RATIONAL DESIGN OF STEAM HEADERS AND PIPING SYSTEMS 
 
 BY 
 
 FRANK MACKNET VAN DEVENTER 
 B. S. University of Illinois, 1917 
 
 THESIS 
 
 Submitted in Partial Fulfillment of the Requirements for the 
 
 Degree of 
 
 MECHANICAL ENGINEER 
 
 IN 
 
 THE GRADUATE SCHOOL 
 
 OF THE 
 
 UNIVERSITY OF ILLINOIS 
 
 1922 
 
Digitized by the Internet Archive 
 in 2017 with funding from 
 
 University of Illinois Urbana-Champaign Alternates 
 
 https://archive.org/details/rationaldesignofOOvand 
 
Pa^e I 
 
 RATIONAL DESISU OF STEAi: KEAPERS ACT PIPING SYSTEIS. 
 
 TABLE OF 00I!TE1:TS. 
 
 Page 
 
 1 - Scope and Foreword. ---------------------- i 
 
 2 - Review and Criticism of I’ethods Usually Pollo\7ed in the 
 
 Selection of Insulation. ------------------ 1 
 
 3 - Proposed Rational I'ethod for the Selection of Insulation. - - - 2 
 
 4 - Cost Factors Involved in the Selection of Insulation.” ----- 2 
 
 5 - Graphic Method of Comparirig Insulation Charges. - -- -- -- - 3 
 
 6 - Fethods Recommended hy Designers and Text Book V7r iters for 
 
 the Proper Pipe Size Determination. ------------ 3 
 
 7 - Proposed Rational I'ethod for Selecting Pipe Sizes. - -- -- -- 4 
 
 8 - Cost Factors Involved in the Selection of Pipe Sizes. ----- 4 
 
 9 - Graphic I.ethod of Comparing Pipe Size Data. - -- -- -- -- - 4 
 
 APPENDIX I. 
 
 DESIGK OF A SIITLE STEAI.' HEADER. 
 
 10 - Description. ------------------------- 6 
 
 11 “ Steam Conditions. ----------------------- 6 
 
 12 - Load Conditions. ------------------------ 6 
 
 13 - Steam Requirements. ----------------------- 6 
 
 14 - Selection of Insulation. -------------------- 8 
 
 15 - Analysis of Costs. ---------------------- 8 
 
 16 - Explanation of Items in Table Lo. l. -------------- 8 
 
 17 - Conclusions on Insulation. ------------------ 12 
 
 18 - Selection of Header Size. ------------------- 12 
 
 19 - Explanation of Itemis in Table ho. 2. - -- -- -- -- -- -- 12 
 
 20 - Conclusions on Header Size. ------------------ 16 
 
 APPEKDIX II. 
 
 DESIGN OF A COITLICATED STEAI: HEADER. 
 
 21 - Description. -------------------------- 18 
 
 22 - Selection of Insulation. ------------------- 18 
 
 23 - Load Conditions. ------------------------ 18 
 
 24 - Steam Requirements. ---------------------- 18 
 
 25 - Provision for Future Extension. ---------------- 20 
 
 26 - Selection of Header Size. ------------------- 20 
 
 27 - Explanation of Items in Table No, 3. -------------- 20 
 
 28 - Conclusions on Header Size, ------------------ 26 
 
 29 - Closing Discussion of the Rational I'ethod. - -- -- -- -- -- 26 
 
 APPEIH)IX III. 
 
 RADIATION LOSSES Ft^OF BARE AND IFSTJLATED PIPES. 28 
 

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Paeje II 
 
 APPEI^DIa IV. 
 
 THE FLOW OF ST£A2f. IE PIPES. 
 
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 The Bahcock Formula. -------------------- 33 
 
 Standard and Extra Strong Pipes. --------------- 33 
 
 Superheated Steam ---------------------- 35 
 
 Exanple of Solution by the Formula. ------------- 36 
 
 G-raphic Chart for the Babcock Formula. - -- -- -- -- -- 36 
 
 Example of Graphical Solution. ---------------- 38 
 

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Page III 
 
 LIST OF TABLES. 
 
 Page. 
 
 1 “ Selection of Steam Pipe Insulation, ----------- 9 
 
 2 - Determination of Economical Header Size. 
 
 (Simple Header). ------------------- 13 
 
 3 - Determination of Economical Header Size, 
 
 (Complicated Header). ---------------- 2I 
 
 4 “ Pressure Loss Analysis, ----------------- 34 
 
 5 - Hadiation Loss from Bare Pipe. -------------- £9 
 
 6 - Efficiency of Asbesto-Sponge-Pelted 
 
 Sectional Insulation. ---------------- 30 
 
 7 - List Prices of Pipe Covering, -------------- 33 
 
 8 - Factor ”F’ for the Modified Babcock Pormula. ------- 34 
 
 LIST OF FICURES. 
 
 1 - Layout of a Simple Steami Header. - -- -- -- -- -- - 7 
 
 2 - Graphic Study of Insulation Thickness, ---------- 11 
 
 3 - Graphic Study of Header Size Determination, 
 
 ( S imple Header 14 
 
 4 - Layout of a Complicated Steam Header, ---------- 19 
 
 5 - Graphic Study of Header Size Detemlnation, 
 
 (Complicated Header). ---------------- 22 
 
 6 - Graphic Steami Plow Chart, - -- -- -- -- -- -- -- - 37 
 
 COHCLUSIOHS. 
 
 Conclusions on Insulation, ---------------- 13 
 
 Conclusions on Header Size, (Simiple Layout)." ------ ^6 
 
 Conclusions on Header Size. (Complicated Layout)." - - - - 35 
 Closing Discussion of the Rational Method, """"""""26 
 
Pa'^ 1 
 
 RATIOEAL DESIGK OF STEAi: HEADERS m) PIPING STSTEKS 
 
 1 - SCOPE AKD FOREWORD . 
 
 The scope of this thesis is limited to that part of design which deals with 
 (a) the selection of heat insulating coverings, and (b) the proper pipe sizes. 
 The remaining two points to be considered in the design of a steam header, name- 
 ly, the location of the pipe, and provision for expansion, are thoroughly treat- 
 ed in text books and will not be considered herein. 
 
 It would seem at the outset that the logical order of treatment would be 
 to first lay out the piping scheme and determine the proper sizes. Having done 
 so, the last item, would be to determine the thickness of insulation to use on 
 the pipe. Under the "rational” method of design, however, the reverse order 
 becomes better suited to the solution. The determination of pipe size involves 
 the amount of heat radiated from the system, which in turn, involves the thick- 
 ness of insulation. Further, it is good practice to set up an "insulation 
 schedule" which indicates the economical thickness of insulation for all sizes 
 of pipe which may occur in the whole plant. By drawing up this schedule first, 
 the proper thicknesses of insulation will be known for the several pipe sizes 
 considered in the calculations for the economical pipe size, 
 
 2 - REVIEW AM) CRITICISE OP MITEODS USUALLY FOLLOWED IE THE 
 
 selegtioe of IESULATION. 
 
 Conversation upon the subject has indicated the surprising prevalence of 
 the idea among designers that "a little insulation does some good, and the more 
 the better", or, as one designer stated, "Modern plants use extreme tempera- 
 tures and the radiation losses become enormous; consequently, too much insula- 
 tion cannot be used" . 
 
 The fallaqy of this idea lies in the fact that the heat saved is not direct- 
 ly proportional to the thickness of the insulation. One inch of insulation 
 under average conditions saves about 89 per cent, of the heat, which would be 
 lost from the bare pipe. Three inches saves about 94 per cent, of the bare 
 pipe loss; so it is seen that the last two inches of insulation, which costs 
 about two times as much as the first inch, is only 5,6 per cent, as effective 
 in saving heat. 
 
 The Magnesia Association of America publishes four charts, based upon four 
 values of steam cost, each chart indicating the proper thickness of 65% magne- 
 sia to use for each pipe size and for various temperature differences. The 
 steam costs represented by the four charts are:- 20^, 40^, 60^, and 80^ per 
 million Btu. When steam costs do not coincide with one of these four values, 
 the result must be obtained by observing the two charts for lesser and greater 
 steam costs, and approximating the intermediate value. This method does not 
 permit of a satisfactorily definite solution. A more important criticism of 
 these charts, is the fact that the curves are regular curves without inflec- 
 tions. In the rational method of analysis it will be found that these cuirves 
 are not regular, due to the fact that the list prices for various thicknesses 
 do not follow a general curve. Hence the accuracy of such charts is to be 
 doubted. 
 

 
 
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Page E 
 
 JoJms-J'anville, in their bulletin "Service to Power Users", publish a 
 brief table v/hich indicates the ininirmmi thickness of steam pipe insulation 
 that should be used for a given character of service, e. g. 25 to 100 pounds 
 steam pressure, 100 to 200 pounds, etc. The results obtained from inter- 
 polation in this table are questionable, and the "minimunf’ thickness does 
 not imply "economical" thickness at all, 
 
 5 - PROPOSED RATIOh^AL liETHOD FOR SELEOTIKG lESULATIOE, 
 
 By "Rational method" is meant that Ciethod which effects the highest 
 economiic efficiency, and "highest economic efficiency" means the lowest total 
 financial charges against the system under consideration. The rational 
 method, then, consists of an analysis of the costs against the system, and 
 the determination of the condition which corresponds to the minimum, value of 
 the total costs. 
 
 4 - COST FAGTORg INVOLVED IK TFR R-RTPHTION OF IKSULATIOl . 
 
 The costs which are chargeable against the installation are: 
 a - Fixed charges - 
 
 b ~ Interest on cost of insulation, in place - 
 
 c “ Effect of nature of naterial. 
 
 d - Effect of thickness of material, 
 
 e - Depreciation of covering, 
 
 f “ Repairs and maintenance, 
 
 g - Miscellaneous (taxes, insurance, etc.) 
 
 h “ Operating charges - 
 
 i “ Cost of heat radiated - 
 
 j ” Effect of natiore of material, 
 
 k - Effect of thickness of material. 
 
 EOTES: 
 
 Item 
 
 a Fixed charges include those which continue throughout the useful life 
 of the material, whether the plant operates or not. 
 
 c Soma materials, having higher insulating efficiency than others, natural- 
 ly corcnand higher prices, and the interest on the installation irust 
 correspond to the first cost, 
 
 d Thick coverings naturally are more costly than thin coverings, and again 
 higher insulation efficiency is accompanied by higher interest charges. 
 
 h Operating charges are those i^diich occur only when the plant is in opera- 
 tion. Most plant operating charges (e. g. fuel, v/ater, lubricants) vary 
 in direct proportion v/ith the quantity of product produced. Radiation 
 from insulated pipe, however, is practically a constant amount, regard- 
 less of the rate of plant operation, 
 
 i, .5 arid k. The amount of heat radiated is proportional to the conplemient 
 of the insulating efficiency of the covering. The efficiency is higher 
 

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Page 3 
 
 for some materials than for others, and increases somewhat with thick- 
 ness, 
 
 5 - SriAPHIC R:ETH0D of GOITARIKS IKSULATIOK GPJ.RGEg. 
 
 The manipulation of aata for the preceding outline is best effected by a 
 tabular arrangement, but the results, costs, are most easily coir:pared and 
 analysed by a graphic presentation. Since thickness is the argument, it is 
 plotted as abscissa. Ordinates are costs, and three cost curves may be 
 plotted for each pipe size; 
 
 ll) Annual fixed charges on insulation, 
 
 (2) Annual cost of heat radiated, 
 
 (3) Total annual cost. 
 
 The minimum value of the total cost curve is the criterion for the 
 economical thickness of covering. If peculiar inflections occur in the total 
 cost curve, the source may be discovered by a glance at the two component 
 curves , 
 
 6 - l-ETHODS REGOM'EKDED BY DESIGNERS AEP TEXT BOOK WRITERS 
 
 FOR PROPER PIPE SIZE BETERFIMTIOK 
 
 Two general methods of selecting pipe sizes have been in comm^on use, 
 namely, the velocity method, and the pressure loss method. 
 
 The velocity method consists in selecting pipe of such size that the 
 velocity of the steam will not exceed certain values. Undoubtedly this rule 
 is based upon the theory that velocities exceeding the prescribed values would 
 result in excessive pressure loss and consequent poor economy. 
 
 This theory is only partially borne out in practice. Pressure loss 
 varies as the square of the velocity, when the v/eight of steam flowing is the 
 variable, and it is found that for velocities mnach in excess of 10,000 feet 
 per miinute that the pressure loss per 100 feet of pipe becomes so great that 
 it is excessive for long runs of pipe. But the average steam header layout 
 is of such design that numerous branch connections, at which steam is fed into 
 or bleu out of the header, effect frequent changes of velocity, such that one 
 or m.ore sections of the header may contain steam at almost zero velocity, 
 while another section may carry steam at an extremely high velocity. It 
 would not be proper to increase the size of the section which carries high 
 velocity steam*, because it is possible that a shifting of the load, by re- 
 placing one or more of the operating boilers by others which have not been in 
 operation, may almost reverse the values of velocity in the two critical 
 sections mientioned. For this reason, it is aavisable in n.ost cases to con- 
 struct the entire heaaer of one size of pipe, and it is seen that if the size 
 were so selected that the maximum velocity in any section is less than 10,000 
 feet per minute, then the velocities in all the other sections woula be too 
 lov/, due to oversize pipe, resulting in excessive superheat loss, or condensa- 
 tion, and capital charges. 
 
 Further, the velocity which corresponds to the miaximum efficiency in one 
 case may be very aifferent from that in another case. For instance, the 
 relative location of boilers and prim.e movers, as ”back to back**, ’’end to end'*. 
 

 
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Page 4 
 
 etc, has a decided effect upon the characteristics of the systea, and upon the 
 velocity v/hich corresponds to Ciaxijrum econony. 
 
 The pressure loss method consists in selecting pipe of such size that the 
 pressure loss in the system v/ill not exceed certain values. The principal 
 difficulty in applying this method is in knowing v/hat pressure loss corresponds 
 to maximum economy. Different designers recommend from five to 20 pounds, 
 and occasionally the theory is advanced that a loss of 50 pounds or more is 
 not objectionable, since the energy remains in the steam as additional super- 
 heat, The latter recomn.enaation of course is based upon a miis interpretation 
 of fact, because although the expansion is practically a constant- total-heat 
 process, the entropy increases during the expansion and the percentage of 
 availability of the energy decreases, so that less is available for conversion 
 in a prime mjover, and more nust be lost in the exhaust. 
 
 It is impossible to assign a definite value for the velocity or pressure 
 loss v/hich will correspond to maximum economy in ell cases, since there are so 
 many factors, such as type of header laj^out, type of prime mover, station load 
 factor, etc which affect the problem. 
 
 7 - PROPOSED HATIOFAL J^THOr FOR SELFTTIKG PIPE SIZES. 
 
 ’’Rational J'ethod”, as previously explained, irc’icates that method v;hich 
 effects the lowest total financial charges against the system; under considera- 
 tion. The rational method of determining economical pipe size, then, consists 
 in analysing the costs against the system with various sizes of pipe, and find- 
 ing the size which corresponds to the minimum: value of total costs, 
 
 8 - GOST FACTORS mCLVED IK TEE SELECT I OK OF PIPE SIZE. 
 
 The costs which are chargeable against the installation are: 
 
 Fixed charges - 
 
 Interest on cost of pipe, fittings, and insulation, erecteu. 
 
 Depreciation of pipe and insulation. 
 
 Repairs and maintenance. 
 
 Taxes and insurance. 
 
 Operating charges - 
 
 Annual cost of steam to operate prine mover. 
 
 Annual cost of heat radiated. 
 
 9 - SRAPHIQ 1:ETHCD OF GOlTARlIIg PIPE SIZE DATA. 
 
 The compilation of data for the preceding outline is best effected by a 
 tabular arrangement, but the variation of the several factors which affect the 
 costs, as well as the costs themselves, are most easily comi>ared and analyzed 
 by a graphic presentation. Since pipe size is the argument, it is plotted as 
 abscissa. Ordinates represent oosts, velocities, etc, to suit the factors 
 plotted. The following items may be shov/n to advantage: 
 
 Steam velocity 
 
 Pressure loss due to friction 
 

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Page 5 
 
 Pressure loss due to velocity head. 
 
 Total pressure loss. 
 
 Water rate of prime mover. 
 
 Annual cost of steam for prime mover. 
 
 Annual fixed charges on pipe, fittings, and 
 insulation. 
 
 Annual cost of heat radiated. 
 
 Total annual costs. 
 

 
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APPELTIX I 
 
 Page 6 
 App, I 
 
 Design of a Siir.-ple Stean Header. 
 
 The plant chosen for this example is Boiler Konse ”1” at Rational V/orks 
 of Kational Tube Company at FcKeesport, Pennsylvania, This installation was 
 completed and placed in operation in Fay 1919, 
 
 10 - DESCRIPTIOK. (SeePig. .1) 
 
 The plant consists of one - 10,000 kw. (80^ power factor) Curtis turbo- 
 generator served by two - 1471 horse power Babcock and V/ilcox cross-drum 
 boilers. The plant is located in a space betv/een tv/o rolling mills, and since 
 there is no rooir for future extension, additional capacity need not be provided 
 for in the design of piping, etc. Also, since the steam conditions differ 
 from those enployed in the general miill system, the plant may be treated as an 
 isolated unit. 
 
 11 - ST£A^; COhDITIOhS, 
 
 Eormal gage pressure at boiler drum - E50 lb, per sq, in. 
 Konnal superheat - 150° P, 
 
 TemiUerature of saturated steam - 406° P, 
 
 Temperature of superheated steam - 556° P. 
 
 Temperature of air (assumed) - 80® P, 
 
 12 - LOAD COPDITIOFS, 
 
 The turbo-generator is intended prinarily to serve seven motor-generator 
 and rotary converter sub-stations, distributed about the mill. It is also 
 connected, through transformers and a high-tension transmission sj'stem, to 
 other power generating and consuming equipment at plants of other subsidiary 
 companies of the United States Steel Corporation, In designing the plant, 
 it v/as anticipated that the normal load on the generator wox7ld be 8000 kv/. , 
 and that this load v/ould be carried during 6400 hours per year. During the 
 remaining 2360 hours, when the rolling miills etc, are not operating, pov;er may 
 be received over the high tension system, from generating stations operating 
 with blast furnace gas or waste heat as fuel. 
 
 13 - STEAl^ REOUIHFITETS. 
 
 The water rate of the turbine at 8000 kw, output is 12,9 lb. per kv;h. 
 with the steam conditions enumjerated. 
 
 With the steam, required for auxiliaries taken from the end of the header 
 farthest removed from, the turbine, the only load which need be considered in 
 the design of the header proper is that required for the turbo-generator. 
 
 At the design load, and under design conditions, the steam required for 
 the turbine = 8000 x 12.9 = 103,200 lbs. per hr. 
 
* KSt’S' 
 
 
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Pa<?^e 8 
 App. I 
 
 14 - SRLEOTIOE of IKSULATIOK. 
 
 Previous studies have indicated that the total annual charges on 85^ 
 IJagnesia covering are about four percent lower than on Asbesto-Sponge-Felted; 
 hence, from the standpoint of cost alone, 85^ I'agnesia v/ould be re coirimended . 
 Hov/ever, Asbesto-Sponge-Felted is considered more durable, more easily removed 
 and replaced, and less liable to deterioration from de-hydration at steam pipe 
 temperatures. These advantages cannot easily be capitalized, but they are 
 considered to more than outweigh the four percent difference in annual costs, 
 and Asbesto-Sponge-Felted covering will be used in this analysis. 
 
 15 - AITALYSIS OF COSTS. 
 
 Table Ko. 1 is the tabular solution of economical thickness for the in- 
 sulation. The table, together with the explanatory notes which follov/ it, is 
 self-explanatory. 
 
 Fig. 2 is a graphic presentation of items 4, 6 and 7 in the table and 
 shows the trend of the component cost lines, as well as the deciding factor, 
 total cost. 
 
 16 - EXPLAKATIOE OF ITEI^P IF TABLE W. 1. 
 
 Item 1 . 
 
 By interpolation and extrapolation frorni Table 5, 
 Appendix III, 
 
 Item 2 , 
 
 With 13,500 Btu. coal at ^3.50 per net ton and 78% boiler efficiency, 
 the cost of heat per million Btu. at the boiler nozzle = 
 
 1.000.000 X 3.50 
 
 13,500 X 0.78 X 2000 
 
 ■ ;^0.166 per miillion Btu. 
 
 Item 2 = Item 1 x 8760 x 0.166 
 
 1,000,000 
 
 0.001455 X Item 1. 
 
 Item 3. 
 
 By interpolation and extrapolation from Table 6, 
 Appendix III. 
 
 Itemi 4. 
 
 Item 4 « Item 1 x (100 - item 3) -r 100. 
 
 Item 5. 
 
 List prices from' Table 7, Appendix III. 
 
 Ket prices r list less 30% (quoted January 19, 1922 by H. W. Johns- 
 I’anville Go.) 
 
 Iter 6. 
 
 Item 6 r (item 5 + 60^ for labor and accessories) x 0.15 = 
 

 
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Page 11 
 App« I 
 
 
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 — Fig, 2.— 
 
 Graphic Study of Insulation Thickme53. 
 
Pa^e 12 
 App. I 
 
 s item 5 x 0,24, 
 
 The fixed charges are assumed to be : interest 6^, depreciation 5^, 
 repairs and maintenance 1^, taxes, insurance, etc, 3^, Total 15^, 
 
 Item 7, 
 
 Item 7 = item 4 + item 6, 
 
 17 - COKOLUSIOES OK IKSULATIGK. 
 
 The curves or item 7 of the table indicate that 2 inches is the 
 economical thickness for all sizes from 10-inch to 18-inch pipe inclusive, 
 and that l-l/2 inches is the most economical for 8-inch pipe, Hov;ever, as 
 the difference between l-l/2 inches and 2 inches on 8- inch pipe is only four 
 mills x)er year per foot, it is considered preferable to sim.plify the specifica- 
 tion by adopting 2 inches as the thickness for the six sizes of pipe considered. 
 
 18 - SELEGTION OF HEADER SIZE, 
 
 Table Ko. 2 is the tabular solution of the header size determination. A 
 comjplete set of explanatory notes follows the table. 
 
 Pig, 3 is a graphic presentation of the im.portant items of the table. The 
 curves are numbered to correspond v/ith the items they represent, 
 
 19 - EXPLOv^ATIOK OF ITEI’F ly TABLE W. 2, 
 
 Item 1. 
 
 From quotation submitted by Pittsburgh Valve Foundry and Construction Go. 
 I'arch, 1922. 
 
 Item 2, 
 
 From quotation submitted by H. W. Johns -l^anvi lie Company dated February 
 17, 1922. 
 
 Item 3, 
 
 Item 3 - 0,15 (item 1 + item 2). The fixed charges are assumed to be: 
 interest 6^, depreciation 5%, repairs and maintenance 1^, taxes, insurance, 
 etc, 2%. Total 15^. 
 
 Item 4, 
 
 Cost of heat lost r length of heaaer (i, e. 202 ft.) x item 4, column 
 3 Table 1, Appendix I. 
 
 Item 5, 
 
 Use formula (2), Appendix IV. 
 p = W2 L V F 
 
 w = 103,200 4 60 = 1720 lb, per min. 
 
 L r 165 ft. (from point midway betv;een boilers). 
 
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V r 2.20 
 
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 then: 
 
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 Item 6. 
 
 Page 15 
 App. I 
 
 Prom "National Pipe Standards”, table p. 649, col, 3. 
 
 Item 7. 
 
 Area, sq. ft. ^ (item 6)^ 
 Item 8. 
 
 Velocity (ft. per min.) = 
 
 1720 X 2.2 - S764 
 area item 7 
 
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 144 
 
 lb. steam per min. x sp. vol, 
 area in sq. ft. 
 
 Item 9. 
 
 Velocity head, lb. 
 
 ( ft, per min. 
 
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 Item 10. 
 
 (ft. per sec.)^ 
 
 per sq. in. z 
 
 sp, vol, X 144 
 
 = ( item 8 
 
 vol. X 144 73,500,000 
 
 The pressure loss from saturated steam dnjm to header, including dry 
 pipe, superheater, non-return valve, feeder, and all interrrediate fittings 
 is 7 lb, per sq, in. (Prom test data on similar boiler, corrected to the 
 proper rating) . 
 
 Item 10 - item 5 + item 9+7. 
 
 I tem 11. 
 
 Item 11 - 250 - item 10. 
 Item 12, 
 
 Btu. per hr. «= length (202 ft.) x item 1* x (1 - 0,01 item 3* ) 
 •Ool. 3, Table 1. 
 
 Item 15. 
 
 Total heat of steam at boiler nozzle (265 lb, per sq. in, abs. 
 and 150° sux^erheat) = 1290.4 
 
 „ item 12 
 
 Total heat of steam at turbine nozzle z 1290.4 - - — 
 
 lb. steam per hr. 
 

 
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Page 16 
 App. I 
 
 Item 14, 
 
 Obtained by interpolation from F. 0. Ellenwood’s ’’Steam Charts”, 
 using item 11 and item 13 as data. 
 
 note that the higher superheat for small pipes than for large pipes 
 is due to tv/o causes: (1) less radiation, and (2) throttling (expansion 
 at constant total heat), and that for 8-inch pipe there is m.ore superheat 
 at the turbine than at the boiler, even though the total heat is lower 
 at the turbine due to radiation. 
 
 Item 15. 
 
 The water rate of the turbine at the design load and steam conditions 
 is given in the guarantee as 12,9 lb, per kwh. With steam at 250 lb, 
 gage and 150 deg. superheat (specifications) the electrical energy obtained 
 
 from one pound of steam, is ^ . 264,50 Btu. per pound. 
 
 12 « ^ 
 
 A Study of the pressure corrections used by the Westinghouse Electric 
 and J’fg, Company and a check calculation by thermodynamics indicate that 
 the loss of available energy amounts to 0,25 Btu, per pound of steam, for 
 each pound decrease of pressure, within the range of this problemi. 
 
 The heat lost by radiation has a airect effect by reducing the available 
 energy per pound of steam by an amount equal to the total Btu. lost by 
 radiation per hour, divided by the total weight of steam flowing per hour. 
 
 The net electrical energy available per pound of steam then is 264.50 
 minus the losses due to pressure drop ana radiation, and the corrected 
 water rate of the turbine is equal to 3412 divided by the net available 
 energy per pound of steam. 
 
 Item 16. 
 
 Heat carried by one lb. steam from fuel to turbine nozzle r 
 item 13 - feed water tem,p. (i. e. 210°) + 32 = item. 13 - 178. 
 
 kw. hr. V/. r. Btu. steam Coal 
 
 8000 X 6400 X item 15 x (item 13 - 178) x 3,50 
 
 Item 16 - - 
 
 13,500 X 0.78 X 2000 
 
 Coal eff ton 
 
 8,51 X item 15 (item 13 - 178), 
 
 Item 17, 
 
 Item 17 = item 3 + item. 4 item 16. 
 
 20 - COECLUSIOEF OH HEATHER SIZE. 
 
 An inspection of the total cost curve of Fig. 3 and item 17 of Table Ko. 
 
 2 indicates that a 12-inch header is the economical size to install. It is 
 noted further that any of the six sizes considered would involve an annual loss 
 of less than .^800. 00 as compared v/ith the economical size. This is true because 
 the disaavantages of increased cost and increased radiation loss for the larger 
 

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 App, I 
 
 sizes are nearly counterbalanced by the advantage of less pressure loss. It 
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 that any size within a wide range will constitute an economical selection. (See 
 conclusions at end of Appendix II). 
 
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Pa^e 18 
 App. II 
 
 APPmiX II. 
 
 DEE IGF OF A aOlTLICATED TTEAi: HPADER. 
 
 21 - DESGRIPTIOF. (See Fig. 4) 
 
 The plant consists of four 15,000 kr;, (80^ power factor) tiirho-generators 
 served by eight 1500 hp, "boilers, A 1500 kw. d. c. turho-generator , and a 
 Kotor-generator set receiving power froir the main station generators, supply 
 auxiliary power, the tv;o irachines providing a flexible link for the manipula- 
 tion of exhaust steam to effect a station heat balance. One turbine driven 
 feed pump and steam jet air exhausters receive steam from an auxiliary header 
 located under the main header under the generator room.. 
 
 22 - SELECT lOF OF IFSULATIOF. 
 
 The steam conditions are the same as in Appenuix I, and with the same 
 coal cost, colorific value, and boiler efficiency, the insulation specification 
 v;ill be the san,e, viz., 2-inches of Ashes to-Sponge-Fel tea for all sizes. (See 
 par, heading #14ff,) 
 
 23 - LOAD GOIDITIOl.S. 
 
 The anticipated loaa is an industrial load consisting of several steel 
 miills connected electrically by a super-power system.. The normal design load 
 is 45,000 kv/. during 6400 hours per year. 
 
 24 - STEAi: REOUIHEI'.'EhTS. 
 
 The steam requirements for the plant (excluaing inteniiittent denands such 
 as soot-blowers, ash dumps, etc.) under design load conditions are: 
 
 Item EauiTanent 
 
 a Fain generators 
 
 45,000 kw. @ 12.75 lb. 
 
 b Auxiliarj' generator 
 
 1200 kw. C 30 lb. 
 
 c Other steam auxiliaries 
 
 Total 
 
 Lb, steam, per hr. 
 
 573.750 
 
 36.000 
 
 20.000 
 
 629.750 
 
 The main generator load -would be normally carried on three machines, but 
 as any one of the four might be off the line, it is assumed for design purposes 
 that each machine carries one fourth the total load. Similarly, seven boilers 
 would normally carry the load, but it is assumed that each carries one eighth of 
 the total requirement. The actual steam distribution in the header system, 
 would be different for each possible combination of units in service, and it is 
 quite certain that the assumptions made closely represent average conditions. 
 
 The steam required by each turbine = 
 
 = 143,440 lb. per hr. 
 
 4 
 

 
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Page 19 
 App. II 
 
 — Fi6. 4 — 
 
 — Layout Of a Complicated 5team Header. 
 
Pa»e 20 
 App. II 
 
 It is assumed that one-half of the 20,000 Ih, per hr. used by 
 miscellaneous auxiliaries is taken from each end of the main header under the 
 generator room. The steam distribution in the header is discussed under item 
 5, par. heading # 27 . 
 
 25 - PRCVISIOK FOR FUTURE EXTEITPIOK. 
 
 The possibility of future extension must not be overlooked. In a layout 
 like Figure 4, however, extension may be disregarded, since additional 
 generators would be accompanied by additional boilers, and the piping would be 
 extended with additional cross-branches, the system thus expanding similarly to 
 the "Unit System", and each succeeding unit possessing characteristics similar 
 to the original unit. 
 
 26 - SELECTION OF HEADER SIZE. 
 
 Table l;o. 3 is the tabular solution of the header size problem, A com- 
 plete set of explanatory notes follows the table. 
 
 Fig, 5 is a graphic presentation of the important item.s of the table. The 
 curves are numbered to correspona with the itemis they represent, 
 
 A study of Fig. 5, (or Fig, 3) is enlightening. It is noted that curve 17 
 is a "U"-curve. Its components are curves 3, 4, and 16, Curves 3 and 4 are 
 increasing functions, i. e. they increase as the pipe size increases, Hadiation 
 increases because of the greater amount of surface exposea, and the fixed 
 charges increase because of the higher cost of materials. Curve 16 is a de- 
 creasing function because the v/ater rate of the generators (curve 15) decreases 
 due to the lesser pressure loss in large pipes (curve 10). The sum of an in- 
 creasing and a decreasing function always results in a "U" -curve, which must 
 have a minimum value. The finding of this minimum value by analytical con- 
 siderations is the basis of the "Rational" method of design, 
 
 27 - KXPLAI^ATIOK OF ITEi:S IP TABLE ITO, 5, 
 
 Item 1, 
 
 From quotation submitted by the Pittsburgh Valve Foundry and Con- 
 struction Company, Farch, 1S22. (Correction made for header length). 
 
 Item 2, 
 
 From quotation submitted by H, W. Johns -Fanville Company, dated 
 February 17, 1922, (Correction made for header length). 
 
 Item 3, 
 
 Itemj 3 - 0,15 (item 1 + item. 2), The fixed charges are asstuned to 
 be: interest 6^, depreciation 5^, repairs and maintenance 1^, taxes, 
 insurance, etc. 3^. Total 15^, 
 
 Item 4, 
 
 Cost of heat lost = length of header (i. e. 632 ft.) x item 4, 
 colunn 3, Table 1, Appendix I. 
 

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 Page 21 
 App, II 
 
Page 23 
 App. II 
 
 Item 5« 
 
 In order to determine the pressure loss in a complicated header, it is 
 necessary to determine the distribution of steam in the various parts of 
 the header. Figure 4 and Table Ko. 4 demonstrate the method of calcula- 
 tion. Each section of the header is given a designating letter, which 
 appears in column 1 of the table (4). 
 
 In column 2 the length of each section is indicated. 
 
 In column 3 the weight of steam^ flov/ing in each section is listed. 
 
 This distribution is based upon the assumiption that all boilers are on the 
 line, and the first trial assumes that the three cross branches. A, B, and 
 G, carry equal flov/. The flow from each boiler outlet is equal to the 
 total steamj flow divided by the number of outlets, - 
 
 629,750 7 16 - 39,360 lb. per hr. The flow in each of the cross branches; 
 
 629,750 . 3 - 209,920 lb. per hr. Golumm 3 can nov/ be filled in by 
 star ting *T/ith any convenient branch, as A, and adding or subtracting, as 
 the case may be, as steam is fed into or bled from] the header. Column 4 
 need not be filled in unless the first trial is found to be satisfactory. 
 
 Column 5 is obtained by applying the formula method, as in item 5, 
 
 Table Eo. 2. 
 
 Eov;, if the steam distribution as assinmed is correct, the system will 
 be in dynamic equilibrium, and the pressure loss betv/een any two points, 
 such as X and Y, figure 4 will be the same, whether the path be taken via 
 A, B, or C. 
 
 The pressure loss from X to Y via A for 14-inch pipe r 
 D + A-I-E+I-Er 1.265 lb. per sq. in. Via B = 
 
 B + J ; 0.872 lb. per sq. in. Via C =G+G+E+F+L+J-F-K= 
 1.212. Comparison of these three losses shows that the flow through B 
 was assumed too lov/ as the loss by that route is lower than by A or C. 
 
 The average of these losses is 1.116 lb. tier sq. in. 
 
 Second trial: To approximate a corrected flow for A, B, and C, the 
 
 flow in each of these branches is multiplied by the square root of 1.116 
 and divided by the square root of the first trial loss. 
 
 Columns 6 and 6 constitute the second trial. The calculation is the 
 sanje as for columns 3 and 5, 
 
 The loss from X to Y with the values tabulated in column 8 is: via A 
 1.095, via B 1.075, via G 0.973. The average is 1.048. There is still 
 som-e variance betv/een these values, but a third trial is not aavisable, 
 since there is a variation betv/een the pressure drops to the various 
 turbines anjwvay, hence the average of the three values, or 1.048 is taken 
 as the drop to the point Y, or turbine #2. 
 
 Column 7 is calculated by: 
 
 Vel., ft. per min. = lb. per hr. x sp. vol. 3 0.0343 x Col. 6. 
 
 60 X area, sq. ft. 
 

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 Pressure Loss Analysis of Fig. 
 For 14-Inch Header. 
 
 
 
 Second Trial 
 
 Pressure 
 
 loss 
 
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Page 25 
 App. II 
 
 Since the pressure drop to turbine #2 is 1.048 lb. per square inch, 
 the drop to other turbines mavV be obtained by adding or subtracting the 
 losses in sections between the tee for turbine #2 and the tees for the 
 other turbines. The losses to the various turbines are found to be: 
 
 #1 - 1.038, #2 - 1.048, #3 - 1.083, #4 - 1.079. The average is 1.062, 
 which is entered in colunm 4 of Table Eo. 3 for item 5. The xa*essure 
 loss for the other sizes is calculated by multiplying 1,062 by the ratio 
 of the respective values of factor P from Table Eo. 8, Appendix IV. 
 
 Item 6. 
 
 From •’rational Pipe Standards”, table p. 649, col. 3, 
 
 Item 7. 
 
 Area, sq, ft. - (item 6)^ 
 
 0.7854 
 
 X 2 0,00545 (item 6)2 
 
 144 
 
 Item 8, 
 
 Velocity (ft. per min.) in interconnections. A, B, and C, - 
 lb. steam per min, x so, vol. r 9870 x 2.2 z 7.238 
 Area in sq. ft. 3 x area item 7 
 
 Item 9. 
 
 Velocity head, lb, per sq. in. z 
 
 ( ft. -per min. )^ _ 
 
 ' 3600 X 2 X 32,2 x sp, vol, x 144 
 
 Item 10. 
 
 (ft. per sec. ) ^ 
 
 2"g 
 
 sp. vol. X '144 
 
 ( i tem 8 ) 2 
 73,500,000 
 
 The pressure less from saturated steam drum to hesuier, including dry 
 pipe, superheater, non~retum valve, feeder, and all intermediate fittings 
 is 7 lb. per sq. in. (From, test data on similar boiler, corrected to the 
 proper rating). 
 
 Item 10 s item 5 + item 9+7, 
 
 Item 11. 
 
 Item 11 - 250 - item 10. 
 
 Item 12. 
 
 Btu, per hr. z length (632 ft.) x item 1* (1 - 0.01 item 3*). 
 
 ♦Col. 3, Table 1. 
 
 Item 13. 
 
 Total heat of steam at boiler nozzle (265 lb. per sq. in. Abs. and 
 
 150° superheat) z 1290.4 item 12 
 
 Total heat of steam at turbine nozzle z 1290.4 - 
 
 lb, steam per hr. 
 
Page 26 
 App. II 
 
 Item 14. 
 
 Obtained by interpolation from P. 0. Ellenwood’s **Steam Charts”, 
 using item 11 and item 13 as data. 
 
 Eote that the higher superheat for small pipes than for large pipes 
 is due to two causes: (1) less radiation, and (2) throttling (ex- 
 pansion at constant total heat), and that for all sizes of pipe there is 
 more superheat at the turbine than at the boiler, even though the total 
 heat is lov/er at the turbine due to radiation. 
 
 Item 15. 
 
 The water rate of the turbine at the design load and steam conditions 
 is given in the guarantee as 12.75 lb, per kwh. With steam at 250 lb. 
 gage and lOO deg. superheat (specifications) the electrical energy 
 obtained fror one pound of steam Is ^1^ 
 
 12.75 
 
 A study of the pressure corrections used by the Westinghouse Electric 
 and llfg. Company and a check calculation by thermodj^'namics indicate that 
 the loss of available energy amounts to 0.25 Btu. per pound of steam for 
 each pound decrease of pressure, within the range of this problem. 
 
 The heat lost by radiation has a direct effect by reducing the avail- 
 able energj^ per pound of steam by an amount equal to the total Btu. lost 
 by radiation per hour, divided by the total weight of steam flov/ing per 
 hour. 
 
 The net electrical energy available per pound of steam, then, is 268 
 minus the losses due to pressure drop and radiation, and the corrected 
 v/ater rate of the turbine is equal to 3412 divided by the net available 
 energy per pound of steam. 
 
 Item 16. 
 
 Heat carried by one pound of steam from fuel to turbine nozzle - 
 item 15 - feed water temp. (i. e. 210°) + 32 = item 13 - 178. 
 
 kw hr. w. r. Btu. steam Coal 
 
 Item 16 - 45,000 x 6400 x item 15 x (item 13-178) x 3.50 
 
 13,500 X 0.78 X 2000 
 Coal eff. ton 
 47.9 X item 15 x (item 15 - 178). 
 
 Item 17. 
 
 Item 17 r item 3 + item 4 + item 16. 
 
 28 - GOHCLUSIOES OH HEADER SIZE. 
 
 Inspection of the total cost curve of Pig. 5 and item 17 of Table Eo. 3 
 indicates that a 14-inch header is the economical size to install. 
 
 29 - CLOSIEG DISCUSSION OF THE RATIONAL IvETHOB. 
 
 The failure of the velocity method is proved by a comparison of Tables 
 
iWf- 
 
Pa^ 27 
 App. II 
 
 Fos. 2 and 3. In tatle Ko. 2 it is found that the velocity corresponding to 
 the economical size is 5000 ft. per min. Kow, if the second design problem 
 (Table Ko. 3) were solved on the basis of 5000 ft. per m.in. velocity in the 
 BAin branches. A, B, and C, a 17-inch (0. D.) heavier would have been selected. 
 Item 17 indicates that the annual charges against this header would be v350,00 
 per year greater than those against the 14-inch. Hence, if a designer’s time 
 is required for one month (which is much longer than should be required) to 
 make a rational analysis, his salary v/ould be saved in fromj one to two years, 
 which is considered a good investment. Further, in col. 7 of Table Ho. 4 it 
 is found that velocities in the 14-inch header range from 270 to 8060 ft. per 
 min. Thus the velocity method loses most of its significance at once. 
 
 It is interesting to note that the total pressure loss for the economical 
 headers in the tv/o problems are 8,16 and 8.68 lb. per sq. in. respectively. It 
 does not follow, however, that 8 to 9 lb. m^ay be assumed as the economical drop 
 for all cases. Tv/o exairples v/ill serve to point out the fallacy of such a 
 conclusion, (l) There are ma,ny factors which affect the probler , one of which 
 is fuel cost. In some localities fuel costs are double those in other 
 localities, and v/here the cost is high, larger headers are warranted since the 
 energy lost through pressure drop has a greater value than with lov; fuel cost. 
 The effect of high fuel cost on Fig, 5 is to raise curve 16, v/hich tends to 
 shift the minimum value of curve 17 towards the right, (2) It is obvious that 
 a greater pressure drop is warranted in a stand-by plant operating with a low 
 yearly load factor than in a high load factor plant, since in the case of the 
 former the financial cost of an "excessive” pressure drop for only a few hours 
 a day or month is small, and the high fixed charges on the greater cost of a 
 large header are not warranted. 
 
 A well known Central Station designer has criticised the rational method, 
 claim.ing that too much time is required, that a designer who is ijroficient 
 enough to do such v/ork is worth much more on other phases of the work, and that 
 satisfactory results are obtained by a good guess based upon experience. This 
 criticism may have some Justification, but it is the author’s firm contention 
 that even if the pressure of time does require ”a good guess” rather than com- 
 plete analysis, that a much m^ore intelligent guess may be made if the designer 
 has gone through at least one complete problem by the rational method, which 
 will endow him v/ith a knowledge of the various factors affecting the problem, 
 and their relative importance. 
 
 Further, for a designer who proposes to use the pressure loss method of 
 design, the additional v/ork required to complete the rational method is not 
 great, and it will undoubtedly be found to be Justified. 
 
 In view of the facts brought out in this studj’’, the rational method is 
 recommended by the author as the most satisfactory method of steam header de- 
 sign. 
 

 
 
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Page 20 
 App. Ill 
 
 APPEKDIX III. 
 
 HALIATIGIj LOSSES FEOF BARE APE lESULATED PIPES. 
 
 Protably the most reliable experimental data available on radiation 
 losses, are those reported by Ej:. L. B. Eclvlillan in Vol« 37 of Trans. A.S.E.E, 
 
 Table Eo. 5, published in ” Johns-Eanville Service to Power Users” is based 
 upon EcEillan' s experimental data, and is considered reliable. The tempera t\ire 
 differences at the column headings in this table refer to those between outside 
 pipe surface and surrounding air. Analysis of Ecllillan’s experiments indicates 
 that with zero velocity inside the pipe, the inner surface and metal resistance 
 for bare pipes is about 1.27 percent of the total resistance for saturated 
 steam, and 9.45 percent for superheated steam. The magnitude of the inner 
 surface resistance is known to decrease as velocity increases, but the exact 
 relation between these two quantities is not known. It is known, however, 
 from tests made with air, that a small increase in velocity is accompanied by a 
 large decrease in surface resistance. It may therefore be concluded that at 
 the customary high velocities in steam headers, the inner surface resistance is 
 less than one or tv'O percent of the total resistance, and hence sufficient 
 accuracy is obtained by neglecting the resistances imposed by the inner surface 
 and the pipe metal. Table Eo. 5 may then be used by interpreting the column 
 headings as "temperature difference between steam and surrounding air”. 
 
 The efficiency of an insulating covering is defined as the ratio of the 
 amount of heat saved by using the insulation, to the amount v/hich wou'ld be 
 lost if the pipe were left bare, expressed as a percentage. 
 
 To determine the amount of heat radiated from an insulated pipe, then, 
 it is necessary to determine the amount radiated from a bare pipe, and multiply 
 this loss by the efficiency of the insulation. 
 
 The efficiencies of comrercial pipe insulating materials vary from about 
 50 percent to about 97 percent, depending upon the nature of the material, the 
 thickness of the insulation, the temperature difference, and the pipe size. 
 
 Table Ko. 6 taken from ” Johns-Manville Service to Pov/er Users” shows the ef- 
 ficiencies of Johns -Eanvi lie "Asbesto-Sponge-Felted” insulation. 
 
 Table Ko. 7, from " Johns-Eanville Service to Power Users” gives the list 
 prices of all classes of pipe coverings. Discounts vary with the grade of 
 material and market value. 
 

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Page 29 
 App. Ill 
 
 TAPU ITO. 5. 
 
 RADI AT TOP LOSg BARE PIPE. 
 
 Total Heat Loss in B. t. u. Per Hour Per Lineal Foot of Bare Pipe of Different Sizes and 
 Per Square Foot of Flat Surfaces and at Various Temperature Differences 
 
 (For finding losses at temperatures between those shown, the B. t. u. Differences per Degree are given in small type between the Main Columns) 
 Area of Temperature Differences 
 
 Pipe Sur- 50° 
 
 
 100° 
 
 
 150° 
 
 
 200° 
 
 
 250° 
 
 
 300° 
 
 
 350° 
 
 
 400° 
 
 
 450° 
 
 
 500° 
 
 Pipe 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Size 
 
 lin. ft 
 
 
 
 
 
 
 
 Heat Loss m B. t 
 
 u. per lineal 
 
 ft. per Hour 
 
 
 
 
 
 
 
 K" 
 
 .220 
 
 21.5 
 
 *.52 
 
 47.3 
 
 ♦.64 
 
 79.2 
 
 *.76 
 
 117.3 
 
 *.go 
 
 162.3 
 
 *1.06 
 
 215.2 
 
 ♦1.28 
 
 279.1 
 
 *1.52 
 
 355.1 
 
 *1.93 
 
 451.4 
 
 *2.37 
 
 569.8 
 
 H " 
 
 .274 
 
 26.8 
 
 .64 
 
 59.0 
 
 .79 
 
 98.6 
 
 .96 
 
 146.8 
 
 1.11 
 
 202.1 
 
 1-33 
 
 268.5 
 
 I.S8 
 
 347.6 
 
 1.89 
 
 442.2 
 
 2.40 
 
 562.2 
 
 2.95 
 
 709.7 
 
 1" 
 
 .344 
 
 33.6 
 
 .8i 
 
 74.0 
 
 1. 00 
 
 123.8 
 
 1. 19 
 
 183.4 
 
 I.4I 
 
 253.7 
 
 1.67 
 
 337.4 
 
 1.98 
 
 436.5 
 
 2.37 
 
 555.2 
 
 3-03 
 
 705.4 
 
 3-69 
 
 891. 
 
 IK" 
 
 .435 
 
 42.5 
 
 1. 01 
 
 93.6 
 
 1.26 
 
 156.6 
 
 1. 51 
 
 231.9 
 
 1.78 
 
 320.8 
 
 2.09 
 
 425.4 
 
 2. S3 
 
 551.9 
 
 3.00 
 
 702.1 
 
 3.80 
 
 892.6 
 
 4.68 
 
 1126.7 
 
 IK" 
 
 .498 
 
 48.7 
 
 1. 17 
 
 107.2 
 
 1.44 
 
 179.3 
 
 1.72 
 
 265.4 
 
 2.04 
 
 367.3 
 
 2.39 
 
 487. 
 
 2.90 
 
 631.8 
 
 3-44 
 
 803.8 
 
 4-36 
 
 1021.9 
 
 5.36 
 
 1289.8 
 
 2" 
 
 .622 
 
 60.9 
 
 1.46 
 
 133.9 
 
 1.80 
 
 223.9 
 
 2.15 
 
 331.5 
 
 2.S4 
 
 458.7 
 
 2.99 
 
 608.3 
 
 3-62 
 
 789.2 
 
 4.29 
 
 1003.9 
 
 5-45 
 
 1276.3 
 
 6.69 
 
 1611. 
 
 2K" 
 
 .753 
 
 73.4 
 
 1.76 
 
 161.6 
 
 2.18 
 
 270.4 
 
 2.60 
 
 400.3 
 
 3-07 
 
 553.9 
 
 3.61 
 
 734.5 
 
 4-37 
 
 952.8 
 
 S.19 
 
 1212.1 
 
 6.58 
 
 1541.1 
 
 8.08 
 
 1945.1 
 
 3" 
 
 .917 
 
 89.6 
 
 2.15 
 
 197.3 
 
 2.66 
 
 330.1 
 
 3-17 
 
 488.8 
 
 3-75 
 
 676.3 
 
 4.41 
 
 896.8 
 
 5-33 
 
 1163.4 
 
 6.33 
 
 1480. 
 
 8.03 
 
 1881.7 
 
 9.87 
 
 2375. 
 
 3K" 
 
 1.047 
 
 102.3 
 
 2.46 
 
 225.3 
 
 3.03 
 
 376.9 
 
 3.62 
 
 558.1 
 
 4.28 
 
 772.2 
 
 5.04 
 
 1024. 
 
 6.09 
 
 1328.4 
 
 7.23 
 
 1689.9 
 
 9.17 
 
 2148.4 
 
 II. 3 
 
 2711.7 
 
 4" 
 
 1.178 
 
 115.1 
 
 2.77 
 
 253.5 
 
 3-41 
 
 424.2 
 
 4.07 
 
 627.9 
 
 4.82 
 
 868.8 
 
 5.67 
 
 1152.1 
 
 6.85 
 
 1494.6 
 
 8.13 
 
 1901.3 
 
 10.3 
 
 2417.3 
 
 12.7 
 
 3051. 
 
 4K" 
 
 1.309 
 
 127.9 
 
 3-07 
 
 281.5 
 
 3.79 
 
 4 70.9 
 
 4-53 
 
 697.2 
 
 5-35 
 
 964.7 
 
 6.29 
 
 1279.2 
 
 7.61 
 
 1659.5 
 
 0.03 
 
 2111.1 
 
 11.05 
 
 2684. 
 
 14.1 
 
 3387.7 
 
 5" 
 
 1.456 
 
 142.2 
 
 3.42 
 
 313.1 
 
 4.21 
 
 523.8 
 
 5-03 
 
 775.5 
 
 5-95 
 
 1073. 
 
 7.00 
 
 1423. 
 
 8.46 
 
 1846. 
 
 10. 0 
 
 2348.4 
 
 12.7 
 
 2985.7 
 
 15.7 
 
 3768.5 
 
 6 " 
 
 1.734 
 
 169.4 
 
 4-05 
 
 371.9 
 
 S.04 
 
 623.9 
 
 6.00 
 
 923.7 
 
 7.09 
 
 1278.1 
 
 8.34 
 
 1694.9 
 
 10. 1 
 
 2198.7 
 
 12.0 
 
 2797.1 
 
 15-2 
 
 3556.2 
 
 18.6 
 
 4488.5 
 
 7 " 
 
 2.00 
 
 195.0 
 
 4.71 
 
 430.4 
 
 5. 79 
 
 720.0 
 
 6.92 
 
 1066.0 
 
 8.10 
 
 1475.6 
 
 9.61 
 
 1956. 
 
 11.66 
 
 2539. 
 
 13.78 
 
 3228. 
 
 17.46 
 
 4101. 
 
 21.6 
 
 5180. 
 
 8 " 
 
 2.257 
 
 220.6 
 
 5.30 
 
 485.7 
 
 6.54 
 
 812.5 
 
 7.81 
 
 1203. 
 
 9.23 
 
 1664.5 
 
 10.8 
 
 2207.3 
 
 I3-I 
 
 2863.6 
 
 IS.6 
 
 3642.8 
 
 19.8 
 
 4631.4 
 
 24-3 
 
 5845.6 
 
 9" 
 
 2.52 
 
 246.0 
 
 5.92 
 
 542. 
 
 7.30 
 
 907. 
 
 8.72 
 
 1343. 
 
 10.34 
 
 1860. 
 
 12. 1 
 
 2465. 
 
 14-7 
 
 3200. 
 
 17-4 
 
 4070. 
 
 22.0 
 
 5170. 
 
 27.2 
 
 6530. 
 
 10' 
 
 2.817 
 
 275.4 
 
 6.62 
 
 606.2 
 
 8.16 
 
 1014.1 
 
 9-75 
 
 1501.5 
 
 II. 5 
 
 2077.5 
 
 13.6 
 
 2755. 
 
 16.4 
 
 3574.1 
 
 19.5 
 
 4546.6 
 
 24.7 
 
 5780.5 
 
 30.3 
 
 7296. 
 
 11' 
 
 3.08 
 
 300. 
 
 7.26 
 
 663. 
 
 8.92 
 
 1109. 
 
 10.66 
 
 1642. 
 
 12.6 
 
 2272. 
 
 14.76 
 
 3010. 
 
 17.9 
 
 3905. 
 
 21.3 
 
 4972. 
 
 26.9 
 
 6315. 
 
 33.3 
 
 7980. 
 
 12" 
 
 3.34 
 
 326. 
 
 7.86 
 
 719. 
 
 9.68 
 
 1203. 
 
 11.54 
 
 1780. 
 
 13.7 
 
 2465. 
 
 16.02 
 
 3266. 
 
 19-4 
 
 4235. 
 
 23.1 
 
 5390. 
 
 29.2 
 
 6850. 
 
 36.0 
 
 8650. 
 
 14'o. d. 
 
 3.66 
 
 357. 
 
 S-.SQ 
 
 786. 
 
 10.64 
 
 1318. 
 
 12.64 
 
 1950. 
 
 15-0 
 
 2700. 
 
 17.06 
 
 3580. 
 
 21.3 
 
 4645. 
 
 25-2 
 
 5905. 
 
 31.9 
 
 7500. 
 
 39.5 
 
 9475. 
 
 16"o. d. 
 
 4.19 
 
 408. 
 
 9.84 
 
 901. 
 
 12.2 
 
 1510. 
 
 14-5 
 
 2233. 
 
 17.2 
 
 3095. 
 
 20.1 
 
 4100. 
 
 24.4 
 
 5320. 
 
 28.9 
 
 6765. 
 
 36.5 
 
 8590. 
 
 45.2 
 
 10850. 
 
 Flat, 
 
 
 
 
 
 
 
 Heat Loss in 
 
 B. t. 
 
 u. per sq. ft. 
 
 per Hour 
 
 
 
 
 
 
 
 
 Curved. 
 
 or \ . 
 
 97.5 : 
 
 2.3s 
 
 215.2 
 
 2.90 
 
 360.0 
 
 3.46 
 
 533.0 
 
 4.10 
 
 737.8 
 
 4.80 
 
 978.0 
 
 5.83 : 
 
 1269.4 
 
 6.89 1614.0 8.73 2050.6 10.8 
 
 2590.0 
 
 Cylindrical 1 
 
 
 
 
 Heat Loss in 
 
 B. t. 
 
 u. per sq. ft. per degree temperature difference per Hour 
 
 
 
 
 
 
 Surfaces 
 
 
 1.950 
 
 
 2.152 
 
 
 2.400 
 
 
 2.665 
 
 
 2.951 
 
 
 3.260 
 
 
 3.627 
 
 4.035 
 
 
 4.557 
 
 
 5.180 
 
 ♦Example 2" Pipe, 235° Temp. Difference. 235° — 200° = 35°; 35° x 2.54 (B. t. u. per degree)=88.9 B. t. u. 331.5-h88.9 = 420.4; B. t. u. loss 
 at 235° Temp, difference. 
 
TABLE rO. 6. 
 
 EFFICIEKGY OF ASBESTO-SPOESE-FELTED 
 
 SECTIOKAL lESULATIOL. 
 
 Page 30 
 App. Ill 
 
 EfRciencies of Standard Thick Johns-Manville Asbesto-Sponge Felted Sectional Pipe 
 
 Insulation on Various Sizes of Pipes 
 
 Temperature Difference Between Steam in Pipe and Air Surrounding Pipe 
 
 Pipe Size, 
 Inches 
 
 H. 
 
 M. 
 
 IK. 
 1 K- 
 2 . 
 
 2K. 
 
 3 
 
 3K. 
 
 4 
 
 4K. 
 
 5 
 
 6 
 
 7 
 
 8 
 9 
 
 10 
 
 50° 
 
 100° 
 
 150° 
 
 200° 
 
 250° 
 
 300° 
 
 350° 
 
 400° 
 
 450° 
 
 500 
 
 
 
 
 
 Per Cent Efficiencies 
 
 
 
 
 
 68.5% 
 
 71.9 
 
 71.2% 
 
 74.3 
 
 73.3% 
 
 76.2 
 
 75.5% 
 
 78.1 
 
 77.1% 
 
 79.6 
 
 78.7% 
 
 81. 
 
 80.4% 
 
 82.6 
 
 81.9% 
 
 83.8 
 
 83.1% 
 
 85. 
 
 84.5% 
 
 86.2 
 
 74.3 
 
 76.5 
 
 78.2 
 
 79.9 
 
 81.3 
 
 82.6 
 
 84. 
 
 85.2 
 
 86.2 
 
 87.4 
 
 75.7 
 
 n.i 
 
 79.5 
 
 81. 
 
 82.3 
 
 83.5 
 
 84.9 
 
 86. 
 
 86.9 
 
 88. 
 
 77 
 
 79. 
 
 80.5 
 
 82. 
 
 83.2 
 
 84.4 
 
 85.7 
 
 86.7 
 
 87.6 
 
 88.6 
 
 78.6 
 
 80.4 
 
 81.9 
 
 83.3 
 
 84.4 
 
 85.5 
 
 86.7 
 
 87.6 
 
 88.5 
 
 89.3 
 
 79.8 
 
 81.5 
 
 82.9 
 
 84.3 
 
 85.3 
 
 86.3 
 
 87.5 
 
 88.4 
 
 89.2 
 
 90.3 
 
 80.6 
 
 82.2 
 
 83.6 
 
 84.9 
 
 85.9 
 
 86.8 
 
 87.9 
 
 88.8 
 
 89.6 
 
 90.3 
 
 81.2 
 
 82.8 
 
 84.1 
 
 85.4 
 
 86.3 
 
 87.3 
 
 88.3 
 
 89.2 
 
 89.9 
 
 90.6 
 
 81.8 
 
 83.3 
 
 84.5 
 
 85.8 
 
 86.7 
 
 87.6 
 
 88.7 
 
 89.5 
 
 90.2 
 
 90.9 
 
 82.1 
 
 83.6 
 
 84.8 
 
 86. 
 
 87. 
 
 87.9 
 
 88.9 
 
 89.7 
 
 90.4 
 
 91.1 
 
 82.3 
 
 83.8 
 
 85. 
 
 86.2 
 
 87.1 
 
 88. 
 
 89. 
 
 89.8 
 
 90.5 
 
 91.2 
 
 82.7 
 
 84.2 
 
 85.4 
 
 86.5 
 
 87.4 
 
 88.3 
 
 89.3 
 
 90.1 
 
 90.7 
 
 91.4 
 
 83. 
 
 84.5 
 
 85.6 
 
 86.8 
 
 87.6 
 
 88.5 
 
 89.5 
 
 90.2 
 
 90.9 
 
 91.6 
 
 83.4 
 
 84.8 
 
 85.9 
 
 87. 
 
 87.9 
 
 88.7 
 
 89.7 
 
 90.4 
 
 91.1 
 
 91.7 
 
 83.5 
 
 84.9 
 
 86. 
 
 87.2 
 
 88. 
 
 88.8 
 
 89.8 
 
 90.5 
 
 91.2 
 
 91.8 
 
 83.8 
 
 85.1 
 
 86.2 
 
 87.3 
 
 88.2 
 
 89. 
 
 89.9 
 
 90.6 
 
 91.3 
 
 91.9 
 
 Johns- 
 
 Manville Asbesto-Sponge 
 
 Felted 
 
 Sectional Pipe 
 
 Insulation 
 
 on Various Sizes of Pipe 
 
 Pipe Size, 
 Inches 
 
 K. 
 
 1 
 
 IK. 
 
 IK- 
 
 2 
 
 2K 
 
 3 
 
 3H 
 
 4 
 
 4K 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 . 
 10 
 
 Temperature Difference Between Steam in Pipe and Air Surrounding Pipe 
 
 50° 
 
 100° 
 
 150° 
 
 200° 
 
 250° 
 
 300° 
 
 350° 
 
 400° 
 
 450° 
 
 500° 
 
 
 
 
 
 Per Cent Efficiencies 
 
 
 
 
 85.2% 
 
 87. 
 
 70.3% 
 
 73.7 
 
 72.9% 
 
 75.9 
 
 75. % 
 77.7 
 
 76.8% 
 
 79.4 
 
 78.4% 
 
 80.9 
 
 80. % 
 82.4 
 
 81.5% 
 
 83.5 
 
 82.9% 
 
 84.9 
 
 84.2% 
 
 86. 
 
 76.1 
 
 78.1 
 
 79.8 
 
 81.3 
 
 82.7 
 
 84.1 
 
 85.1 
 
 86.3 
 
 87.3 
 
 88.1 
 
 77.8 
 
 79.7 
 
 81.2 
 
 82.5 
 
 83.8 
 
 85.1 
 
 86.1 
 
 87.2 
 
 88.2 
 
 89 
 
 79. 
 
 80.7 
 
 82.3 
 
 83.5 
 
 84.7 
 
 86. 
 
 86.9 
 
 88. 
 
 88.8 
 
 89.9 
 
 81. 
 
 82.7 
 
 84. 
 
 85.2 
 
 86.2 
 
 87.2 
 
 88.1 
 
 89.1 
 
 89.9 
 
 90.6 
 
 82.1 
 
 83.7 
 
 85.1 
 
 86.1 
 
 87. 
 
 88.1 
 
 88.8 
 
 89.8 
 
 90.5 
 
 91.1 
 
 83. 
 
 84.5 
 
 85.7 
 
 86.8 
 
 87.7 
 
 88.7 
 
 89.4 
 
 90.3 
 
 91. 
 
 91.6 
 
 83.6 
 
 85. 
 
 86.2 
 
 87.2 
 
 88.1 
 
 89.1 
 
 89.8 
 
 90.6 
 
 91.3 
 
 91.9 
 
 84.2 
 
 85.5 
 
 86.7 
 
 87.7 
 
 88.5 
 
 89.5 
 
 90.1 
 
 91. 
 
 96. 
 
 92.1 
 
 84.6 
 
 85.9 
 
 87.1 
 
 88. 
 
 88.8 
 
 89.8 
 
 90,4 
 
 91.2 
 
 91.8 
 
 92.3 
 
 85. 
 
 86.3 
 
 87.4 
 
 88.3 
 
 89.1 
 
 90. 
 
 90.6 
 
 91.4 
 
 91.2 
 
 92.5 
 
 85.4 
 
 86.7 
 
 87.8 
 
 88.6 
 
 89.4 
 
 90.3 
 
 90.9 
 
 91.7 
 
 92.2 
 
 92.7 
 
 83.9 
 
 87.1 
 
 88.1 
 
 89. 
 
 89.8 
 
 90.6 
 
 91.2 
 
 91.9 
 
 92.5 
 
 92.9 
 
 86.2 
 
 87.5 
 
 88.4 
 
 89.1 
 
 90. 
 
 90.8 
 
 91.4 
 
 92.1 
 
 92.7 
 
 93.1 
 
 86 4 
 
 87.7 
 
 88.6 
 
 89.3 
 
 90.1 
 
 90.9 
 
 91.5 
 
 92.2 
 
 92.8 
 
 93,2 
 
 86.6 
 
 87.8 
 
 88.8 
 
 89.6 
 
 90.3 
 
 91. 
 
 91.6 
 
 92.3 
 
 92.9 
 
 93.4 
 
OS 
 
 
 r tt i i U w i iiaAift W(ii»tfS‘^iiM|iig.i?» » 
 ‘“W / 
 
 i* r\ 
 
 * I*'. 
 
 .'. 'Jj/sk. -. 
 
 • *'»»* ^ 
 
 . r' 
 
 Slir -isS : -. -f/' ' 
 
 i' 
 
 if ^ -■- 
 
 ■*.Ct 
 
 4 
 
 ¥ 
 
 {*;* 
 
 
 ... -i ;• , 
 
 ' ...'’'•'S^ * A.!'®' .■• ^V'.!r 
 
 ’ Ik* ^ 
 
 , ■ ', \*'' 
 
 y. '..' 
 
 '. ) 
 
 '■■ "^V . '1 :. , - ’ 
 
 . 2 ■■ ,, .■,-- '■ (jg^' 
 

 
 
 
 
 
 
 
 
 Page 31 
 
 
 
 
 
 
 
 
 
 
 App 
 
 . Ill 
 
 
 
 TABLE KO. 6 
 
 - (CCKT’D) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Efficiencies of 2" 
 
 Thick Johns-Manville Asbesto-Sponge Felted Sectional Pipe Insulation on 
 
 
 
 Various Sizes of Pipe 
 
 
 
 
 
 
 
 
 Temperature Difference Between Steam 
 
 in Pipe 
 
 and Air Surrounding Pipe 
 
 
 Pipe Size, 
 
 Inches 
 
 50° 
 
 100° 
 
 150° 
 
 200° 
 
 250° 
 
 300° 
 
 350° 
 
 400° 
 
 450° 
 
 500° 
 
 
 
 
 
 
 Per Cent Efficiencies 
 
 
 
 
 
 34 . . 
 
 73.2% 
 
 75.6% 
 
 77.5% 
 
 79.2% 
 
 80.7% 
 
 82. % 
 
 83.5% 
 
 84.6% 
 
 86.1% 
 
 87.4% 
 
 ^ 
 
 76.5 
 
 78.6 
 
 80.3 
 
 81.8 
 
 83.1 
 
 84.2 
 
 85.5 
 
 86.5 
 
 87.8 
 
 88.8 
 
 r ‘ 
 
 78.8 
 
 80.7 
 
 82.2 
 
 83.6 
 
 84.8 
 
 85.8 
 
 87. 
 
 87.8 
 
 89. 
 
 90. 
 
 134 
 
 80.5 
 
 82. 
 
 83.6 
 
 84.9 
 
 86. 
 
 87.1 
 
 88. 
 
 88.8 
 
 89.8 
 
 90.8 
 
 iH 
 
 2 . . 
 
 81.7 
 
 83.4 
 
 84.7 
 
 85.9 
 
 86.9 
 
 87.8 
 
 88.7 
 
 89.5 
 
 90.4 
 
 91.2 
 
 83.6 
 
 85.1 
 
 86.2 
 
 87.2 
 
 88.1 
 
 89. 
 
 89.9 
 
 90.6 
 
 91.4 
 
 92.1 
 
 2H 
 
 3 
 
 84.3 
 
 86.1 
 
 87.2 
 
 88.2 
 
 89. 
 
 89.7 
 
 90.5 
 
 91.2 
 
 92. 
 
 92.7 
 
 85.6 
 
 86.8 
 
 87.9 
 
 88.8 
 
 89.6 
 
 90.3 
 
 91.1 
 
 91.7 
 
 92.5 
 
 93.2 
 
 SM 
 
 86.2 
 
 87.4 
 
 88.4 
 
 89.3 
 
 90.1 
 
 90.8 
 
 91.5 
 
 92.1 
 
 92.8 
 
 93.5 
 
 4 
 
 86.7 
 
 87.9 
 
 88.8 
 
 89.7 
 
 90.5 
 
 91.1 
 
 91.8 
 
 92.4 
 
 93.1 
 
 93.7 
 
 4 3^ 
 
 .... 87.1 
 
 88.3 
 
 89.2 
 
 90. 
 
 90.7 
 
 91.3 
 
 92.1 
 
 92.6 
 
 93.3 
 
 93.9 
 
 5 ' “ 
 
 87.5 
 
 88.6 
 
 89.5 
 
 90.3 
 
 91. 
 
 91.6 
 
 92.3 
 
 92.8 
 
 93.5 
 
 94.1 
 
 6 
 
 88. 
 
 89.1 
 
 89.9 
 
 90.7 
 
 91.3 
 
 91.9 
 
 92.6 
 
 93.1 
 
 93.8 
 
 94.3 
 
 7 
 
 88.4 
 
 89.4 
 
 90.2 
 
 91. 
 
 91.6 
 
 92.2 
 
 92.8 
 
 93.3 
 
 94. 
 
 94.5 
 
 8 
 
 88.6 
 
 89.6 
 
 90.4 
 
 91.2 
 
 91.8 
 
 92.4 
 
 93. 
 
 93.4 
 
 94.1 
 
 94.6 
 
 9 
 
 88.9 
 
 89.9 
 
 90.6 
 
 91.4 
 
 92. 
 
 92.5 
 
 93.1 
 
 93.6 
 
 94.2 
 
 94.7 
 
 10 
 
 89.1 
 
 90.1 
 
 90.8 
 
 91.5 
 
 92.2 
 
 92.7 
 
 93.3 
 
 93.7 
 
 94.3 
 
 94.8 
 
 Efficiencies ©/■ 2 ^ 
 
 " Thick Johns- 
 
 Manville Asbesto-Sponge Felted Sectional Pipe Insulation on 
 
 
 Various Sizes of Pipe 
 
 
 
 
 
 
 
 
 Temperature Difference Between Steam 
 
 in Pipe 
 
 and Air Surrounding Pipe 
 
 
 Pipe Size, 
 
 Inches 
 
 50° 
 
 100° 
 
 150° 
 
 200° 
 
 250° 
 
 300° 
 
 350° 
 
 400° 
 
 450° 
 
 500° 
 
 
 
 
 
 
 Per Cent Efficiencies 
 
 
 
 
 
 34 
 
 75. % 
 
 77.3% 
 
 78.9% 
 
 80.7% 
 
 82.1% 
 
 83.7% 
 
 84.8% 
 
 85.9% 
 
 87. % 
 
 88.% 
 
 ^ 
 
 78.2 
 
 80. 
 
 81.6 
 
 83.2 
 
 84.4 
 
 85.7 
 
 86.7 
 
 87.7 
 
 88.5 
 
 89.3 
 
 \' 
 
 80.5 
 
 82.2 
 
 83.5 
 
 85. 
 
 86. 
 
 87.2 
 
 88.1 
 
 89. 
 
 89.7 
 
 90.4 
 
 
 
 1 Vi. 
 
 82.2 
 
 83.8 
 
 84.9 
 
 86.2 
 
 87.2 
 
 88.3 
 
 89.1 
 
 90. 
 
 90.6 
 
 91.3 
 
 83.4 
 
 84.9 
 
 86. 
 
 87.2 
 
 88.1 
 
 89.1 
 
 89.9 
 
 90.6 
 
 91.2 
 
 91.9 
 
 2 ' “ . . 
 
 85.2 
 
 86.5 
 
 87.5 
 
 88.6 
 
 89.4 
 
 90.3 
 
 91. 
 
 91.7 
 
 92.2 
 
 92.8 
 
 
 
 3 
 
 86.3 
 
 87.5 
 
 88.4 
 
 89.4 
 
 90.2 
 
 91. 
 
 91.7 
 
 92.3 
 
 92.8 
 
 93.3 
 
 87.1 
 
 88.3 
 
 89.1 
 
 90.1 
 
 90.8 
 
 91.6 
 
 92.2 
 
 92.7 
 
 93.2 
 
 93.7 
 
 3^2 
 
 87.8 
 
 88.9 
 
 89.7 
 
 90.6 
 
 91.2 
 
 92. 
 
 92.6 
 
 93.1 
 
 93.5 
 
 94. 
 
 4 
 
 88.3 
 
 89.3 
 
 90.1 
 
 90.9 
 
 91.6 
 
 92.3 
 
 92.9 
 
 93.4 
 
 93.8 
 
 94.3 
 
 4H 
 
 5 
 
 88.7 
 
 89.7 
 
 90.4 
 
 91.2 
 
 91.9 
 
 92.6 
 
 93.1 
 
 93.6 
 
 94. 
 
 94.5 
 
 89. 
 
 90. 
 
 90.7 
 
 91.5 
 
 92. 
 
 92.8 
 
 93.3 
 
 93.8 
 
 94.2 
 
 94.6 
 
 6 
 
 89.5 
 
 90.4 
 
 91.1 
 
 91.9 
 
 92. 
 
 93.1 
 
 93.6 
 
 94.1 
 
 94.5 
 
 94.8 
 
 7 
 
 89.9 
 
 90.8 
 
 91.4 
 
 92.2 
 
 92.7 
 
 93.4 
 
 93.8 
 
 94.3 
 
 94.7 
 
 95. 
 
 8 
 
 90.1 
 
 91. 
 
 91.6 
 
 92.4 
 
 92.9 
 
 93.5 
 
 94. 
 
 94.4 
 
 94.8 
 
 95.1 
 
 9 
 
 90.3 
 
 91.2 
 
 91.8 
 
 92.5 
 
 93.1 
 
 93.7 
 
 94.1 
 
 94.6 
 
 94.9 
 
 95.2 
 
 10 ... 
 
 90.5 
 
 91.4 
 
 92. 
 
 92.7 
 
 93.2 
 
 93.8 
 
 94.2 
 
 94.7 
 
 95. 
 
 95.3 
 
 Efficiencies of 3" 
 
 Thick Johns-Manville 
 
 Asbesto-Sponge Felted Sectional 
 
 Pipe Insulation on 
 
 
 
 Various Sizes of Pipe 
 
 
 
 
 
 
 
 
 Temperature Difference Between Steam 
 
 in Pipe 
 
 and Air Surrounding Pipe 
 
 
 Pipe Size, 
 
 Inches 
 
 50° 
 
 100° 
 
 150° 
 
 200° 
 
 250° 
 
 300° 
 
 350° 
 
 400° 
 
 450° 
 
 500° 
 
 
 
 
 
 
 Per Cent Efficiencies 
 
 
 
 
 
 14 
 
 76.8% 
 
 78.9% 
 
 80.6% 
 
 82.1% 
 
 83.4% 
 
 84.6% 
 
 85.8% 
 
 87. % 
 
 88.1% 
 
 89.1% 
 
 ^ . 
 
 79.7 
 
 81.7 
 
 83.1 
 
 84.5 
 
 85.6 
 
 86.6 
 
 87.6 
 
 88.6 
 
 89.6 
 
 90.5 
 
 1' ‘ 
 
 81.9 
 
 83.5 
 
 84.8 
 
 86.1 
 
 87.1 
 
 88. 
 
 88.9 
 
 89.8 
 
 90.7 
 
 91.5 
 
 134 
 
 83.5 
 
 85. 
 
 86.2 
 
 87.3 
 
 88.2 
 
 89.1 
 
 89.9 
 
 90.8 
 
 91.6 
 
 92.3 
 
 ri4 
 
 84.7 
 
 86.1 
 
 87.2 
 
 88.3 
 
 89.1 
 
 89.9 
 
 90.6 
 
 91.4 
 
 92.2 
 
 92.8 
 
 2 ' 
 
 86.5 
 
 87.7 
 
 88.7 
 
 89.6 
 
 90.3 
 
 91. 
 
 91.7 
 
 92.4 
 
 93.1 
 
 93.7 
 
 234 
 
 87.5 
 
 88.7 
 
 89.6 
 
 90.5 
 
 91.1 
 
 91.7 
 
 92.4 
 
 93. 
 
 93.5 
 
 94.2 
 
 3’ 
 
 88.4 
 
 89.5 
 
 90.3 
 
 91.2 
 
 91.7 
 
 92.3 
 
 92.9 
 
 93.5 
 
 94.1 
 
 94.6 
 
 3H 
 
 89. 
 
 90. 
 
 90.8 
 
 91.6 
 
 92.1 
 
 92.7 
 
 93.3 
 
 93.8 
 
 94.4 
 
 94.8 
 
 4 
 
 89.5 
 
 90.5 
 
 91.2 
 
 92. 
 
 92.5 
 
 93. 
 
 93.6 
 
 94.1 
 
 94.6 
 
 95.1 
 
 434 
 
 89.9 
 
 90.8 
 
 91.5 
 
 92.2 
 
 92.8 
 
 93.3 
 
 93.8 
 
 94.3 
 
 94.8 
 
 95.2 
 
 5 ’ 
 
 90.2 
 
 91.1 
 
 91.8 
 
 92.5 
 
 93. 
 
 93.5 
 
 94. 
 
 94.5 
 
 95. 
 
 95.4 
 
 6 
 
 90.7 
 
 91.5 
 
 92.2 
 
 92.9 
 
 93.3 
 
 93.8 
 
 94.3 
 
 94.8 
 
 95.2 
 
 95.6 
 
 7 
 
 91.1 
 
 91.9 
 
 92.5 
 
 93.2 
 
 93.6 
 
 94.1 
 
 94.5 
 
 95. 
 
 95.4 
 
 95.8 
 
 8 
 
 91.3 
 
 92.1 
 
 92.7 
 
 93.4 
 
 93.8 
 
 94.2 
 
 94.7 
 
 95.1 
 
 95.5 
 
 95.9 
 
 9 
 
 91.5 
 
 92.3 
 
 92.9 
 
 93.5 
 
 93.9 
 
 94.4 
 
 94.8 
 
 95.2 
 
 95.6 
 
 96. 
 
 10 
 
 91.7 
 
 92.5 
 
 93. 
 
 93.6 
 
 94. 
 
 94.5 
 
 94.9 
 
 95.3 
 
 95.7 
 
 96.1 
 
 
 
 
 
 
 
 
 
 
 
 
Pa^e 32 
 App. Ill 
 
 TABLE i:0. 7, 
 
 LIST PRICES OF PIPE OOVERIEG 
 
 SUBJECT TO DISCOUNT 
 
 Standard 
 Thick . . 
 
 Thick. . 
 2" Thick 
 ♦♦Double 
 Standard 
 Thick . . 
 3" Thick 
 Broken 
 Joints. . 
 
 INSIDE DIAMETER OF PIPE 
 
 
 
 1" 
 
 iM" 
 
 I'A" 
 
 2" 
 
 2H" 
 
 3" 
 
 3}^" 
 
 4" 
 
 4M" 
 
 5" 
 
 6" 
 
 7" 
 
 8" 
 
 9" 
 
 10" 
 
 12" 
 
 *14" 
 
 16" 
 
 18" 
 
 20" 
 
 24" 
 
 30" 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 .22 
 
 .24 
 
 .27 
 
 .30 
 
 .33 
 
 .36 
 
 .40 
 
 .45 
 
 .50 
 
 .60 
 
 .65 
 
 .70 
 
 .80 
 
 1.00 
 
 1.10 
 
 1.20 
 
 1.30 
 
 1.85 
 
 2.10 
 
 2.35 
 
 2.60 
 
 2.85 
 
 3.30 
 
 4.00 
 
 .46 
 
 .49 
 
 .52 
 
 .56 
 
 .60 
 
 .64 
 
 .70 
 
 .76 
 
 .82 
 
 .88 
 
 .94 
 
 1.00 
 
 1.10 
 
 1.20 
 
 1.35 
 
 1.50 
 
 1.65 
 
 1.85 
 
 2.10 
 
 2.35 
 
 2.60 
 
 2.85 
 
 3.30 
 
 4.00 
 
 .75 
 
 .80 
 
 .85 
 
 .90 
 
 .95 
 
 1.00 
 
 1.05 
 
 1.15 
 
 1.25 
 
 1.35 
 
 1.45 
 
 1.55 
 
 1.70 
 
 1.85 
 
 2.00 
 
 2.20 
 
 2.40 
 
 2.70 
 
 3.00 
 
 3.30 
 
 3.60 
 
 4.00 
 
 4.50 
 
 5.50 
 
 .65 
 
 .70 
 
 .75 
 
 .80 
 
 .85 
 
 .90 
 
 1.00 
 
 1.10 
 
 1.20 
 
 1.40 
 
 1.50 
 
 1.60 
 
 1.80 
 
 2.25 
 
 2.50 
 
 2.70 
 
 2.90 
 
 4.10 
 
 4.60 
 
 5.10 
 
 5.60 
 
 6.00 
 
 7.00 
 
 8.40 
 
 1.20 
 
 1.35 
 
 1.40 
 
 1.45 
 
 1.55 
 
 1.65 
 
 1.75 
 
 1.90 
 
 2.05 
 
 2.20 
 
 2.35 
 
 2.50 
 
 2.70 
 
 2.90 
 
 3.15 
 
 3.40 
 
 3.65 
 
 4.10 
 
 4.60 
 
 5.10 
 
 5.60 
 
 6.00 
 
 7.00 
 
 8.40 
 
 
 3^" 
 
 H" 
 
 1" 
 
 IM" 
 
 IH" 
 
 2" 
 
 
 3" 
 
 3H" 
 
 4" 
 
 
 5" 
 
 6" 
 
 7" 
 
 8" 
 
 9" 
 
 10" 
 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 $ 
 
 Elbows 90® & 45®.. 
 
 .30 
 
 .30 
 
 .30 
 
 .30 
 
 .30 
 
 .36 
 
 .42 
 
 .48 
 
 .54 
 
 .60 
 
 .72 
 
 .90 
 
 1.30 
 
 1.80 
 
 2.40 
 
 3.00 
 
 3.60 
 
 Tees 
 
 .36 
 
 .36 
 
 .36 
 
 .36 
 
 .36 
 
 .42 
 
 .48 
 
 .54 
 
 .60 
 
 .75 
 
 .90 
 
 1.20 
 
 1.60 
 
 2.20 
 
 3.00 
 
 3.80 
 
 4.60 
 
 Crosses 
 
 .48 
 
 .48 
 
 .48 
 
 .48 
 
 .48 
 
 .54 
 
 .60 
 
 .70 
 
 .80 
 
 .95 
 
 1.10 
 
 1.50 
 
 2.00 
 
 2.80 
 
 3.60 
 
 4.40 
 
 5.20 
 
 Globe Valves 
 
 .54 
 
 .54 
 
 .54 
 
 .54 
 
 .54 
 
 .60 
 
 .78 
 
 .96 
 
 1.20 
 
 1.50 
 
 1.85 
 
 2.25 
 
 2.80 
 
 3.60 
 
 4.40 
 
 5.30 
 
 6.20 
 
 Flange Covers 
 
 .50 
 
 .50 
 
 .50 
 
 .50 
 
 .50 
 
 .60 
 
 .70 
 
 .80 
 
 .90 
 
 1.00 
 
 1.30 
 
 1.60 
 
 1.90 
 
 2.20 
 
 2.50 
 
 2.90 
 
 3.30 
 
 These pipe insulations are supplied in sections three feet long, canvased and with brass lacquered bands. 
 
 *85% Magnesia is made in Standard (approx. 1"). 2", Double Standard Thick and 3" (broken joint) thicknesses. For 
 
 pipe sizes from and including 14" in diameter it is furnished in segmental form. 
 
 Asbesto-Sponge Felted Insulation is made in thicknesses from " to 3 thicknesses 1 "and under use list prices for standard thick . 
 
 Asbestocel and Air-Cell Insulations are made in M", 1", 2", and 3" thicknesses; for thicknesses 1" and under use 
 
 list prices for standard thick. 
 
 Zero Insulation is made in one thickness only, approximately 1 Use standard thick list prices. Prices on Zero Insulation 
 
 for fittings on request. 
 
 Anti-Sweat Insulation is made only in and 1" thicknesses; use standard thick list prices for all thicknesses. 
 
 Fittings not made for 85% Magnesia or Wool Felt Insulations. 
 
 ♦♦Applies only to 85% Magnesia. 
 
iK 
 
 
 p^"' ■■ 
 
 4 : 
 
 \ ■ '■'■lll•.‘i V'’j*s ™ 
 
 BW:-1‘" 'l. :'. i 
 
 mmm 
 
 *'. j I' i" ^ 
 
 -MW 
 
 51 M 
 
 i ‘’^t‘ 
 
 
 i^j^i T'>/iV *' '.I t 
 
 . 'iv ' rT'’Ut ^w^^kSv' '...> ' 
 
 r->v. .'viL-v ^ 
 
 Jf'l* • 
 
 ‘>v;> 
 
 •’■'■■ " \T'h 
 
 '^\r> ■ * ' ■'' 
 
 S'f^ ■•; V^vrv , ■ ‘ . \^J|P|1K Vjk.^' : " . ,• a-..- ,™ 
 
 .^h > ' - . „■ '>' ;■ ,. , - v .■ rg, 
 
 :„■> ,v'5 '■‘'TV'".- ' lvV^^- .'’ 2^1 
 
 
 
 
 ,. ,"• ;:m 
 
 ."/'i'il 
 
 <: t ^ I 'ffc* .'i i . ■'.* 
 
 I, :■■■'■, '’'vl^ ■ r *' sw 
 
 H 
 
 M 
 
 ■>; 
 
 ■ :•!■ v,„, ;.;gyt.ji«i- ",'fcii ../mi 
 
 ' I lA’ i' •'( ’•■ ■' ^ 'r.<i ' •' -■ 
 
 »w .*'<.■, '/v _ /'/'■. '•■.% -I K /.Vto " m’’ 'ms|Bk^?,p, * ./. .N*. ,.^i'.,^,‘‘' 
 
 :: o ' ■■ j ' ' /' '.i' . ^'a.v ' /v,",- rffift 
 
 ■ ^1* ,>T MW'-M:#’ — 
 
 
 
 
 •oyyr ' * / ^ ' **' . ’*< *»' •*:? 
 
 ■i 
 
Page 33 
 App. IV 
 
 APPENDIX IV. 
 
 TEE FLOW OF STEAM IE PIPES. 
 
 30 - THE BABCOCK FOHIULA. 
 
 Heliable experiinental oata on the friction loss of steajE under various 
 pressures, and particularly when superheated, are unfortunately lacking. 
 
 The n;ost generally accepted forirula for steam flow is Babcock’s: 
 
 P r 0,000,131 (1 + X w^ L formula (1) 
 
 ^ D d5 
 
 The use of this formula may be greatly facilitated by rearrangement to 
 the foTOiS: 
 
 p r w2 L V P formula (2) 
 
 or 
 
 P I w^ L F formula (3) 
 
 D 
 
 Nomenclature: 
 
 p r pressure loss, lb, per sq, in. 
 w = steam flow, lb. per min. 
 
 L r length of pipe or section, feet, 
 
 D = average specific density of steam, lb, per cu. ft, 
 
 V z average siiecific volume of steam, cu. ft. per lb. 
 
 Note: For superheated steam use D and V for the superheated 
 steam - not the saturated value. (See calculation, paragraph 
 32). 
 
 d r inside diameter of pipe, inches. 
 
 P a a factor vtoich is a function of the pipe diameter only, z 
 0.000,151 ^ (see Table No. 8). 
 
 Since the value F is a function of only one variable, viz. pipe diam;eter, 
 it may be tabulated. In Table No. 8 columns 1 and 4 indicate regularlj^ manu- 
 factured nominal pipe sizes from l/2 inch upward. Oolumns 2 and 5 show the 
 "actual” inside diameters corresponding to columns 1 and 4, Columns 3 and 6 
 indicate the values of factor ”F" to be used in formulae 2 and 3 corresponding 
 to columns 1 and 4. 
 
 31 - STA1:DABI) and EXTHA STRONC PIPES. 
 
 It should be noted particularly that column 3 applies only to standard 
 
if . ' 
 
 • tjr!- <’^‘ 
 
 ' ..y 
 
 
 I 
 
 I 
 
 
 f 
 
 
 1 
 
 -sV-.r ». 
 
 ri 
 
 - 4 >i/.. 
 
 $ 
 
 MB 
 
 , ■)' • ' '.V 
 
 . '.- .■ 
 
 iv , '.?' 
 
 » 
 
 I;' 
 
 i 
 
 I 
 
 !? 
 
 i.^ 
 
 <t 
 
 i 
 
 t 
 
 (y 
 
 S 
 
 « 
 
 r 
 
 V 
 
 ( 
 
 »:’: 
 
 r'-' 
 
 r 
 
 (, v:r. -[ 
 
 
 b 
 
 v> 
 
 r 
 
 1 r 
 
 % 
 
 
 ■‘ V 
 V' 
 
 
 •<^ ; ’ >- J 
 
 .■ ' 1^61 > 7 ■ 
 
 ■^Ity > 
 
 
 ♦ •> 
 
 v»f< ' 
 
 ff; » / > 
 
 •i:i 
 
 . r,:r!v«/ •■•-. ■ '< 
 
 ■■'■:f,'; 'T' » ■■ . r ■' 
 
 ft ■ » 
 
 ffi*' 
 
 
 • . 
 
 . I f ^ : 'iw- ■! 
 
 • i i y i'i ', '■^. ' . 
 
 ■•’■^''T ', 'I 
 
 •, ' ?i^’ 'fU-liTW 
 
 I •? • 
 
 , 4 .' ' V - 
 
 ‘ ; , »('l ' ’ 4 ,f : ■ 
 
 A 
 
 . ' ' ' O Vi -', ' - •' i'lti' 
 
 - , . i ' r.‘. 1 ‘ . «•-• (# 1 ®I 
 
 :■ V -iv-. nbtff 
 
 •r \ ‘ ^a■ lr«■^. 
 
 !■ ■ 
 
 r<. '.'t - 
 
Page 34 
 App. IV 
 
 TABLE KO. 8. 
 
 FAGTOH FOR THE FCLIFIED BABOOGK FORl^LA. 
 
 StiiiuUircl Wcijcht PijM' 
 
 F.xlra Heavy Pipe 
 
 Nominal 
 
 Actual 
 
 J^rt ssuro Lo.ss 
 
 Nominal 
 
 ■ .-Vctual 
 
 Prcs.sure Loss 
 
 Size, 
 
 Itisulo 
 
 Factor, /•’ 
 
 '^ize, 
 
 Inskle 
 
 Factor, F 
 
 Inches 
 
 ])iarn. 
 
 
 Indies 
 
 Diam. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 i 
 
 0 022 
 
 9.5.51. X 10 ' 
 
 5 
 
 0 .540 
 
 20.51 
 
 X lO--' 
 
 a. 
 
 0,824 
 
 1847. 
 
 
 0 . 742 
 
 340,8. 
 
 10-': 
 
 1 
 
 1 . 049 
 
 457 . 1 
 
 1 
 
 0 . 957 
 
 777.1 
 
 “ 
 
 M 
 
 1 , 380 
 
 94 32 
 
 li 
 
 1 , 278 
 
 140 7 
 
 
 15 
 
 1.610 
 
 39.14 
 
 15 
 
 1 .500 
 
 58 . 0.5 
 
 “ 
 
 2 
 
 2 . 067 
 
 9. 519 
 
 2 
 
 1 . 939 
 
 13 . 05 
 
 
 25 
 
 2.409 
 
 .3510. x'lO » 
 
 25 
 
 2.323 
 
 4938. 
 
 X 10-5 
 
 3 
 
 3 . 008 
 
 1017. 
 
 3 
 
 2.900 
 
 1432. 
 
 
 35 
 
 3 . 7)48 
 
 ■109.4 
 
 35 
 
 3 . 304 
 
 029 . 5 
 
 
 4 
 
 4 . 020 
 
 234.0 
 
 4 
 
 3 . 826 
 
 310.1 
 
 
 ■I 2 
 
 4 . oOO 
 
 120.9 
 
 15 
 
 4 . 290 
 
 105 . 8 
 
 
 n 
 
 ,■>.017 
 
 08.54 “ 
 
 5 
 
 4.813 
 
 88 . 00 
 
 
 i) 
 
 6.00.) 
 
 2.5.44 
 
 0 
 
 5 .701 
 
 33 . .5 4 
 
 
 7 
 
 7 . 023 
 
 11.60 
 
 7 
 
 0 025 
 
 1.5.84 
 
 
 8 
 
 8.071 
 
 5.531. X 10 -'2 
 
 8 
 
 7 . 025 
 
 7482. 
 
 X 10 
 
 s 
 
 7.981 
 
 .5870. 
 
 0 
 
 8 . 025 
 
 3890 . 
 
 
 9 
 
 8.941 
 
 3210. 
 
 10 
 
 9 750 
 
 2030 . 
 
 
 10 
 
 10 192 
 
 1012 
 
 11 
 
 10.7.50 
 
 1217. 
 
 
 10 
 
 10.130 
 
 1559. 
 
 12 
 
 1 1 . 7.50 
 
 704 . 1 
 
 
 10 
 
 10.020 
 
 1703. 
 
 13 
 
 13.000 
 
 450.5 
 
 
 11 
 
 1 1 . OOO 
 
 1080. 
 
 14 
 
 14.000 
 
 300 2 
 
 
 12 
 
 12.090 
 
 0.58.2 
 
 15 
 
 15.000 
 
 213.9 
 
 
 12 
 
 12.000 
 
 084.4 
 
 17 OD 
 
 10 000 
 
 153 0 
 
 
 13 
 
 13.2.50 
 
 407.9 
 
 18 '• 
 
 17.000 
 
 111.8 
 
 
 14 
 
 14.2.50 
 
 270 2 “ 
 
 20 ■■ 
 
 19.000 
 
 02 . 93 
 
 
 l.j 
 
 1.5,2.50 
 
 190.3 
 
 22 “ 
 
 21 ,000 
 
 37 . 57 
 
 
 17 OI) 
 
 16.214 
 
 M3.0 
 
 24 •• 
 
 23 . 000 
 
 23 54 
 
 
 18 •' 
 
 17.182 
 
 105.8 
 
 
 
 
 
 20 “ 
 
 19.182 
 
 .59.91 
 
 
 
 
 
Pa^e 35 
 App. IV 
 
 weight pipe, and column 6 to extra strong pipe. It might he supposed from the 
 nearness of agreement hetv/een the actual diarrieters of standard and extra strong 
 pipes that no distinction between the two need he made v/hen calculating pressure 
 loss. That this supposition is erroneous may he seen hy comparing columns 3 
 and 6 of the table. Since the pressure loss is directly proportional to factor 
 ”F**, the relative friction losses in the tv/o kinds of pipe for a given nominal 
 'size may he observed hy the ratio of the two values of factor Such a 
 
 comparison reveals the fact that if column 3 he used for problems involving 
 extra strong pipe, the error would he -10 percent for 12- inch pipe, -55 percent 
 for 1/2- inch pipe, and the average error for all sizes from l/2-inch to 12- inch 
 inclusive would he -28 percent. 
 
 32 - SUPERHEATED STEAl.?. 
 
 Since experimiental data on the flow of superheated steam are not available, 
 it is necessary to deduce some relation from the flov/ of saturated steam.. 
 
 There are tv;o conditions which differ for wet and superheated steam, viz., 
 surface condition and velocity. The difference in surface condition, is that 
 in the case of superheated steam the inner pipe surface is dry, v/hereas in the 
 case of wet steam the surface is supposedly flushed with a film^ of water. 
 
 Several theories are based upon this fact. One is that the v/ater on the wetted 
 surface fills up the irregularities in the pipe surface, resulting in a lower 
 coefficient of friction for wet steam than for dry or superheated steam.. 
 
 Another theory, exactly contradictory- to the foregoing, is that the moisture 
 presents a more or less viscous filament v\hich imposes a drag on the flov/ing 
 stream of vapor, and consequently the coefficient of friction should he greater 
 for wet steam. 
 
 The correctness of either of these theories has not been proved, and it is 
 possible that both of the effects, acting in conjunction, counterbalance one 
 another, resulting in the same coefficient of friction for superheated or dry 
 steam as for wet steam/. The difference, in any event, is undoubtedly small, 
 and since the effect of velocity is of considerable magnitude, the effect of 
 surface condition may well be disregarded. 
 
 The effect of the velocity of flow upon the pressure loss is not a simple 
 one. Friction for most fluids is supposed to vary as the square of the 
 velocity, but a studj^ of the Babcock formula shows that this relation is not 
 universal for steam. Velocity is affected by: (1) the weight of steam flowing, 
 (2) the cross-sectional area of the pipe, and (3) the specific volume of the 
 steam. 
 
 (1) Inspection of the Babcock formula indicates that pressure loss 
 varies as w^ , and since the velocity is proportional to w, it follows that tlie 
 pressure loss varies as the square of the velocity, which would be expected. 
 
 (2) By plotting factor ”P* against velocity on logarithmic cross- 
 section paper, it is found that the friction varies approximately as the 2.6 
 pov/er of the velocity, or som/evAiat greater than the square. The probable ex- 
 planation is that as pipe size is aecreased, the mean hydraulic radius decreases, 
 presenting a compairatively greater frictional surface. 
 
 (3) A set of calculations v/ith saturated steam, mahing steam pressure 
 the only variable, indicates that friction varies as the first pov/er of the 
 
4 
 
 i 
 
 i 
 
 I 
 
 1 
 
 1 
 
 1 
 
 I 
 
 i 
 
 1 
 
Page 36 
 APP« IV 
 
 velocity. The explanation of this unexpected fact probably lies in the fact 
 that as the pressure is decreased, although the specific volume and hence 
 velocity are greater, the density is correspondingly decreasea, and the number 
 of molecules of steam in contact with unit surface of pipe is proportionately 
 less. 
 
 In view of the relation found in the preceding paragraph, it is the 
 logical conclusion that, since the effect of surface condition may be disregard- 
 ed, the friction for various amounts of superheat will vary as the first power 
 of the velocity. 
 
 The solution for pressure loss with superheated steam may be made in 
 either of two v/ays, as will be explained. 
 
 (1) Since the velocity of flow varies as the specific volume of the 
 steam, either of the formulae, (l), (2), or (3) may be used directly by merely 
 substituting the proper value of s]Decific density or specific volume for '*!)” or 
 ”V" respectively from the superheated steam tables. This is the preferred 
 method when superheated steam tables are at hand. 
 
 (2) A careful examination of the properties of superheated steam indi- 
 cates that the increase in volume at anj^ given pressure is very nearly 16 per- 
 cent for every 100 degrees of superheat. This assumption is so nearly exact 
 that the v/orst error due to its use is less than two percent, which is beyond 
 criticism since there is four percent variance between the experimental co- 
 efficients of friction as deteimiined by Babcock and Carpenter. The second 
 method of handling superheated steam, then, is to use any reliable formula or 
 chart designed for saturated steam, and increase the pressure loss 16 percent 
 for every 100 degrees of superheat, 
 
 33 - EXAJlPhE OF SOLUTION BY THE FORIPLA. 
 
 Data: 
 
 Steam pressure - 225 lb. per sq. in, abs. 
 
 Superheat - 150 deg. F. 
 
 Steam Flow - 2000 lb, per min. 
 
 Pipe - 12- inch extra strong. 
 
 Determine: Pressure loss per 100 feet of pipe. 
 
 Solution: Use formula (2) 
 
 w r 2000 w^ s 4,000,000. 
 
 L = 100 feet. 
 
 V = 2,56 cu. ft. per lb. (from steam tables) 
 
 F 2 764.1 X 10"^^ (from Table Ko. 8). 
 
 p = 4,000,000 X 100 X 2.56 x 764.1 x lO'^^ _ 
 
 0,782 lb, per sq, in, 
 
 34 - ORAPHIG CHART FOR TEE BABCOCK FORJITLA. 
 
 Although the solution of the miOdified formulae is quite simple v/hen Table 
 Ko, 8 and a slide rule are available, the logarithmic chart. Fig. 6, permits a 
 quick and easy solution of flow problemis, and it is preferred in m:Ost cases. 
 
< 
 
 i 
 
 I 
 
Page 38 
 App. IV 
 
 The error involved in its use is not more than three percent if reasonable care 
 is exercised in the solution. 
 
 This form of chart was first published in 1912 by H. V. Carpenter. The 
 original chart, hov/ever, v/as limited in its direct application to saturated 
 steam and standard weight pipe, and the range of the quantity of flow scale 
 was not extensive enough for many modern problems. Pig. 6 was drawn by the 
 author to meet these criticisms and the chart as presented is practically 
 universal in its application. 
 
 35 - EXAMPLE OF GRAPHICAL SOIUTION. 
 
 The heavy dash lines on the chart indicate the solution of the same 
 problem as solved under "Examiple of Solution by the Formula". The solution 
 is self-explanatory and needs no further comirient. 
 
T 
 
 >*