mountains extending from Alaska to Pata- 
 gonia bears evidence of having been at once one 
 of the loftiest and oldest of the great upheavals 
 
I O IN TROD UCTOR Y REMA RKS. 
 
 of geological time. From one extremity to the 
 other it is ribbed with metallic veins, which 
 through the ages have been worn down and 
 away, and their debris deposited by rivers and: 
 i^ses- and glaciers, in all the various ways in 
 which nature works. And these great deposits, 
 consisting of old channel-beds, forsaken bars, 
 grass and forest covered moraines, and sterile 
 terraces, contain, beyond a doubt, more millions 
 than have yet been mined. The great Bine Lead 
 of California, which has been traced for seven 
 hundred miles along the western flank of the Si- 
 erras ; the channels and bars of Montana, which 
 
 7&?v/"C-^L 
 
 represent the pathway of the Missoun^of old; 
 
 the great morainal deposits of Western- Colorado; 
 
 /i 
 ated the arid and dry terraces and ravines of 
 
 A 
 Arizona all these are nature's gold-filled vaults, 
 
 inviting the enterprise, the energy, and the in- 
 genuity of tfee=3pfe*fee man, and promising, not 
 the irregular and doubtful returns which charac- 
 terize precious-metal mining of the present day, 
 but steady and continuous results, based on an 
 imkustry -as legitimate and safe as agriculture or 
 general trade. 
 
 
 
CHAPTER I. 
 
 GENERAL PHYSICAL CONDITIONS. 
 
 GKAVEL deposits containing gold are gene- 
 rally considered to be the disintegrated remains 
 of mountains which were originally seamed with 
 auriferous quartz-veins, or of strata of rock in 
 which the metal was disseminated, or both. 
 The material forming these deposits consists of 
 gravel, rounded boulders, sand, and clay, gene- 
 rally being in .conformable layers or strata, b.ut 
 at times disposed without regularity. These de- 
 posits are beyond doubt the result of mechanical 
 precipitation. The occurrence of gold dissemi- 
 nated through the gravel is generally ascribed to 
 the same cause, though some are inclined to be- 
 lieve that chemical action has supervened in the 
 case of the metal. The point is one of more 
 scientific than practical interest, though the lat- 
 
I 2 fft DRA ULIC MINING. 
 
 ter theory will perhaps explain why placer gold 
 is purer than vein gold. 
 
 Gravel deposits may be subdivided as follows : 
 
 {a) Ancient river-channels. 
 
 () Recent " " 
 
 (6-) Bars. 
 
 (d) Moraines. 
 
 (e) Terraces. 
 
 (/) Lake-bottoms (ancient and recent). 
 
 In general it may be stated that gold will be 
 found in greater quantities and in coarser frag- 
 ments in deposits which are 
 
 1. Nearest to the original deposits. 
 
 2. Have been deposited on the steepest grades. 
 
 3. Contain the most gravel and boulders. 
 
 4. Contain the most iron. 
 
 There are many cases in America, however, 
 where the gold is found almost exclusively in the 
 clay or cement layers, but this does not appear 
 to be the rule. 
 
 Where gravel deposits are made up of several 
 layers of differently-sized material, often some of 
 these layers are wholly barren, or at least un- 
 profitable. In general the metal is found in 
 
HYDRA ULIC MINING. I 3 
 
 greater quantities in the lower layers of the gra- 
 vel, near and on the bed-rock. 
 
 Frequently in exploring and testing gravel de- 
 posits it is necessary or convenient to find the 
 weight of the mass ; this operation will be facili- 
 tated by the following table : 
 
 One cubic ft. of dry, loose loam weighs 72 to 80 Ibs. 
 
 packed " " 90 to 100 " 
 
 " " wet, loose " " 66 to 68 " 
 
 " " packed' 4 " 85 to 95 " 
 
 " " solid quartz " 165 " 
 
 " broken " " 94 " 
 
 solid limestone " ....170 " 
 
 " " broken " " 96 " 
 
 " " fine sand, dry, " 100 to 117 " 
 
 ordinary gravel, free from 
 cement, and containing no heavy boul- 
 ders (dry), weighs 90 to 100 " 
 
 One cubic ft. filled with boulders not over 
 
 six inches in diameter (dry) weighs 95 to 105 " 
 
 Auriferous gravel deposits are formed on all 
 kinds of bed-rock, such as granites, limestones, 
 slates, and quartzites, and even sandstones. The 
 nature of the bed-rock rarely, if ever, affects the 
 
1 4 H YDRA ULJC MINING. 
 
 quality of the deposit, though, as will Be seen 
 hereafter, it may affect its economic value. 
 
 GOLD. 
 
 The precious metal is of a fine yellow color 
 when chemically pure, and weighs about nine- 
 teen times as much as an equal bulk or volume 
 of water. Hence 
 
 One culno inch of gold weighs 696 Ibs. 
 
 One cubic foot " " 1204 " 
 
 Its value per standard Troy ounce is $20 67, 
 and per pound (Troy) $248 04 
 
 In nature gold never occurs pure, but is inva- 
 riably accompanied with some silver, and often 
 with other metals. In this condition it presents 
 a whitish or reddish yellow color, according as 
 the bulk of the accompanying metal is silver or 
 copper. 
 
 The metal is exceedingly tenacious, malleable, 
 and melts at a temperature of 2,016 deg. Fan. 
 
 In practice its comparative purity is expressed 
 by the term "fineness," and this is estimated on 
 the basis of 1,000 as a unit of measurement. 
 
H ) DRA ULIC MINING. I 5 
 
 Thus, a mass or nugget of gold containing 78 
 per cent, of gold, 18 per cent, of silver, and 4 
 per cent, of other substances will be said to be 
 .780 (seven hundred and eighty thousandths) 
 fine. 
 
 In the gravel deposits gold occurs as nuggets 
 (masses of irregular shape and size) ; shot-gold 
 (rounded pellets like very small bird-shot) ; 
 leaf-gold (thin sheets sometimes one-tenth of an 
 inch square) ; coarse flat gold (same size as the 
 latter, but thicker) ; and dust, which is often so 
 fine as to be inappreciable to the naked eye. 
 Occasionally wire-gold is found, but that is rare. 
 The physical qualities of this metal are such 
 that, while it will remain almost wholly intact 
 under the action of chemical reagents, it is 
 easily affected by abrasion, and, if carried for 
 considerable distances together with gravel and 
 ice, is ground rapidly to the finest powder. 
 
 It does not always follow that a gravel deposit 
 containing even a goodly quantity of gold per 
 yard can be worked with profit. The particles 
 of metal, to be capable of being saved by cheap 
 mechanical means, must possess a combination 
 
1 6 // YDRA ULIC MINING. 
 
 of weight and shape which will permit the ac- 
 tion of gravity to a. maximum degree. In other 
 words, if the bulk of the gold in a deposit is 
 either in the condition of a very fine dust or 
 very flat, thin scales, it will float away and resist 
 the most careful endeavors to precipitate it. 
 
 WATER. 
 
 At ordinary temperatures water is a 
 colorless liquid, weighing about 6&J- Ibs. per 
 cubic foot. At 32 deg. Fah. it becomes a solid, 
 and in the act of solidification expands one- 
 twelfth of its volume. At 212 deg. (sea-level) 
 it boils, and passes ofl: as vapor. Water is 
 slightly compressible at a pressure of 4,500 Ibs. 
 per square inch, but on removal of the force re- 
 turns instantly and completely to its former vol- 
 ume. When expanding under the influence of 
 heat or cold it is capable, as is well known, of 
 exerting enormous force. 
 
 The following table of equalities will be found 
 at times useful: 
 
H YDRA ULIC MINING. I / 
 
 1 cubic inch of water weighs 086 Ibs. 
 
 1 " foot " " 62.5 " 
 
 1 " yard " " 1680.75 " 
 
 1 " foot of ice " 57.3 " 
 
 1 U. S. gallon " 8.34 
 
 The standard measure for water in hydraulic 
 mining is the miner's inch. 
 
 The quantity of water which will escape from 
 a reservoir through an aperture in its side 1 inch 
 square, whose centre is 6 inches below the con- 
 stant level of the water, is termed a miner's 
 inch. This measure is necessarily a rough one, 
 and has doubtless been often erroneously ap- 
 plied. The aperture should have no tube or 
 conduit leading from it, and its section through- 
 out should be uniform and possess practically no 
 length. These conditions are not, however, at- 
 tained in common practice. The most common 
 illustration of the miner's inch is a hole 1 inch 
 square through an inch board. In this case the 
 length of the aperture is clearly equal to its dia- 
 meter. Where the aperture discharges a large 
 number of inches at once its diameter is of 
 course much larger, and the proportion of its 
 length to its diameter is much less. 
 
1 8 H YDRA ULIC MINING. 
 
 In round numbers the miner's inch has the 
 following values : 
 
 Cubic feet. Pounds. U. 8. gal. 
 
 Discharge per second . .0271= 1.69= 0.2026 
 
 min... 1.626 = 100. = 11.99 
 
 hour.. 97.56 = 5937. = 711.96 
 
 day(12h.)1170.7 = 71250. =8543.29 
 
 day(24h.)2341.4 =142560. =17095.78 
 
 The miner's inch as a standard of water mea- 
 surement is very defective. In the early days of 
 placer-mining, when the water was owned by 
 one set of people, who sold it in small quanti- 
 ties to another set (the miners), this standard 
 was a necessity. At present it would be better 
 if the cubic foot could be used as a measure, but 
 the change is one impossible to be made. 
 
CHAPTER II. 
 
 GENERAL METHODS OF PLACER-MINING. 
 
 THE general theory of hydraulic mining com- 
 prehends first, breaking down the gravel ; sec- 
 ond, passing it through sluice-boxes while held 
 in suspension by water; and, third, cleaning up 
 the gold caught in the boxes. 
 
 The pan, rocker, long torn, sluice, boom, and 
 hydraulic have been successively adopted in al- 
 most every gravel-mining district in America. 
 Unfortunately, exact records of the possible work 
 with each are almost unattainable, and, even if 
 they were, variations in the character of the 
 gravel would to a large extent nullify their 
 value. The following comparative table, giving 
 figures of work performed, first, on ordinary 
 gravel, which is quite tractable, and, second, on 
 cemented gravel, which is perhaps the most re- 
 fractory known, will perhaps be of value to the 
 
2O HYDRAULIC MINING. 
 
 miner. The two may bo regarded as extremes. 
 The table shows the number of cubic yards of 
 dirt which may be washed per day of 10 hours 
 per man in the first two cases each man work- 
 ing alone, and in the last four in pairs, or 
 economically- arranged gangs : 
 
 Ordinary. Cemented. 
 
 By the pan 1 cu. yd. cu. yl. 
 
 " rocker 2 " 2 ' 
 
 " long torn... 5 to 6 " 3 to 5 " 
 
 " sluice 10 to 20 " 6 to 12 
 
 " hydraulic .. 100 to 1000 " 100 to 1000 " 
 
 " boom unlimited. unlimited. 
 
 It will be understood by every miner that no 
 exact figures can be given in a comparison of 
 this nature, and that the character of the 
 ground will very largely affect the amount of 
 work done. With the pan, which will hold 
 from fifteen to thirty pounds of gravel, only 
 a very little ground can be washed under any 
 circumstances. If the ground abounds in large 
 boulders which can be removed by the hand 
 with ease, a miner will wash twice as much as 
 otherwise. One hundred pans are considered as 
 a good day's work for a careful operator. The 
 
HYDRA ULIC MINING. 2 I 
 
 same consideration that of boulders applies 
 to the work in a rocker and long torn. The 
 latter permits a more easy and thorough break- 
 ing np of cement, and the water generally 
 being supplied automatically, it is operated at 
 a smaller cost. But neither arc adapted for 
 operations on a large scale, nor in any ground 
 carrying less than three to five dollars per 
 yard. 
 
 The ground -sluice is a device which com- 
 mends itself for banks not too high to cause 
 danger from caving, and when a good grade 
 in the pit can be obtained. The unfavorable 
 point in this system lies in the fact that all 
 boulders must be moved twice, and that no 
 clean-up can be made till the end of the sea- 
 son. In consequence, either the work is pro- 
 longed, with great discomfort to the men, into 
 the period of cold weather, or much water is 
 allowed perforce to run to waste. 
 
 Whore extensive operations are contemplat- 
 ed the miner has to decide between the boom 
 and hydraulic, or a favorable combination of 
 the two. In California the boom is wholly 
 
22 // 1 'DRA ULIC MINING. 
 
 abandoned in favor of the hydraulic, and in 
 Colorado it is rapidly being superseded. Yet, 
 as a system of placer-mining, it has many 
 strong recommendations, and. according to 
 some of the best Colorado authorities, is often 
 the superior method. It seems to possess most 
 merits when either the water is very abundant 
 or very scarce. 
 
 The boom will undoubtedly cave more ground 
 per day and at a less cost than the hydraulic, 
 unless it is a very hard cement. In its opera- 
 lion it is the counterpart of the work of nature 
 in natural ravines. For the purpose of clean- 
 ing off top dirt of poor quality it has no supe- 
 rior, and for ground carrying no leaf -gold it is 
 claimed by some to be greatly preferable. Much 
 depends upon the sluice and the manner of 
 operating it. 
 
 But where the ground is hard and force is 
 necessary to tear it to pieces, where the banks 
 are low and the gravel tenacious, the hydraulic 
 is, by the testimony of most practical miners, 
 the most advantageous. In many cases the two 
 can be combined with most beneficial results. 
 
H YDKA ULIC MINING. 2 3 
 
 In deciding which plan to adopt the miner will 
 do well to bear in mind the principle that he 
 is working, as a first consideration, to make 
 money .not only to tear away the largest pos- 
 sible amount of gravel. Consequently, that 
 method or combination of methods is the cor 
 rect one which will deliver the largest quantity 
 of gravel (with its gold) at his head box in the 
 shortest time provided always that he has 
 sluice capacity and water sufficient to wash it 
 thoroughly. 
 
 In nine cases out of ten the method to be 
 adopted is decided by the amount of water 
 available ; and if the supply is unlimited (which 
 is very rarely the case) the hydraulic is always 
 better than the boom, if the two cannot be used. 
 The quantity of work possible to be done with 
 the hydraulic varies, of course, with the nature 
 of the gravel, the size of the stream, and the 
 head. A very sound practical authority gives 
 the following rough estimates : 
 
 No. 1 nozzle, supplied with 100 miners' inches 
 of water, under a head of 100 feet, assisted by a 
 
24 HYDRAULIC MINING. 
 
 ground-sluice of 100 inches, will wash 600 cubic 
 yards per day ; 3 men. 
 
 No. 4 nozzle, supplied with 700 inches, under 
 a head of 150 feet, will wash 3,000 cubic yards 
 per day ; 4 men. 
 
CHAPTER IIL 
 
 DIRECTIONS FOR THE MINER. 
 
 I ATTEMPT in this work to give rales and di- 
 rections for solving all the simpler engineering 
 problems which the practical hydraulic miner 
 (who in most cases is unacquainted with higher 
 mathematics) will have presented to him. To 
 be successful the miner must make himself 
 thoroughly acquainted with the contents of this 
 chapter, which is intended to be explanatory of 
 such mathematical operations as will be noted. 
 He who is able to add, subtract, multiply, and 
 divide will find nothing in this book beyond 
 his ability, if this chapter is carefully studied, 
 and if the same hard common sense and intel- 
 ligence which in all other matters distinguishes 
 the American miner from. other classes of work- 
 
26 HYDRAULIC MIXING. 
 
 ingmen is brought to bear on the subject. Hy- 
 draulic mining is a branch of engineering, and 
 because its operations can be guided wholly by 
 mathematical rules it presents so much of cer- 
 tainty and so little of risk. Consequently, the 
 miner who desires to improve nis property and 
 increase his profits, but is unable from various 
 causes to obtain the assistance of an experi- 
 enced engineer, will certainly find it to be 
 worth his while to gain the power of solving, 
 alone and unaided, a majority of the problems 
 which will be presented for consideration in 
 the ordinary course of his business. 
 
 I will call the reader's attention, therefore, to 
 the following subjects : 
 
 1. The use of decimals ; 
 
 2. The method of transforming fractions into 
 decimals ; and, 
 
 , 3. The principle of expressing the terms of a 
 problem in a uniform and correct manner. 
 
 DECIMALS. 
 
 The decimal system is a method of numerical 
 expression based upon a division of the unit 
 
HYDRAULIC MINING. 2/ 
 
 one (1) by ten (10) or multiples of ten (as, 100, 
 1,000, 10,000). For example, instead of say- 
 ing one-half () say five-tenths ( T 5 ), and instead 
 of saying one-quarter (J) say twenty-five one- 
 hundredths (-$/V). The system, however, does 
 not stop here, but includes a system of nota- 
 tion which does away completely with the form 
 of the fraction thus : 
 
 -f- is written .5 
 
 TTT .25 
 
 fVo " .84 
 
 TO " -012 
 
 yVoV w -611 
 
 Toifoo " .00014 
 
 Hence, to write down a decimal fraction deci- 
 mally, follow this rule : 
 
 1. Eeplace the figure 1, which is always the 
 first figure of the lower part of the fraction, by a 
 dot ( . ). 
 
 2. Rub out as many of the last figures of 
 the lower part of the fraction as there are 
 
28 HYDRAULIC MINING. 
 
 figures in the upper part, and place these figures 
 in the room of the figures rubbed out. 
 
 For instance, to express decimally the frac- 
 tion four hundred and eleven ten-millionths 
 
 Replacing the 1 by a dot, we have .0000000. 
 
 Second, as there are three figures in the upper 
 part of the fraction, we rub out the last three 
 ciphers of the above, and replace them with 411, 
 making .0000411 
 
 Again, express decimally three hundred Jind 
 one thousandths (yVoV)' 
 
 Replacing the 1 by a clot gives .000 
 
 and placing in the 301 gives .301 
 
 Again, express thirty-two tenths (ff). This 
 fraction is evidently the same as three and two- 
 tenths (Sy 2 ^), which, treated by the rule, gives 3.2. 
 
 The addition of decimals is performed exactly 
 as any other addition. Place the two or more 
 quantities under each other, taking care that the 
 decimal-points, the dots ( . ), are in a line, and 
 place the decimal-point in the answer or result 
 in the same position, thus: 
 
H YDRA I LIC MINING. 2Q 
 
 .0104 
 
 3.26 
 .192 
 114. 
 
 117.4624 
 
 In subtracting adopt precisely the same 
 
 course, thus: 
 
 1.242 
 
 .012 
 1.230 
 
 ,61306 
 .4 
 
 .21306 
 
 In multiplying place the quantities in the or- 
 dinary way, multiply as usual, and point off as 
 many figures in the result as there are decimals 
 in the two quantities multiplied, thus: 
 
 1.264 
 .06 
 
 .07584 
 
.SO HYDRAULIC MINING, 
 
 Agai n : 
 
 .1103 
 .17014 
 
 4412 
 1103 
 
 7721 
 1103 
 
 .018766442 
 
 The division of decimals is performed as fol- 
 lows: 
 
 Set down the figures as in the ordinary style 
 of long division. Annex to the dividend (the 
 quantity to be divided) first as many ciphers as 
 may be necessary to make the number of deci- 
 mal figures in the dividend equal in number to 
 those in the divisor, and, second, as many more 
 as may be necessary to obtain a figure large 
 enough to divide. 
 
 Divide as in the ordinary method. 
 
 Point oft' in the result as many places for de- 
 cimals as the number of decimals in the dividend 
 exceeds those in the divisor. 
 
HYDRA ULIC MINING. 3 1 
 
 NOTE. If the divisor or dividend consists of 
 decimals commencing with a cipher or several 
 ciphers (as, .0218 or .00014), these ciphers may be 
 wholly disregarded in the operation of division. 
 
 The following examples cover all cases : 
 (a) When the divisor is larger than the divi- 
 dend as, to divide 1.265 into .04: 
 
 1.265).04000000(3162 
 3795 
 
 2050 
 1265 
 
 7850 
 7590 
 
 2600 
 2530 
 
 In this case, there being 8 decimals in the di- 
 vidend and 3 in the divisor, the difference 5 will 
 be the correct number for the quotient or an- 
 swer, which, instead of being 3162, will be .03162. 
 
32 HYDRAULIC MINING. 
 
 (b) When the divisor is less than the dividend 
 as, to divide .142 into 4.6: 
 
 .142)4.600(32 
 426 
 
 340 
 
 284 
 
 There being an equal number of decimals in 
 both divisor and dividend in this case, the quo- 
 tient remains unaltered as 32. But if, instead of 
 annexing two ciphers, we had annexed, say, six, 
 the quotient would have been 323943, we would 
 have had four more decimals in die dividend than 
 in the divisor, hence the result would have been 
 32.3943. 
 
 In the division of decimals, ciphers may be an- 
 nexed to any extent desirable until no remainder 
 occurs; this makes the division perfect. Other- 
 wise it is an approximation. But in all calcula- 
 tions except those of a most delicate nature it is 
 sufficiently accurate to annex only enough ci- 
 phers to produce three decimal figures in the 
 result. 
 
H YDRA ULIC MINING. 3 3 
 
 (c) \Vhere ciphers are prefixed to dividend or 
 divisor, or both, a study of the following opera- 
 tion will explain the method. Thus, to divide 
 .0014 into .0000403 : 
 
 .0014). 0000403 (28 
 28 
 
 123 
 
 112 
 
 There being 7 decimals in the dividend and 
 4 in the divisor, the answer should contain the 
 difference, or 3 figures, giving, in place of 28, 
 the quantity .028. 
 
 TRANSFORMATION OF FRACTIONS INTO 
 DECIMALS. 
 
 When a problem under consideration contains 
 fractions it is always necessary to reduce these 
 to decimals. This is done by simply dividing 
 the numerator of the fraction (the top figure) 
 by the denominator (the bottom figure). Thus, 
 to reduce J to decimals divide 1 by 2 = .5 ; or to 
 reduce -f, divide 3 by 8 = .375 ; or to reduce J, 
 
34 HYDRAULIC MINING. 
 
 divide 3 by 4=.75. The division need not be 
 carried to more than three figures. 
 
 This must be done in all cases. As an exam- 
 ple, if the grade of a flume is found by experi- 
 ment to be 3^ inches per box, the fraction is 
 to be reduced to decimals by dividing 5 by 12, 
 thus : 
 
 12)5.000(416 
 48 
 
 20 
 12 
 
 80 
 
 72 
 
 Pointing off the result (416) according to the 
 rule of division of decimals, the grade is found 
 to be 3.416 inches per box. 
 
 THE PRINCIPLE OF EXPRESSING THE TERMS OF 
 A PROBLEM UNIFORMLY. 
 
 At the beginning of a problem it is necessary 
 to reduce all the elements to the right shape and 
 form. If this is done confusion will be avoided. 
 
HYDRAULIC MINING. 3.5 
 
 If it is not done the results will be false almost 
 invariably. Hence, 
 
 Express perimeter, lengths of flumes, ditches, 
 piping, head, diameters, etc., in linear feet and 
 decimals of a foot. 
 
 Express areas (such as sections of flumes and 
 piping, and mouths of nozzles) in square feet 
 and decimals of a foot. 
 
 Express discharge in cubic feet per second. 
 
 Express velocity in linear feet per second. 
 
 Express grade in decimals of a foot per linear 
 foot. 
 
 Thus, discharge from a flume or pipe, which 
 is frequently given in miners' inches, should be 
 reduced to cubic feet (see Miner's Inch) ; grade, 
 which is generally expressed in inches per box 
 (12 feet) or inches per rod (16 feet), must inva- 
 riably be altered to feet per foot ; as, for in- 
 stance, a grade of 1 inch per box equals 1 inch 
 per 12 feet, or -fa of an inch per 1 foot. But 1 1 2 - 
 of an inch equals y^ of a foot, which, reduced 
 to decimals, equals .007 of a foot nearly. The 
 correct mode of expression, therefore, will be 
 .007 feet ner foot. 
 
36 HYDRAULIC MINING. 
 
 Velocity must be expressed in feet per second, 
 and perimeters in decimals of a foot. A flume 
 having a perimeter of 20 inches measures If of 
 a foot. Reducing this to decimals, we have, in 
 place of 20 inches, 1.666 feet. 
 
 DEFINITIONS. 
 
 The subjoined definitions and explanations 
 will be found necessary to a perfect understand- 
 ing of the technical phrases used in succeeding 
 pages. The reader is therefore invited to im- 
 press on his mind the exact meaning and value 
 of each term defined : 
 
 Mass. The quantity of matter which a body 
 contains irrespective of whether that quantity 
 be diffused through a large space, through the 
 influence, for example, of heat (as in the case 
 of steam) ; or compressed into a small space, 
 through the influence, for example, of cold (as 
 in the case of ice) is called its mass. 
 
 Volume. The amount of space occupied by a 
 body is denominated its volume. 
 
 Weight. When a body is freely acted upon by 
 gravity, but is prevented from moving by some 
 
HYDRAULIC MINING. 37 
 
 supporting obstacle, the pressure on the point 
 of support is termed its weight. 
 
 Jet. A jet is the mass of water escaping from 
 a vessel through an orifice in its side or bottom, 
 which orifice, of course, must be below the level 
 of the water. 
 
 Flow. The volume of water which escapes 
 from a vessel through an orifice (which may be 
 wholly or partly under the water) in any given 
 time is its flow for that time. 
 
 Velocity. The distance passed over by any 
 given mass of water in any given time is called 
 its velocity. The direction of the motion is 
 immaterial. 
 
 Head. The vertical distance between the level 
 of standing water in -i reservoir, and the centre 
 of the orifice from which it flows into the air, 
 is called its head. 
 
 Wet Perimeter. If a flume or ditch is 20 
 inches wide, 6 inches deep, and full of water, 
 its wet perimeter is 20+ 6+6=32 inches. If 
 of the same dimensions, but only containing 
 3 inches of water, the wet perimeter is 20+3 
 -j-3=26 inches. The same flume again, if 
 
38 H YDRA ULJC MINING. 
 
 empty, has no wet perimeter at all. In other 
 words, the wet perimeter of a water- channel is 
 the length of so miicli of its base and sides as is 
 wetted by the water. This measurement deter- 
 mines friction. 
 
 Friction. When one body slides upon an- 
 other, the inequalities and roughnesses of the 
 two surfaces interlock and cause a resistance, 
 which is termed friction. If, now, the sliding 
 body has not sufficient weight and cohesion to 
 create abrasion or wear among these irregulari- 
 ties and roughnesses, the degree of friction which 
 arises bears a well-known proportion to the 
 weight of the sliding body. This is the case 
 when water slides along the floor of a flume or 
 ditch, and the proportion of friction developed 
 to the weight of the water is called 
 
 THE CO-EFFICIENT OF FRICTION. 
 
 This co-efficient, of course, varies as the water 
 is muddy or clear, or as the flume floor is rough 
 or smooth. It is however, wholly independent 
 of the areas of the surfaces in contact. In other 
 words, two flumes of different size, if made of 
 
HYDRAULIC MINING. 39 
 
 the same quality of lumber and carrying similar 
 water, will develop identical co- efficients of fric- 
 tion the proportion of friction to the moving 
 weights will be the same. But the weights of 
 water in each being different, the amount of fric- 
 tion developed in the larger flume will be greater 
 than in the smaller. 
 
 Momentum. The quantity of force which a 
 body in motion is capable of exerting when 
 stopped suddenly is called its momentum. Proba- 
 bly the best illustration of this is the power ex- 
 hibited by a jet of water when it strikes a bank 
 of gravel. It may be measured by multiplying 
 the weight of the striking body by the velocity 
 ' at which it moves. For example: A nozzle de- 
 livering a stream of water 3 inches in diameter, 
 with a velocity of 150 feet per second, will hurl 
 against a bank every second a force equal to the 
 weight of a column of water 3 inches in diame- 
 ter and 150 feet high, multiplied by 150, or 3-H 
 tons nearly. But it is to be remembered that 
 this is the amount of force developed at the 
 mouth of the nozzle only. Immediately on 
 passing into the air the stream of water, acted 
 
4O HYDRAULIC MINING. 
 
 upon by the force of gravity and the resistance 
 of the air, and further weakened through its own 
 disintegration, becomes less powerful. At a suf- 
 ficiently great distance from the mouth of the 
 nozzle the velocity will be wholly lost, and no 
 force or power remains except that due to the 
 weight of each particle of water under the influ- 
 ence of gravity. Again, it is not to be thought 
 that if a gravel-bank is struck with the force 
 above mentioned 34 tons of earth must be 
 moved per second. This statement appears to 
 be unnecessary, though it may be logically de- 
 duced from the first, unless it be remembered 
 that vast quantities of force must be expended 
 in destroying the cohesion of the gravel and 
 overcoming its inertia. Once in a state of mo- 
 tion, the force transmitted from the nozzle to 
 the gravel would, if the force could be applied 
 .at a point which would equally affect the whole, 
 give it as rapid motion as the water, less fric- 
 tion. But this can never be accomplished in 
 practice. 
 
 MENSURATION. 
 
 A few questions in mensuration will arise in 
 
HYDRAULIC MINING. 41 
 
 working the problems presented in the following 
 pages. These are as follows : 
 
 1. To find the Area of a Circle. Multiply 
 the diameter (in inches) by the decimal 3.14 
 and the product by one-quarter of the diameter. 
 The result will be the area in square inches. 
 Divide this by 144, and the result will be the 
 area in square feet. 
 
 EXAMPLE. What is the area of a circle 18 
 inches in diameter ? 
 
 16 multiplied by 3.14=50.24 multiplied by 4 
 (which is one-quarter of the diameter) =201. 06 
 square inches, which divided by 144= 1.32 square 
 feet. 
 
 2. To find the Area of a Section of a Flume 
 with Straight Sides. Multiply the width of 
 bottom (in inches) by the height of sides (in 
 inches); the, product will be the area in square 
 inches, which, divided by 144, gives the area in 
 square feet. 
 
 EXAMPLE. What is the area of a section of a 
 flume 20 inches wide and 15 inches high ? 
 
 20 multiplied by 15=300, which divided by 
 144=2.08 square feet. 
 
42 ff\ DRA UIJC MINING. 
 
 3. To find the Area of the Section of a Ditch 
 with Sloping Sides. Add together the width at 
 top and bottom (in inches), multiply this sum 
 by the depth (in inches), and divide the result 
 by 2. The quotient, divided by 144, will be the 
 area in square feet. 
 
 EXAMPLE. What is the area of the cross-sec- 
 tion of a ditch 60 inches wide at the top, 36 
 inches at the bottom, and 12 inches deep ? 
 
 60 plus 36 = 96, which multiplied by 12-1152, 
 and this divided by 2=576 square inches, which 
 divided by 144=4 square feet. 
 
 4. To find the Area of the Cross -Section of a 
 Ditch whose Sides slope to a Point at the Bot- 
 tom. Multiply the width (in inches) by half 
 the depth (in inches), and divide the product 
 by 144. The result is the area in square feet. 
 
 EXAMPLE. What is the area of a pointed 
 ditch 60 inches wide and 18 inches deep in the 
 centre ? 
 
 60 multiplied by 9 (half the depth) = 540 
 square inches, which divided by 144=3.75 
 square feet. 
 
CHAPTER IV. 
 
 THE PROPERTIES OF WATER. 
 
 IN hydraulic mining the properties of water 
 are to be considered in but two conditions: 
 
 (a) When at rest as in the case of dams, re- 
 taining walls, and pressure-boxes ; and 
 
 (if)) When in motion as in ditches and 
 flumes, 
 
 WATER AT REST. 
 
 The three principles here laid down will be 
 worth consideration by the miner who desires to 
 work understandingly. 
 
 1. Water at Rest transmits Pressure equally 
 in all Directions. If a pressure of 100 Ibs. is 
 exerted on the entire surface of the water in a 
 reservoir whose section is 10 square feet, this 
 pressure is transmitted in its entirety not only 
 to the base, but to every 10 square feet of its 
 sides. Thus, if the interior surface of the reser- 
 
44 HYDRAULIC MINING. 
 
 voir (base and sides) measures 250 square feet, 
 and a pressure of 100 Ibs. is placed on the water- 
 surface (of 10 square feet), the base and walls 
 will receive a total pressure of 2,500 Ibs. Or if 
 the box be so closed at the top as to leave but 
 one square foot of water exposed, and if a pres- 
 sure of 100 Ibs. be applied on this one square 
 foot, an equal pressure will be transmitted to 
 every square foot of interior surface, and the 
 total will consequently be 25,000 Ibs. Or, to 
 illustrate this remarkable property still more 
 thoroughly, suppose the top of the vessel to be 
 covered with the exception of one square inch. 
 If on this a pressure of 100 Ibs. is placed, every 
 square inch of interior surface will be pressed 
 outward with this weight, which, for the size 
 box under consideration, would amount alto- 
 gether to 1,800 tons. 
 
 This is the principle utilized in the hydraulic 
 press. 
 
 2. The Pressure exerted by Water on the 
 Horizontal Bottom of a Vessel is wholly inde- 
 pendent of the shape of the vessel^ and is equal 
 to the weight of a column of water whose base is 
 
H } DRA ULIC MINING. 4$ 
 
 the area of the horizontal bottom, and whose 
 height is equal to the depth of the liquid. 
 
 3. The Pressure of Water on the sides of a 
 Vessel is equal to the weight of a column of 
 water whose base is equal to the area of the side, 
 and whose height is equal to one-half the depth 
 of the liquid. 
 
 Owing to this law the pressure on the walls 
 and base of a cubical vessel is equal to three 
 times the weight of the water contained. 
 
 The two principal problems in hydraulic min- 
 ing arising under the head of water at rest are 
 those connected with the construction of dams 
 and reservoirs and water-boxes. 
 
 Keferring to the third principle just enun- 
 ciated, it will be seen that the pressure on any 
 surface under water depends upon two things 
 the depth of water and the area of the surface 
 pressed. For example, what will be the pres- 
 sure against the inner slope of a dam 50 feet 
 long, 12 feet wide, and 12 feet deep at the bot- 
 tom? Multiply the area of the slope (50x12= 
 600) by the average vertical depth in feet of the 
 centre of gravity of the slope (6) =3, 600, and 
 
46 HYDRAULIC MINING. 
 
 multiply this by 62.5 (the weight of a cubic foot 
 of water) =225,000 Ibs. 
 
 It will be noted that the pressure is not a 
 pound greater if the water reaches back from the 
 face of the dam for miles, than if it were a reser- 
 voir only a few feet broad. Hence, if a reservoir 
 is built simply for storage, make it large and 
 shallow rather than small of area and deep. 
 The loss by solar evaporation will, it is true, be 
 much grenter, but this disadvantage will be 
 counterbalanced, first, by the small leakage ; 
 second, by the cheapness of the dam ; and, third, 
 by the great safety of the construction. A 
 miner cannot go to his work under more de- 
 pressing circumstances than with the thought 
 that at the head of the gulch in which he is im- 
 prisoned is a dam whose embankment of 15 or 
 20 feet in height may at any time give way and 
 destroy not only himself and comrades, but 
 every trace of improvements that have been the 
 labor of years. 
 
 Probably the best and safest embankment, 
 where there is no carpentry or masonry, is that 
 one which is modelled on the plan of the beaver- 
 
HYDRAULIC MINING. 47 
 
 dam. This is a familiar sight in the West, and 
 its details can be easily studied. The beaver- 
 dam is seldom if ever "known to give way, and 
 this quality of stability is what is of all things 
 most desirable. 
 
 The water or pressure box has three uses. It 
 determines permanent and steady head ; it offers 
 an opportunity to clear the water from gravel 
 and other debris before passing it into the pipe, 
 and it should be the means of freeing it from a 
 large portion of the air which it absorbs while 
 travelling at a high velocity. 
 
 Construction. The pre.?sure-box should be a 
 deep vessel, with a pyramidal bottom pointing 
 downward and provided with a trap. This, on 
 being opened from time to time, will clear out 
 gravel and sand which has collected in the bot- 
 tom, and which, if allowed to accumulate, would 
 in time rise to the level of the outflow. The 
 pressure-box is best built when its height, ex- 
 clusive of pyramidal bottom, is three times its 
 greatest width. The section should be longer 
 one way than another. It should have a lip 
 overflow on one of the short sides, and the water 
 
48 HYDRAULIC MINING. 
 
 should enter the box at the centre of its top, 
 and from the same side as the discharging-lip. 
 All screening should be done in the flume. A 
 partition reaching down below the outflow, and 
 parallel with the longest sides, is highly recom- 
 mended by good authorities. The discharge- 
 hole should be two-thirds of the distance from 
 top to bottom (no increase of power is gained by 
 placing it at the bottom), and should be in one 
 of the long sides. If these directions are ob- 
 served a large quantity of the gravel unavoidably 
 carried into the box will be prevented from pass- 
 ing into the pipe, much of the air will also be 
 kept out, and a steady and even head will be se- 
 cured. 
 
 We have now to consider only the strength of 
 the box. That this is an important point may 
 be judged by the fact that if its height is 12 feet, 
 and its section 3 by 4 feet, it will have to sustain 
 a pressure of not less than 35 tons. 
 
 MEASURING THE WATER OF STREAMS. 
 
 If the channel of the stream has a moderately 
 even outline, measure its depth at regular in- 
 
HYDRA ULIC MINING 49 
 
 tervals from shore to shore. Add all these 
 depths together, and divide the sum by the 
 number of soundings. An average depth is thus 
 gained. Calculate then the area of the section 
 according to Rule 2, page 41. Measure the velo- 
 city by means of a float, and make the test about 
 half-way between the bank and the centre. Mul- 
 tiply the area by the velocity, and the product 
 will be the flow. Of course the test for velocity 
 should be made at the same point where the 
 measurements for depth are made, and a place 
 on the stream should be selected for both where 
 the banks are as nearly parallel as may be, ana 
 where the current and flow is the most tranquil. 
 
 EXAMPLE. A stream is 24 feet broad, and ten 
 soundings at every two feet on a line from bank 
 to bank give 2, 6, 8, 9, 7, 11, 11, 10, 9, and 2 
 inches as the depths. The average velocity as 
 determined by float is 4 feet per second. What 
 is the flow ? 
 
 The sum of the 10 soundings is 75 inches, 
 which gives an average depth of 7.5 inches, 
 equal to .625 of a foot. The area of the section 
 then is 24 multiplied by .625 = 15 square feet. 
 
5O HYDRAULIC MINING. 
 
 The velocity being 4 feet per second, the flow is 
 equal to 15 multiplied by 4=60 cubic feet per 
 second. 
 
 If the stream runs over a bottom so irregular 
 tli at an average depth cannot be gained or an 
 average velocity measured, there is no recourse 
 but to construct an artificial channel having no 
 grade, into which it may be turned while mea- 
 sures are made. The same rule applies in this 
 case as before, and it should be understood' that 
 in both the results are very rough approxima- 
 tions. To reduce the result to miners' inches 
 refer to the table of equalities, page 18. 
 
CHAPTER V. 
 
 CONSTRUCTION OF WATER-WAYS. 
 
 WHEIST the miner has measured the stream 
 from which he is to draw his water-supply, and 
 has determined that point where he will tap it, 
 he is prepared to consider the question of water- 
 channels. These may be of three kinds the 
 ditch, the wooden flume, and the iron pipe. The 
 ditch is the most indestructible, the cheapest, 
 and the easiest to repair. Instead of deteriorat- 
 ing, it improves in condition year by year if 
 carefully built. On the other hand, more water 
 is lost by evaporation, and in stormy seasons it is 
 subject to injury by overflows, land-slides, caves, 
 etc., etc. The wooden flume eliminates the ele- 
 ment of loss by leakage, but not by evaporation. 
 It occupies the middle ground in point of cost, 
 but requires much watching. It is, moreover, 
 the most easily destroyed by fire and flood. The 
 iron pipe prevents all loss on the way, is most 
 
52 HYDRAULIC MINING. 
 
 easily cared for, and costs the most. It is seldom 
 considered to be the best method of water trans- 
 portation, except when a necessity, as in the case 
 of siphon-bends or very steep grades, or on the 
 rocky side of mountains where ditching would 
 be costly. 
 
 It is generally desirable to have the least pos- 
 sible fall in a water channel, or, in other words, 
 to bring the water to as high a point of the 
 ground to be worked as circumstances will allow. 
 As the friction of the sides and bottom of a 
 channel retards the flow, and necessitates a high- 
 er grade than would be necessary if there were 
 none, it becomes of importance to decrease this 
 element as much as possible. On this score 
 wood and iron water-ways present decided ad- 
 vantages, owing to their comparative smooth- 
 ness. In any case, however, the quantity of 
 friction developed depends upon the wet perime- 
 ter of the channel used. The following law will 
 therefore be found of service : 
 
 TJie least wet perimeter that will hold or carry 
 a given volume is attained when the width of bot- 
 tom is from If to 2% times the depth of the side*. 
 
HYDRAULIC MINING. 53 
 
 For example, a channel having a cross- section 
 of 510 square inches will develop the least amount 
 of friction when its dimensions are 15 by 34, or 
 17 by 30, or somewhere between these measure- 
 ments. 
 
 A knowledge of this fact will be found ser- 
 viceable in constructing flumes. The least peri- 
 meter, of course, requires the least lumber, and 
 many thousand or million feet may be saved in 
 a long flume by building in the correct pro- 
 portion. 
 
 When the head of the flume is above timber- 
 line, or in high altitudes where ice forms early in 
 the fall, it is an advantage in many respects to 
 have it so narrow in width that an ice-crust can 
 easily form itself from bank to bank. If this is 
 secured water will often flow a month or six 
 weeks longer than otherwise. The reasons are 
 obvious. 
 
 In making the preliminary survey of a placer- 
 claim a sound authority advises as follows : First, 
 lay off the dump ; second, decide how much 
 grade and fall to give the sluices ; and, third, 
 find the least fall necessary between source of 
 
54 HYDRAULIC MINING. 
 
 water and water-box. The remaining distance 
 will then be the greatest head attainable. The 
 suggestion is pertinent, because it brings to mind 
 the fact that a good dump and an abundant 
 grade for sluices are fully as necessary for econo- 
 mical gravel-washing as a heavy head of water. 
 
 When the linear distance be; ween the sources 
 of supply and the water-box is determined, and 
 the least fall that will carry the water ascer- 
 tained (after considering the questions of fric- 
 tion, evaporation, and leakage), the grade per 
 foot is found by dividing the total fall in feet by 
 the total length in feet. Multiplying the result 
 (which will generally be a decimal) by 100 or 
 1,000 -will give the grade per 100 or 1,000 feet. 
 Having now the grade per foot and the quantity 
 of water to be carried (as determined by gaug- 
 ing the stream or streams tapped by the ditch or 
 flume the proper deductions having been made 
 for leakage and evaporation), the area of cross- 
 section of the water-way may be determined by 
 the rule for the determination of the least wet 
 perimeter, which has just been given. 
 
 Solar evaporation is very active at high alti- 
 
HYDRAULIC MIMXG. 55 
 
 tudes. The ordinary figures representing loss 
 through evaporation ( T V to -f^ of an inch of sur- 
 face per day) are much too small for ditches 
 above an altitude of 6,000 feet. Evaporation 
 also proceeds much more rapidly in shallow water 
 than in deep, and when the velocity is high. 
 Experiments made during 1877 on the 12-mile 
 wooden flume of the Fuller Company, on the 
 Swan River, Colorado, indicated a loss of from 
 10 to 18 per cent, daily. This flume is, how- 
 ever, an extreme case, being about 10,000 feet 
 above sea-level. Probably an inch of surface 
 would be an average loss. , 
 
 Leakage occurs most extensively in gravelly 
 soils. From 1 to 5 inches of surface per day 
 are extreme losses, with an average, perhaps, of 
 about 2 inches, which it will be always safe to 
 count on, except in old ditches. A high velo- 
 city decreases loss through the soil. 
 
 Water-channels of uniform section should al- 
 ways have a uniform grade. Otherwise there will 
 be an accumulation in some points and a thin- 
 ning-out in others, with deposits of sand and 
 silt in the latter case, and in each case with in- 
 
56 HYDRAULIC MINING. 
 
 creased danger of breakage. It will also be 
 found highly advantageous in earth ditches to 
 have a complete system of waste-weirs to carry off 
 surplus waters occasioned by floods and to lessen 
 the damage of breaks. These should be put in 
 just below wherever a new stream falls into the 
 diich, and just above those places where, by rea- 
 son of a shelly or crumbly soil, the ditcli is weak. 
 A break is bad, not only because it must be re- 
 paired, but because while being mended all min- 
 ing operations must cease. 
 
 In the spring, difficulty is often encountered 
 in starting the water through the heavy accumu- 
 lation of snow in the ditch, which, if it be long, 
 can be flushed out only with great trouble 1 . 
 This operation will be materially hastened if the 
 ditch is cleaned out in short sections of a mile or 
 two each. Cut a hole in the bank a mile from 
 the head, and when the water has soaked that 
 far it will carry off the unmelted snow through 
 this break with great rapidity. As soon as clear 
 the hole is mended and another made a mile 
 further on. Time will be saved by thus taking 
 the ditch in sections. 
 
H YDRA ULIC MINING. 5 7 
 
 Cost. When the plough and scraper can be 
 used ditching can be done at 20 cents per cubic 
 yard. If the soil is so rocky as to call for the 
 pick and shovel, it will cost from 30 to 40 cents. 
 A safe figure to be taken for the construction of 
 a ditch 3 feet wide at bottom, 4|- feet wide at 
 top, and 18 inches deep is $1.25 per rod. It 
 can be done for less. The larger the ditch the 
 less costly it will be in proportion. 
 
CHAPTER VI. 
 
 FLO W OF WATER IN FLUMES AND DITCHES. 
 
 THE following rules for the solution of prob- 
 lems concerning the flow of water in ditches and 
 iiumes are commended to the miner, only with 
 the proviso that the directions laid down in 
 Chapter V he strictly complied with. Before 
 doing any figuring let every element of the prob- 
 lem, as grade, area of section, velocity, wet peri- 
 meter, discharge, and length, be reduced from 
 the ordinary measurements usually given to 
 those laid down in the "Directions." If this is 
 done the results may be depended upon ; other- 
 wise they will be of no value. 
 
 It is to be remembered, however, that these 
 rules do not take into account leakage and 
 evaporation two elements of loss which have 
 been spoken of already. It will be impracticable 
 in this manual to enter into the details of these 
 elements of loss, as the subjects are too intri- 
 
 58 
 
HYDRAULIC MINING. 59 
 
 cate ; and, in addition, it would be unnecessary, 
 inasmuch as the records of experience are more 
 satisfactory and nearer the truth. 
 
 1. What grade per foot must be given to a 
 flume or ditch of uniform section to enable it to 
 discharge a given quantity of water in a given 
 time? 
 
 RULE 1. Divide the number of cubic feet of 
 discharge required by the area in square feet of 
 the section of the flume. This result is the 
 velocity necessary, expressed in feet per second. 
 
 Multiply this result by itself. 
 
 Multiply this product by the wet perimeter, 
 expressed in feet, and multiply this product by 
 the decimal .0001114. 
 
 Divide this product by the area of the section 
 of flume, expressed in square feet. Call the re- 
 sult A. 
 
 Multiply the velocity in feet per second by the 
 wet perimeter, expressed in feet, and multiply 
 this product by the decimal .00002426. 
 
 Divide this product by the area of the. section 
 of the flume, expressed in square feet. Call the 
 quotient B. 
 
6O HYDKA ULIC MINING. 
 
 Add together A and B. 
 
 The result is the grade per foot (expressed in 
 decimals of a foot) which must be given to the 
 flume to make it carry the required water. 
 
 EXAMPLE. What grade per foot of length 
 must be given to a 20-inch flume whose sides are 
 12 inches high, in order that it may deliver 28 
 cubic feet of water per second steadily ? 
 
 Wet perimeter, say 42 inches = 3.5 feet. 
 
 Area of section, 240 sq. inches^ 1.66 sq. " 
 
 Discharge, =28.00 cubic " 
 
 Then, dividing the discharge (28) by the area 
 of section (1.66), we have 16.86 as the velocity in 
 feet per second. 
 
 Following the rule, the velocity (16.86) multi- 
 plied by itself equals 284.25 ; multiplying this 
 by wet perimeter (3.5) produces 994.87 ; multi- 
 plying again by the decimal .0001114 produces 
 .1108 ; dividing this by urea of section (1.66) 
 gives .0667. Call this A. Multiplying the ve- 
 locity (16.86) by wet perimeter (3.5), and the 
 product by .00002426, produces .0014315, which 
 divided by the area of the section of the flume 
 (1.66) =.00086. Call this B. Adding A (.0667) 
 
HYDRAULIC MINING. 6 1 
 
 to B (.00086), we have as a final result .06756, 
 which is the grade per foot (expressed in deci- 
 mals of a foot). If we multiply this result 
 (.06756) by 1,000, we have the grade per thou- 
 sand feet, which will be 67.5 feet (near enough). 
 
 To reduce this result to the ordinary terms 
 viz., inches per box of 12 feet divide first 1,000 
 by 12, which produces 83.33 (which of course 
 represents the number of 12-foot boxes in a 
 1,000-foot flume). Then, the grade being 67.5 
 feet in 83.33 boxes, for each box it would be the 
 result of d viding 67.5 by 83.33, which is .79, or 
 the grade would be .70 of a foot per box of 12 
 feet. Finally, there being 12 inclu ^ in a foot, 
 we multiply .79 by 12 and obtain 9.48 inches per 
 box, or nearly 9^ inches. 
 
 2. What is the average velocity and discharge 
 secured in a flume or ditch of uniform cross- 
 section and grade ? 
 
 KULE 2.- Multiply area of cross-section in 
 square feet by the grade in feet per foot, and the 
 product by 9,000. 
 
 Divide this result by the wet perimeter in 
 feet. 
 
62 HYDRAULIC MIMXG. 
 
 Extract the square root of the quotient. (See 
 table at end of book. ) 
 
 From the result subtract .1089. 
 
 The result equals the mean velocity of the 
 water (expressed in feet per second). 
 
 Multiply the area of cross-section by the mean 
 velocity. 
 
 The result equals the discharge (expressed in 
 cubic feet per second). 
 
 EXAMPLE. What is the discharge attained in 
 a 30-inch flume with 12-inch sides, having a 
 uniform grade of f -* )Tr (.01) of a foot for every 
 foot of length ? 
 
 Multiplying the area of cross-section (2.5 
 square feet) by the grade (.01) produces .025 ; 
 multiplying this by 9,000 yields 225 ; dividing 
 this by the wet perimeter (4.5) gives 50, whose 
 square root is 7.0711; subtracting from this the 
 decimal .1089, we have 6.9622, which is the mean 
 velocity (expressed in feet per second). 
 
 This calculation is in reality accurate only for 
 a flume. In a ditch, where friction is greater, it 
 will be necessary to subtract about 10 per cent, 
 (or .6962) from the result found, leaving 6.266 
 
HYDRAULIC MINING. 63 
 
 as the correct figure. Then continuing, multi- 
 ply the mean velocity (6.9622) by the area of 
 cross-section (2.5) ; we have 17.40, which is the 
 discharge (expressed in cubic feet per second). 
 
 3. What must be the section of a ditch or 
 Hume of uniform grade which will discharge a 
 given quantity of water in a given time ? 
 
 There is no simple rule that will solve this 
 problem, and an answer must be sought experi- 
 mentally upon the following plan : 
 
 RULE 3. Assume a convenient section, and, the 
 grade being known, calculate its discharge ac- 
 cording to Rule 2, page 61. If this discharge is 
 greater or less than the required one try again 
 with a smaller or larger section until the correct 
 one is found. 
 
 Cost. With lumber at $12 to $15 per thou- 
 sand, delivered at the head of the flume, so that 
 it can be floated down, a flume 2 feet wide and 
 2J feet high can be finished at a cost of $3.85 
 per box (of 12 feet in length) ; and one 6 feet 
 wide and 3-J- feet high at $8.50 per box. 
 
CHAPTER VII. 
 
 IRON PIPING. 
 
 THE problems which arise in operating iron 
 pipes are the following : 
 
 1. What is the velocity attained in a cylindri- 
 cal iron pipe, laid straight or with easy curves, 
 its head, length, and diameter being known? 
 
 BULE 1. Multiply the diameter in feet by the 
 head in feet. Call this product A. 
 
 Add together the total length of pipe in feet, 
 and .54 times its diameter in feet. Call this 
 sum B. 
 
 Divide A by B. 
 
 Extract the square root of the quotient (see 
 table at end of book) ; multiply this root by 48. 
 The product will be the velocity in feet per 
 second. 
 
 EXAMPLE. What velocity will be attained in 
 a pipe 12,600 feet long, 6 inches (.5 of a foot) in 
 diameter, and having a head of 200 feet ? 
 
// } DRA ULIC MINING. 65 
 
 Multiply diameter (.5) by head (200) =100; 
 call this product A. Add to the total length 
 (12,600 ft.) 54 times its diameter: .5 multiplied 
 by 54 equals 27=12,627. Call this sum B. Di- 
 vide A (100) by B (12,627) =.0079. Extract the 
 square root of this resul f , which = .0889. Mul- 
 tiply this root by 48=4.26, which is the velocity 
 per second, in feet. 
 
 2. How many cubic feet of water per second 
 will be discharged from a cylindrical iron pipe, 
 straight or with easy curves, its head, length, 
 and diameter being known ? 
 
 RULE 2. Ascertain the velocity by preceding 
 rule. Then multiply the velocity thus attained 
 by the area in square feet of a section of the 
 pipe. The result will be the discharge per sec- 
 ond, in cubic feet. 
 
 3. What head of water is necessary for a 
 cylindrical iron pipe, straight or with easy 
 curves, its diameter and length being known, 
 to produce a given discharge per second ? 
 
 RULE 3. Multiply the required discharge 
 (expressed in cubic feet) by itself. Call this 
 A. 
 
66 HYDRAULIC MINING. 
 
 To tne total length of pipe add 54 times its 
 diameter. Call this B. 
 
 Multiply A by B. Call the product C. 
 
 Divide the diameter (expressed in feet) by 
 .235. 
 
 Multiply this product by itself continuously 
 four times. 
 
 Divide C by this product. 
 
 The quotient will be the head in feet. 
 
 EXAMPLE. What head is necessary to pro- 
 duce a discharge of 12 cubic feet per second at 
 the end of a pipe 8 inches (.666 feet) in diame- 
 ter and 350 feet long, the pipe being straight 
 or with easy curves ? 
 
 Multiply the discharge (12) by itself = 144; 
 call this A. To the total length (350) add 54 
 times its diameter (36) =386 ; call this B. 
 Multiply A (144) by B (386) =55,584 (C). Di- 
 vide the diameter (.666) by .235 = 2.834. Mul- 
 tiply this product (2.834) by itself continuously 
 four times =182.801. Divide C (55,584) by this 
 product (182.801) = 3.04 feet nearly, which is the 
 required head. 
 
 4, Wliat diameter of pipe is necessary to carry 
 
H YDRA ULIC MINING. 67 
 
 a given quantity of water per second, its length 
 and total head being known ? 
 
 RULE 4. Multiply the head in feet by 5,280, 
 and divide the product by the length in feet. 
 Call this A. 
 
 Multiply the discharge in cubic feet per sec- 
 ond by itself, and multiply this product by 
 5,280. Call this B. 
 
 Divide B by A. 
 
 Extract the fifth root of the result (see tables 
 at close of book). 
 
 Multiply this by the decimal .235. 
 
 The product is the diameter (in feet). 
 
 EXAMPLE. What must be the diameter of a 
 pipe 6,000 ft. long, with a head of 400 feet, 
 which will discharge G cubic feet of water per 
 second ? 
 
 Multiply the head (400) by 5,280=2,112,000, 
 and divide this product by the length (6,000) = 
 352 (A). 
 
 Multiply the discharge (6) by itself =36, nd 
 multiply this product by 5,280=190,080 (B). 
 
 Divide B (190,080) by A (352) =540. 
 
 Extract fifth root of this quotient (540) =3.52. 
 
68 HYDRAULIC MINING. 
 
 Multiply this root (3.52) by .235 .8272, which 
 is the required diameter (expressed in decimals 
 of a foot). 
 
 Curves. Curves and bends in pipes always 
 cause some loss of power. They also furnish a 
 place for the accumulation of air and sediment, 
 as well as weaken the tube. They are, how- 
 ever, unavoidable in practice, and the rules by 
 which to calculate the additional amount of 
 head necessary to counteract their influence, or 
 the amount of power lost, are perhaps too com- 
 plex for the aim of this work. An angular bend 
 in a pipe should be avoided, if at all possible. 
 In most placer districts there are workers of 
 sheet-metal of sufficient ability to produce cir- 
 cular elbows. The latter should be made with a 
 radius never less than five times the length of 
 their diameter. To ascertain this curve mea- 
 sure the diameter of the pipe, and cut a string 
 that will be just five times this length. Then 
 if one end of the string be held fast the other 
 will describe the correct curve. A still larger 
 radius is better when possible. In fact, the 
 gentler the curve the better. 
 
HYDRA UL1C MINING. 69 
 
 Care should be taken to back up piping very 
 solidly at each change of direction. The neces- 
 sity of this precaution will be self-evident. 
 Cases have occurred where whole sections of 
 piping poorly backed have been torn to pieces 
 as soon as the head was put on. 
 
 The cost of piping, finished and set up, may 
 be approximated as follows : 
 
 Cost at manufactory 4^c. per Ib. 
 
 Freight, 1,500 miles 3^c. 
 
 Making into pipe 3c. " 
 
 Grading, laying, ballasting, and fas- 
 tening ,c. " 
 
 12c. per Ib. 
 
 The hydraulic grade-line is an imaginary 
 straight line, extending from a point on the 
 side of the water-box or reservoir, denominated 
 the velocity-head, to the mouth of the nozzle. 
 If the pipe be constructed exactly on this line, 
 the water flowing through it, no matter what its 
 velocity or volume, will exert no bursting pres- 
 sure. In other words, the grade of the hydraulic 
 grade line is such that the velocity caused by the 
 grade is exactly sufficient to carry down all that 
 
70 HYDRAULIC MINING. 
 
 'the pipe will hold, and there is no outward pres- 
 sure exerted except that on the bottom of the 
 pipe due to the water's weight. If, however, 
 there he a change in the diameter of the pipe at 
 any point this equilibrium ceases to exist. It is 
 never possible in practice to adopt this line as a 
 course, but generally close approximations can 
 be made to it. As will be shown further on, it is 
 highly advantageous to do this wherever possible. 
 
 To find the Hydraulic Grade-Line. RULE 1. 
 Calculate the velocity in pipe due to the total 
 head. (See Rule 1, page 64.) 
 
 Look in Table 3, and find the head correspond- 
 ing to this velocity. 
 
 Lay off this head on the side of the reservoir 
 from the surface of the water. Its termina- 
 tion will mark the line of the velocity-head. 
 From this point sight to the nozzle of the pipe ; 
 the line of sight is the hydraulic grade-line. 
 
 In constructing a line of piping three cases 
 may arise by reason of the inequalities of the 
 ground to be passed over : 
 
 1. The pipe may lie below the hydraulic grade- 
 line. 
 
// 1 'DRA I 'LIC MIKING. 7 I 
 
 3. T,he pipe may lie above the hydraulic grade- 
 line. 
 
 3. The pipe may lie both above and below. 
 
 CASE 1. Pipe below Hydraulic Grade- Line. 
 There is here a bursting pressure, varying in 
 amount according to its distance below the line. 
 To find this pressure at any point, ascertain the 
 distance of that point vertically below the hy- 
 draulic grade-line. Call this measurement the 
 bursting-head as, for example, A, E, Fig. 1, 
 which assume to be 6 feet. The pressure, then, 
 on each square inch of pipe at that point is equal 
 to the weight of a column of water whose base 
 measures 1 square inch and whose height is 
 6 feet. Thus, 1 square inch multiplied by 6 feet 
 (72 inches) =72 cubic inches =.04166 cubic 
 feet multiplied by 62.5 (wt. of cubic foot of 
 water) =2. 6 Ibs., which is the pressure per 
 square inch. Consequently, if the pipe lies con- 
 siderably below the hydraulic grade-line, it will 
 need to be of thicker iron than the rest. This 
 law applies in crossing deep hollows. 
 
 CASE 2. Pipe above the Hydraulic Line. 
 There is now a decided loss of head, and conse- 
 
72 H\DRAULIC MINING. 
 
 quently of power, in portions of the pipe, if it be 
 of the same diameter throughout. Find now 
 that point in the pipe which is highest above 
 the -hydraulic grade-line (H), and from that 
 point draw Uo new grade lines, one to the 
 pressure -box (H V) and one to the nozzle (H 
 N). Along the former calculate the bursting 
 pressure as above, measuring the different heads 
 from the new line (as F E). Along the latter 
 there will be no bursting pressure, for the grade 
 of the nozzle end of the pipe will be so much 
 greater than that of the reservoir end that it will 
 carry off the water very much faster, and will, in 
 fact, act like a gutter, and be partially empty. 
 The remedy for this is to put in pipes having a 
 decreased diameter. To calculate the requisite 
 diameter, assume that the pipe ended at that 
 point where it is highest above the hydraulic 
 grade-line (H). Calculate the discharge in cubic 
 feet at that point according to Rule 2, page (55. 
 This will give the amount of water in cubic feet 
 per second which the nozzle section (H N) must 
 carry. The head will be the vertical distance 
 from H to N. Then, by Rule 4, under the head 
 
H YDRA UL1C MINING. J 3 
 
 of Iron Piping, the requisite diameter may be 
 calculated. 
 
 CASE 3. Pipe both above and below the Hy- 
 draulic Grade- Line. The problem now becomes 
 more complicated. 
 
 Divide the pipe into sections for every passage 
 it makes above the hydraulic grade-line, and 
 make the divisions at the several points (A, H, 
 and I) where the pipe attains its highest posi- 
 tion. Calculate (Rule 2, page 61) the discharge 
 at the end of each section. The first section 
 will have a head equal to the vertical distance 
 between its discharge and the velocity-head in 
 the pressure-box. All succeeding heads will be 
 measured from the level of the discharge just 
 below them to their own discharge. For ex- 
 ample, the head at A is the vertical distance 
 between A and the water-level in the reservoir, 
 less the velocity-head. At H the head is the ver- 
 tical distance between H and A. At I it is the 
 distance between I and H, etc. These measure- 
 ments will furnish a series of heads and grades 
 from which the diameters of pipe necessary may 
 be calculated according to Rule 4, p. 66. 
 
74 HYDRA ULIC MINING. 
 
 If it be desired to calculate bursting pressure 
 in Case 3, measure the heads of different points 
 from the ne \v hydraulic grade-lines, and proceed 
 as directed in Case 1. 
 
 In building and laying lines of iron piping, 
 whether to conduct water from one reservoir to 
 another or from the water-box to the pit, money 
 will be saved by paying close attention to this 
 subject. It will easily be seen that if the pipes 
 are larger than is necessary, iron, which is gene- 
 rally costly in mining communities, will be un- 
 necessarily used, while at the same time the 
 pipes will become filled with air, and much of 
 the force thereby lost. Again, if the pipes are 
 too small, the danger from bursting is greatly 
 augmented. 
 
 The pipe, after being laid, should be carefully 
 anchored at many points, and, when possible, 
 protected from the weather. 
 
 The three conditions arising under unequal 
 and varying grades are shown by the following 
 figures : 
 
HYDRA ULIC MINING 7 5 
 
 Fig. 1. Pipe below Hydraulic Grade- Line. 
 Fig.1. 
 
 W.- Water-box. F. E. N. Line of Pipe. V. A. N. Hydraulic 
 Grade-Line. A. E. Bursting-head. 
 
 Fig. 2. Pipe above Hydraulic Grade- Line. 
 Fig. 2. 
 
 W. Water-box. E. H. N. Piping. V. N.-Hydraulic Grade-Line. 
 F. E. Bursting-head. V. H. and H. N. Supplementary Hy- 
 draulic Grade-Lines. 
 
 Fig. 3. Pipe above and beloiv Hydraulic Grade" 
 Line. 
 Fig.3. 
 
 W.-Water-box. A. E H. F. I. N.-Piping. V. N.-Hydraulic 
 Grade-Line. V A, A H, H I. I N Supplementary Hydraulic 
 Grade-Lines. 
 
7 6 
 
 HYDRA ULIC MINING. 
 
 Sheet iron, from which the piping is made, is 
 manufactured of various thicknesses. The stan- 
 dard of measurement is the inch, and a size 
 known, for example, as No. 16 is approximately 
 ^ of an inch in thickness. The following table 
 will give the strength of sheet-iron piping, and 
 will be found of service. 
 
 STRENGTH OF IROtf PIPING. 
 
 This table gives the thickness In Inches and decimals of an Inch 
 which Iron piping must have to stand a given pressure. 
 
 Heud of Water, in feet. 
 
 I - 
 
 150 
 
 200 250 300 : 400 500 
 
 600 800 
 
 1,000 
 
 (; Resulting Pressure against Sides of Pipe, i:i Its. per sq 
 
 ^ 
 
 inch. 
 
 | ' 48 - 4 
 
 65.1 
 
 87 | 109 130 174 217 
 
 260 347 
 
 434 
 
 Q ] Required I hick ness of Pipe, in in ches or decimci Is of an 
 
 inch. 
 
 2 j .009 
 
 .013 
 
 .018 .022 .027 .036 ! .045 
 
 .055 .075 
 
 .095 
 
 8 .013 
 
 .020 
 
 026 .033 .040 .054 ! .068 
 
 .082 .112 
 
 .143 
 
 4 .017 
 
 .026 
 
 .035 .045 .053 .072 .090 
 
 .110 , .149 
 
 .191 
 
 5 ; .022 
 
 .033 
 
 .044 .056 .067 .090 , .113 
 
 .137 .186 
 
 .237 
 
 6 .026 
 
 .040 
 
 .053 .067 .080 .'08 .136 
 
 .165 .224 
 
 .287 
 
 7 .030 
 
 .046 
 
 .062 .078 .093 .126 j .159 
 
 .193 .261 
 
 .333 
 
 8 ! .034 
 
 .053 
 
 .071 .089 .107 .144 .181 
 
 .220 .298 
 
 .382 
 
 9 .039 
 
 .059 
 
 .079 .101 .120 .163 j .205 
 
 .247 .335 
 
 .427 
 
 10 .044 
 
 .1166 
 
 .089 .112 .134 .181 .227 
 
 .275 .373 
 
 .475 
 
 12 i .053 
 
 .080 
 
 .106 .134 .161 .217 i 573 
 
 .330 .448 
 
 .575 
 
 14 .061 
 
 .093 
 
 .124 .156 .187 .253 i .318 
 
 .387 .523 
 
 .666 
 
 16 j .069 
 
 .106 
 
 .142 .178 .214 .288 .363 
 
 .440 i .596 
 
 .763 
 
 18 \ .078 
 
 .120 
 
 .159 .201 .242 .326 1 .409 
 
 .495 .670 
 
 .850 
 
 20 ! .088 
 
 .132 
 
 .177 .223 .267 .361 ; .454 
 
 .549 .746 
 
 .950 
 
 24 .105 
 
 .159 
 
 .2i3 .268 .321 .433 i .545 
 
 .660 .895 
 
 l.iro 
 
 30 .132 
 
 .198 
 
 .267 .336 .402 .543 .681 
 
 .825 1.120 
 
 1.4J) 
 
 36 .156 
 
 .238 
 
 .318 .402 .483 .651 , .8 9 
 
 .990 ! 1-340 
 
 1710 
 
 42 i .184 
 
 .279 
 
 .372 .469 .562 .759 .955 
 
 1.160 j 1.570 
 
 2.000 
 
 48 ; .210 
 
 .317 
 
 .425 .535 .641 .866 1.090 
 
 1320 1.790 
 
 2.290 
 
HYDRAULIC MINING. fj 
 
 For example : What thickness of iron should 
 be used to make a 20-inch pipe which must 
 bear 200 feet head of water ? The figure given 
 in the table is .17? inch, which, by the follow- 
 ing table, corresponds to between No. 5 and No. 
 6 iron. Or, the head being 100 feet and the 
 pipe 10 inches in diameter, the thickness will be 
 .044 inches, which corresponds nearly to No. 17. 
 In selecting the iron it will always be safer to 
 take the size one larger than that called for by 
 the figures. 
 
 Table showing the thickness, in decimals of 
 an inch, of the different sizes of sheet-iron from 
 No. 4 up to No. 30 : 
 
 No. 4 has a thickness of .204 of an inch. 
 ;< 5 " " .181 " 
 " 6 " " " .162 " 
 
 9 u 114 
 
 10 u " " .101 
 
 11 " <( " .090 
 
 12 " " ' .080 
 
 13 " " l< .071 
 
 14 " " .064 
 
 15 '' " " .057 
 
 16 " ' .050 
 
HYDRA ULIC MINING. 
 
 No. 17 has a thickness of .045 of an inch. 
 
 18 
 
 " .040 " 
 
 19 
 
 " .035 " 
 
 20 " 
 
 " .031 " 
 
 21 
 
 " .028 " 
 
 22 
 
 " .025 " 
 
 23 
 
 " .022 " 
 
 25 
 
 u .020 " ' 
 < 017 
 
 26 
 
 " .015 " 
 
 27 
 
 " .014 " 
 
 28 
 
 " .012 " 
 
 29 
 
 " .011 " 
 
 30 
 
 " .010 " 
 
 It must be remembered that tlicse figures ap- 
 ply only in cases where the end of the pipe is 
 closed and no discharge occurs, or where the 
 discharge is on the same level as the inflow. Of 
 course if the pipe is discharging at one end the 
 pressure is relieved, and the pipe is called upon 
 to sustain only that bursting pressure due to its 
 depression below the hydraulic grade-line. As 
 in practice the depression of the pipe leading 
 from the water-box to the pit is rarely more than 
 5 to 20 feet below the hydraulic grade-line, the 
 iron will be compelled to resist a pressure never 
 over 10 Ibs. to the square inch. This, ordinary 
 stove-pipe iron would generally do. 
 
CHAPTER VIII. 
 
 NOZZLES AND DISCHARGE. 
 
 THEORETICALLY, the quantity of water dis- 
 charged from the nozzle of a pipe may be de- 
 termined by the following rule: 
 
 KULE 1. Extract the square root of the head, 
 and multiply this root by 8.03. The product 
 will be the velocity in feet per second with 
 which the water escapes from the mouth-piece. 
 
 Multiply the area of the mouth-piece (see- 
 page 41) by this velocity, and the result will be 
 the discharge in cubic feet per second. 
 
 EXAMPLE. What quantity of water will be 
 discharged from a pipe, under a head of 100 
 feet, through a 3-inch nozzle ? 
 
 The square-root of the head (100) is 10, 
 which, multiplied by 8.03, gives 80.3 feet as 
 tin- velocity per second. The diameter of nozzle 
 
8O H YDRA ULIC Mh\ ING. 
 
 being 3 inches (.25 of a foot), its area would 
 be .25 multiplied by 3.14 multiplied by .0625 = 
 .04906 square feet, which, multiplied by the ve- 
 locity 80.3, equals 3.93 cubic feet, which is the 
 discharge per second. 
 
 The actual discharge is probably about 80 per 
 cent, of the theoretical one in well-made nozzles, 
 provided with inside flanges to prevent revolu- 
 tion of the stream, and in this case would be 
 3.14 cubic feet per second. 
 
 This, reduced to miners' measure (see page 18), 
 would represent about 115 inches. The power 
 of the stream thrown by a nozzle has been dis 
 cussed under the head of Momentum (page 39), 
 and nothing remains to be said on the subject, 
 except that every precaution should be taken to 
 prevent the stream from issuing in a ragged con 
 dition. Its effectiveness depends very largely 
 upon its smooth and cylindrical form. If this 
 is secured it will travel through the air for 
 a much longer distance without disintegration 
 than otherwise. The mouth-piece, therefore, 
 should be very smooth, and the arrangements 
 of the pressure or water box so perfect as to 
 
H YDRA ULIC MINING. 8 1 
 
 exclude all sand and gravel, and, if possible, all 
 air. Fine specks of quartz passing through the 
 mouth-piece will not onlv cut the metal, but will 
 spoil the shape oi tne jet. 
 
CHAPTER XX. 
 
 THE SLUICE. 
 
 UPON the construction and operation of these 
 channels almost everything in placer-mining de- 
 pends. It is a comparatively simple matter to 
 disintegrate the most cohesive gravel-bank and 
 deliver it at the head -box, but by no means so 
 easy to so conduct the washing as to save even a 
 respectable amount of gold. In former days 
 miners were content with saving from 30 to 50 
 per cent., for the ground worked at those times 
 was rich enough to pay handsomely even then. 
 The miner of to-day, however, has to deal with 
 a lower grade of material worth from 15 to 25 
 cents to the cubic yard, and must work closer to 
 produce a profit. In California ground worth 
 only 4 cents to the cubic yard is worked suc- 
 cessfully. In Colorado and Montana there is no 
 need as yet (and in fact there is none in Cali- 
 fornia) to touch such poor gravel, for there are 
 
HYDRAULIC MINING. 83 
 
 millions of acres still unopened which will pro- 
 duce 20 to 30 cents. This circumstance, how- 
 ever, affords no legitimate excuse for careless 
 working. It will be found at the present day 
 to be just as expensive to save 50 as 90 per cent, 
 in mines where there is any pretence to careful 
 work. And the sooner the business of gravel- 
 washing is reduced to a science, the sooner it 
 will attract the attention of investors and re- 
 ceive the benefit of their assistance. 
 
 Steadiness of flow in a sluice is of great im- 
 portance. The quantity of water passing, and 
 its velocity, must be uniform to secure the de- 
 position of a maximum of gold. Again, it is no 
 economy to crowd a flume with dirt beyond cer- 
 tain limits, which will be noted further on. If 
 the gravel is caved in too large quantities it will 
 be found economical to erect other sluices. It is 
 to be remembered, also, that water always tra- 
 vels faster in the centre of the channel, and is 
 also higher in level. Consequently the bulk of 
 the gravel and boulders will travel down the 
 middle of the flume. 
 
 Dimensions The maximum quantity of wa- 
 
84 HYDRAULIC MINING. 
 
 ter which may be advantageously used in a sin- 
 gle sluice of correct dimensions when the ground 
 is ordinarily full of boulders, is set down by good 
 practical authorities at 1,000 miners' inches. 
 This corresponds to a discharge of 95,000 cubic 
 feet per hour, which, with gravel and boulders, 
 would represent about double that amount of 
 moving substance in the sluice. When more 
 than this is used the current will be so strong 
 that men cannot work to any advantage in the 
 head-box. Sluices intended to clear off top dirt 
 must be short and large. In this case the top 
 dirt is presumed to be nearly free of gold and 
 of boulders. 
 
 The test of friction is perhaps the correct one 
 on which to base calculations for the correct di- 
 mensions. The general behavior of this force 
 is referred to on page 38, and on page 52 will be 
 found the law of the least wet perimeter. In a 
 sluice, the object being to move all the gravel 
 from the head-box to the dump by means of the 
 forces of water and gravity, it is important that 
 the least amount of the former should be lost in 
 overcoming extraneous resistance. We may in- 
 
HYDRAULIC MINING. 85 
 
 crease the work of the water by giving it veloci- 
 ty through the instrumentality of heavy grade, 
 but if the flume is of incorrect dimensions there 
 is always a loss for which the miner receives no 
 compensation, and which may be avoided. 
 
 To secure this point let the miner first decide 
 upon the largest sized boulder which he will 
 allow to go through his flume. Tf it be 2 feet 
 in diameter, then it is clear that his flume must 
 carry at least 2 feet in depth of water. We 
 have then a figure for a side measurement. Ac- 
 cording to the law on page 52 the bottom should 
 be from If to 2| times the height of the side, or, 
 taking the side at 30 inches, the bottom should 
 be 52J to 67J inches wide. If, however, the 
 ground is free from large boulders, and it be 
 merely necessary to ascertain the dimensions 
 best adapled to carry the greatest economical 
 quantity of water (1,000 inches), Eules 2 and 3, 
 on pages 41 and 42, will furnish the correct area 
 of section. 1,000 inches is equal to 27.1 cubic 
 feet per second. Double this discharge to make 
 room for the gravel. The flume must then dis- 
 charge 54.2 cubic feet of material per second. 
 
86 HYDRAULIC MINING. 
 
 Having ascertained the area of section in square 
 feet, we may resolve it into correct dimensions 
 by the following rules : 
 
 RULE 1. The width to be 2J times the sides. 
 
 Multiply the area in square inches by 4, and 
 divide the product by 9. Extract the square 
 root of the quotient. The result will be the 
 height of side in inches. 
 
 RULE 2. The width to be 1J times the sides. 
 
 Multipl} the area in square inches by 4, and 
 divide the product by 7. Extract the square 
 root of the quotient. The result will be the 
 height of side in inches. 
 
 Those who have a preference for shallow boxes 
 will adopt Rule 1, and those who incline towards 
 deep ones will take Rule 2. 
 
 Grade. Grade creates velocity. Velocity in- 
 creases the work of water, and consequently 
 where the quantity, of water is small it must be 
 assisted by giving it a greater velocity. As practi- 
 cally the whole question of power with water in 
 sluices depends upon the velocity with which it 
 moves, the question of grade is of great impor- 
 tance. The miner, however, does 'not merely 
 
HYDRAULIC MINING. 8/ 
 
 seek for power in his sluice. While there are 
 boulders and gravel to wash away there is gold 
 to be saved. Consequently, that velocity is the 
 best which will wash away a maximum quantity 
 of gravel and rock and a minimum of gold. Let 
 the miner, therefore, study for a while the com- 
 position of his banks. 
 
 If the boulders are rounded and well worn 
 they will roll down the sluice with ease under a 
 small head, but if flat they will need more power. 
 And the same is true if they be angular, though 
 not to so great an extent. 
 
 Scale and leaf gold will float a long distance 
 in a turbid and rapid stream. 
 
 Generally the physical quality of gold may be 
 determined by an examination of the gravel. 
 The miner should not trust to that caught in his 
 riffles, for much may be washed away which he 
 can never examine. If the gravel and boulders 
 are angular and large the gold will have the 
 same characteristics ; but if the former are pol- 
 ished the gold is round or leafy, and much will 
 be a fine dust. 
 
 The moving power of water in sluiceways may 
 
88 HYDRAULIC MINING. 
 
 be approximately judged by the following 
 table : 
 
 16 feet per minute begins to wear away fine clay. 
 
 30 " just lifts fine sand. 
 
 39 " ' lifts sand as coarse as linseed. 
 
 45 " ' moves find gravel. 
 
 120 " ' " inch pebbles. - .J 
 
 200 t( ' " pebbles as large as eggs. 
 
 320 " ' " boulders 3 to 4 inches thick. 
 
 400 " ' " 6 to 8 
 
 600 " " " 12 to 18 
 
 We have, then, the following rule for the es- 
 tablishment of grades in sluices when the veloc- 
 ity needed is decided upon : 
 
 RULE 3. Multiply the velocity expressed in 
 feet per secomi by itself, and the product by 
 the wet perimeter in feet. 
 
 Divide this result by twice the area in square 
 feet. The result is the total fall in feet per 
 mile. 
 
 EXAMPLE. What grade must be given to a 
 sluice 12 inches broad and 6 inches deep, that it 
 may carry a velocity of 320 feet per minute, 
 or 5.3 feet per second ? 
 
 Multiplying the velocity (5.3) by itself, and 
 
HYDRAULIC MINING. 89 
 
 the product by the wet perimeter (24 inches =2 
 feet), we have 56.18. This, divided by the area 
 (72 square inches =.5 of a foot), and doubled 
 =56.18, which is the fall in feet per mile. 
 
 To reduce grades expressed in feet per mile 
 to inches per box of 12 feet, multiply by the 
 decimal .027. Thus, a grade of 56.18 feet per 
 mile equals a grade of 1.5, or 1, inches per 
 box. To reduce to inches per rod (16 feet), 
 multiply by the decimal .036. 
 
 Prof. Silliman's calculations on California 
 cement gravel, after being disintegrated by 
 blasting, indicate that 1?-|- cubic yards of wa- 
 ter, equal to nearly 15 tons, are necessary to 
 wash 1 cubic yard of gravel. For ordinary 
 gravel, after being caved, probably 8 to 12 
 tons would suffice. 
 
 When the course of the sluice is curved the 
 outer edge must be raised, to prevent unequal 
 wear and an accumulation of material. This 
 is much more imperative in the sluice' than in 
 the flume. 
 
 Riffles. It is not possible within the limits 
 of this work to discuss the subject of riffles 
 
QO HYDRAULIC MINING. 
 
 thoroughly. Nor is it yet decided which of 
 the systems (wood, boulder, or railroad iron) 
 presents the most advantages in the majority 
 of cases. The first is the most extensively 
 used, and will probably always hold its place. 
 Some experiments made in California witli 
 railroad iron demonstrate that that style of 
 riffle was strongly to be recommended for very 
 rocky ground at least. The great efficacy of 
 boulder riffles is well known, and is thorough- 
 ly illustrated in the ground-sluice. 
 
 As already stated, the bulk of gravel and 
 boulders travels down the centre of a sluice, 
 where there is at once the most water and 
 the greatest velocity. Consequently, it will be 
 found advantageous to have the riffles higher 
 in the centre than in the sides. This will 
 cause a distribution of deposit over the en- 
 tire width of box, and will also prevent the 
 formation of a channel of depression in the 
 bottom of the sluice. 
 
 The cost of wooden block-riffles, cut from 
 peeled round lumber and squared, will average 
 about $50 per 1,000. A thousand of these 
 
HYDRAULIC MIXIXG. gi 
 
 blocks averaging about 8 inches diameter will 
 cover 80 square yards of bottom. Laying and 
 fastening, and all other expenses concurrent with 
 arranging the bottom of the sluice for work, will 
 bring the total cost to 75 cents per square yard. 
 It will be impossible to quote the expense of rail- 
 road-iron riffles. Old irons are, of course, just 
 as good as new. The cost will be mainly that of 
 transportation. 
 
9 2 
 
 H YDRA ULIC MINING. 
 
 TABLE I. 
 
 TABLE OF SQUARE KOOTS. 
 
 The following table of the square roots of numbers from 1 to 200, in 
 elusive, will probably answer all requirements of problems proposed 
 in the preceding examples. If the iigure whose root is to be extracted 
 is not found in the table, take the root of the figure nearest to it. 
 For example, if it is necessary to extract the root of 132.6, take the 
 root of 133. 
 
 .Yb.i Root. No. Root, 
 
 11.8823 
 
 11.8743 
 
 11.9164 
 
 11.9583 183 
 
 12. 184 
 
 12.0416 II 185 
 
 12.0830 
 
 12.1244 
 
 12.1655 
 
 I2.30M 
 
 12.2474 
 
HYDRAULIC MINING. 
 
 93 
 
 TABLE II. 
 
 FIFTH BOOTS. 
 
 The following table of numbers and roots will cover all problems 
 that come to the miner. The numbers are printed in heavy type and 
 the roots in light. If the exact number is not found, take the roots of 
 the number nearest to it : 
 
 No. 
 
 Root. 
 
 No. 
 
 Root. 
 
 No. 
 
 Root. 
 
 7.59 
 
 1.5 
 
 5032.84 
 
 5.5 59049. 
 
 9. 
 
 32. 
 
 2. 
 
 7776. 
 
 6. I 77378. 
 
 9.5 
 
 97.65 
 
 2.5 
 
 11603. 
 
 6.5 
 
 100000. 
 
 10. 
 
 243. 
 
 3. 
 
 16807. 
 
 7. 
 
 136638. 
 
 10.5 
 
 525.21 
 
 3.5 
 
 28730. 
 
 7.5 
 
 161051. 
 
 11. 
 
 1024. 
 
 4. 
 
 32768. 
 
 8. 
 
 201035. 
 
 11.5 
 
 1845.28 
 
 4.5 
 
 44370. 
 
 8.5 
 
 248832, 
 
 12. 
 
 3125. 
 
 5. 
 
 
 
 
 
94 7/i 'DRA UL1C MINING . 
 
 TABLE III. 
 
 VELOCITIES AND DISCHAKGES. 
 
 Head in feet 
 per 100 feet. 
 
 1 
 
 fc 
 
 Ci 
 
 1 
 
 DixfJairqe in cu. 
 j ft. per 24 hours. 
 
 .0019 
 
 .0038 
 
 .1 
 .2 
 
 .208 
 .293 
 
 .1633 
 .2301 
 
 14,114 
 
 19.880 
 
 .0057 
 
 .3 
 
 .359 
 
 .2819 
 
 24,360 
 
 .0076 
 
 .4 
 
 .415 
 
 .3267 
 
 28,229 
 
 .095 
 
 .5 .464 
 
 .3638 
 
 31,435 
 
 .0114 
 
 .6 
 
 .508 .3989 
 
 34,464 
 
 .0132 .7 
 
 .549 .4311 
 
 37,427 
 
 .0151 
 
 .8 .585 .4602 
 
 39,760 
 
 .0170 
 
 .9 .623 .4901 
 
 42,343 
 
 .0189 
 
 1.1 
 
 .656 .5144 
 
 44,431 
 
 .0237 
 
 1.25 .735 .5753 
 
 49,701 
 
 .0284 1.50 .805 .6322 
 
 54,604 
 
 .0331 1.75 .871 .6832 
 
 59,011 
 
 .0379 
 
 2. 
 
 .928 .7276 
 
 62,870 
 
 .0426 2.25 
 
 984 .7696 
 
 66,484 
 
 .0473 
 
 2.50 
 
 1.040 .8168 ! 7U,'572 
 
 .0521 
 
 2.75 
 
 1.080 ! .8482 73,284 
 
 .0568 
 
 3.00 
 
 1.130 .8914 76,982 
 
 ;0758 
 
 4. 
 
 1.310 
 
 1.028 
 
 88,862 
 
 .0947 
 
 5. 
 
 1.47 
 
 1.150 
 
 99,403 
 
 .1136 
 
 6. 
 
 1 61 
 
 1.264 
 
 109,209 
 
 .1325 
 
 7 
 
 1.74 
 
 1.366 
 
 1 18,022 
 
 .1514 
 
 8. 
 
 1.86 
 
 1.455 125,740 
 
 .1703 
 
 9. 
 
 1.96 
 
 1.539 
 
 132,969 
 
 .1894 
 
 10. 
 
 2.08 
 
 1.633 
 
 141,145 
 
 .2273 ! 12. 
 
 2.27 
 
 1.782 153,964 
 
 .2J52 14. 
 
 2.45 
 
 1.924 166,283 
 
 .3030 16. 
 
 2.62 
 
 2.057 177,724 
 
 .3409 
 
 18. 
 
 2.78 
 
 2.183 
 
 188,611 
 
 .3788 
 
 20. 
 
 2.93 
 
 2.301 
 
 198,806 
 
 .4735 
 
 25. 
 
 3.28 
 
 2.573 
 
 222,150 
 
 .5682 
 
 30. 
 
 3.59 
 
 2.819 
 
 243,604 
 
 .6629 
 
 35. 
 
 3.88 
 
 3.047 
 
 268,960 
 
 .7576 
 
 40. 
 
 4.15 
 
 3.21)7 
 
 282,288 
 
 .8523 
 
 45. 
 
 440 
 
 3.451 
 
 298,209 
 
 .9470 
 
 50. 
 
 4.64 
 
 3.638 
 
 314,352 
 
95 
 
 TABLE III. Continued. 
 
 VELOCITIES AND DISCHARGES. 
 
 Head in feet 
 per 100 feet. 
 
 jjj 
 
 i 1 ! 
 
 2 ^ 
 ^ a. 
 
 Discharge in cu. 
 ft. per 24 hours. 
 
 
 |& 
 
 pi 
 
 I" 1 
 
 
 1.1360 
 
 60. 
 
 5.08 
 
 3.989 
 
 344,649 
 
 1.3260 
 
 70. 
 
 5.49 
 
 4.311 
 
 372,470 
 
 1.5150 
 
 80. 
 
 5.85 
 
 4.602 397,613 
 
 1.7040 
 
 90. 
 
 6.23 
 
 4.900 423,435 
 
 1.8940 
 
 100. 
 
 6.56 
 
 5.144 
 
 444,312 
 
 2.0830 
 
 110. 
 
 6.87 
 
 5.395 
 
 466,138 
 
 2.2720 
 
 120. 
 
 7.18 
 
 5.639 
 
 487,209 
 
 2.4620 
 
 130. 
 
 7.47 
 
 5.866 
 
 506,822 
 
 2.8410 
 
 150. 
 
 8.05 
 
 6.322 
 
 546.048 
 
 3.0300 
 
 160. 
 
 8.30 
 
 6.534 
 
 564,576 
 
 3.2190 
 
 170. 
 
 8.55 
 
 6.715 
 
 580,176 
 
 3.4080 
 
 180. 
 
 8.80 
 
 6.903 
 
 596,418 
 
 3.5960 
 
 190. 
 
 9.04 
 
 7.100 
 
 613,440 
 
 3.7880 
 
 200. 
 
 9.28 
 
 7.276 
 
 628,704 
 
 4.2610 
 
 225. 
 
 9.84 
 
 7.696 
 
 664,848 
 
 4.7350 
 
 250. 
 
 10.40 
 
 8168 
 
 705,728 
 
 5.2080 
 
 275. 
 
 10.8 
 
 8.482 
 
 732,844 
 
 5.6820 
 
 300. 
 
 11.3 
 
 8.914 
 
 769,824 
 
 6.6290 
 
 350. 
 
 12.3 
 
 9.621 
 
 831,168 
 
 7.5760 
 
 400. 
 
 13.1 
 
 10.280 
 
 888,624 
 
 8.5320 
 
 450. 
 
 13.9 
 
 10.910 
 
 943,056 
 
 9.4700 
 
 500. 
 
 14.7 
 
 11.50 
 
 994,032 
 
 10.4100 
 
 550. 
 
 15.4 
 
 12.09 
 
 1,044,576 
 
 11.3600 
 
 600. 
 
 16.1 
 
 12.64 
 
 1,092,096 
 
 12.3000 
 
 650. 
 
 16.7 
 
 13.11 
 
 1,132,704 
 
 13.2500 
 
 700. 
 
 17.4 
 
 13.66 
 
 1,180,224 
 
 14.2000 
 
 750. 
 
 18. 
 
 14.13 
 
 1,220,832 
 
 15.1500 
 
 800. 
 
 18.6 
 
 14.55 
 
 1,257,408 
 
 16.0900 
 
 850. 
 
 19.1 
 
 15.00 
 
 1,296,000 
 
 17.0-100 
 
 000. 
 
 19.6 
 
 15.39 
 
 1,329,696 
 
 17.99CO 
 
 950. 
 
 20.3 
 
 15.94 
 
 1,377,216 
 
 18.9400 
 
 1000. 
 
 20.8 
 
 16.33 
 
 1,411,456 
 
 2;>.700 
 
 1290. 
 
 22.7 
 
 17.82 
 
 1,539,648 
 
 26.5200 
 
 1400. 
 
 24.5 
 
 19.24 
 
 1,062,336 
 
 30.3009 
 
 1600. 
 
 26.2 
 
 20.57 
 
 1,777,248 
 
 37.8700 
 
 2000. 
 
 29.3 
 
 23.01 
 
 1,988,064 
 
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