jcieo MINISTRY OF MUNITIONS AND DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH Technical Records of Explosives Supply 1915-1918 No. 9 HEAT TRANSMISSION Published for the Department of Scientific and Industrial Research by His Majesty's Stationery Office 1922 The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004360446 Cornell University Library 260.G78 echnical records of explosives supply 3 1924 004 360 446 BASEMENT STORAGE TECHNICAL RECORDS OF EXPLOSIVES SUPPLY Volume No. 9— Heat Transmission. Errata. Page i, bottom line, equation to read log - = — — nearly. a a „ 9, line 14, for t x read t,. „ 12, line 16, equation to read t' — t — {tf — Qe~ (n ~ 1)Kx \ t' — t „ 12, line 2r, equation to read t — t —— ? (1 — e- {n ~ 1)kx ). n — 1 „ 12, line 22, equation to read t ' — t = n (t f — t ) (1 — e ~ ( " " 1)Kx ). n — 1 „ 20, table headed Air Cooling, for Therma capacity C.H.U. read Thermal capacity C.H.U. ,, 26, line 5, for gives read give. ,, 32, line 35, for affect read effect. /T „ 36, bottom line, equation to read v = 298 /\/ — . „ 43, line 1, for "0415 =0' 40% read '0415 x 0-408. „ 43, line 4, read 0-014756 lb. „ 43, line 6, for '014756 = 1035 read '014756 x 1035. „ 44, line 10, following Table ya, read — 5 — _^. 3-91 X 60 X 60 ,, 46, line 10, read "01341 x 1035 = I 3"88 B.Th.U. Fig. 9, facing page 29, read Coefficients. (B34-53)T Wt. 25385— 1353 500 1/23 H&SLtd. Gp. 34 *J A 1\UL. 1 MINISTRY OF MUNITIONS AND DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH Technical Records of Explosives Supply 1915-1918 No. 9 HEAT TRANSMISSION LONDON : Published for the Department of Scientific and Industrial Research by His Majesty's Stationery Office, and to be obtained from the addresses given on the back of the cover. 1922 NEW YORK D. VAN NOSTRAND COMPANY EIGHT WARREN STREET The following reports dealing with other aspects of the work of the Department of Explosives Supply have already been published by His Majesty's Stationery Office : — Second Report on Costs and Efficiencies for H.M. Factories CONTROLLED BY FACTORIES BRANCH, DEPARTMENT OF EXPLOSIVES Supply. Price js. 6d. (by post 8s.). This report also contains most of the general information originally included in the First Report on Costs and Efficiencies, issued by the Ministry of Munitions, . and now out of print. Report on the Statistical Work of the Factories Branch. Price 4s. 6d. (by post 5s.). Preliminary Studies for H.M. Factory, Gretna, and Study for an Installation of Phosgene Manufacture. Price 15s. (by post 16s.). Copies of the above and of the present series of reports may be obtained through any bookseller or direct from H.M. Stationery Office at the addresses given on the back of the cover. PREFATORY NOTE This is the ninth and last of a special series of reports which have been published in order to make available, for the benefit of the indus- tries concerned, results of scientific and industrial value contained in the technical records of the Department of Explosives Supply of the Ministry of Munitions (see list below). The work recorded in these Reports was done at, or in connexion with, some of the National Factories during the war. The preparation of the necessary abstracts of information was begun by the Ministry of Munitions at the close of the war, and arrangements were afterwards made by the Department of Scientific and Industrial Research to complete them. The Depart- ment wish it to be clearly understood that the interesting information contained in this series of reports is the result of the labours of the Ministry of Munitions, and has been { Compiled by Mr. W. Macn ab, C.B.E., F.I.C., an officer of that Ministry attached to the Department for this work. Professor A. W. Porter, D.Sc, F.R.S., has been good enough to supervise the preparation of the present report and to draw up those portions of it relating to the theoretical aspect of the subject. Department of Scientific and Industrial Research, 16 and 18 Old Queen Street, London, S.W.i. July, 1922. Previous volumes in this series : — No. 1. Recovery of Sulphuric and Nitric Acid from Acids used in the Manufacture of Explosives : Denitration and Absorption. Price 12s. 6d. (by post 13s.). No. 2. Manufacture of Trinitrotoluene (TNT) and its Intermediate Products. Price 17s. 6d. (by post 18s.). No. 3. Sulphuric Acid Concentration. Price 12s. (by post 12s. yd.). No. 4. The Theory and Practice of Acid Mixing. Price 12s. (by post 12s. 6d.). No. 5. Manufacture of Sulphuric Acid by Contact Process. Price 25s. (by post 26s.). No. 6. Synthetic Phenol and Picric Acid. Price 15s. (by post 15s. yd.). No. 7. Manufacture of Nitric Acid from Nitre and Sulphuric Acid. Price 10s. (by post us.). No 8. Solvent Recovery. Price 3s. (by post 3s. 3^.).- (37)16288 Wt 19252 500 8/22 CONTENTS PAGE Theoretical Section - - i Fundamental principles - i Criterion for turbulence - ... 4 Determination of coefficients of transmission - - - 5 Application of method of dimensions - ... 6 Application of coefficient of transmission to specific problems - 9 Construction of alignment charts ... 14 Experimental Section - - - - - - -16 Method of investigation - - 17 First series - ... 18 Examination of experimental results - - - - 20 Second series - - 21 Acid coolers at Queen's Ferry „ - - 27 Water economy and efficient cooling - - 27 Lead coolers in denitration plant - - - ' - 28 Superheater at denitration plant - - 30 The effect of stirring - - - 32 Surface condensers - - - - 34 Heat interchange in a cylinder in which a heat-producing reaction takes place 35 Surface loss ...... -35 Application of the principle of Quinan's Bubbler-Scrubber to the cooling of condensing water 36 Amount of air passed through J-in. diameter hole for various pressure differentials ...... 36 Velocities for various pressure differentials .... 37 Volume of air which will pass through plate - - - "37 Temperature gradient of water passing over 1 ft. length of plate for various velocities - - 39 Air efficiency ...... 44 Air required to cool 1,000 lb. water per hour - - - 45 Power required - - - - - - - "45 Summary - - - - - - - - "45 Example ..... ..45 Alignment Charts Over-all coefficient of transmission - 3 Coefficient of transmission for pipes carrying water - - facing 8 „ „ », „ ,. „ gases - - facing 8 To find economic length of pipe- - ... facing 11 THEORETICAL SECTION. Fundamental principles. — One of the most important physical problems in factory practice is concerned with the laws governing the flow of heat through the walls of pipes. For example, when heat is produced in a chemical reaction, the mixture so heated can be cooled by letting it flow slowly through a tank in which coils of pipe are placed, these pipes carrying cold water; or, on the other hand, it may be necessary to raise the temperature of a reacting mixture to a point at which the desired reaction proceeds most advantageously. This can be effected by means of steam passed through pipes contained in the mixture. The same kind of problem enters in the case of steam condensers in ordinary engineering practice. A great many varieties of cases present themselves for consideration. The property of a material which specifies its power of conducting heat is the thermal conductivity K. It is defined as the heat transferred in unit time across unit area when the gradient of temperature is unity; i.e., H = KAG x time. In dealing with the transmission through pipes it is advantageous to specify instead a quantity introduced by Kelvin and called the coefficient of transmission k. This is defined as follows : Let, the temperatures just inside and just outside the wall of the pipe be t t and t 2 respectively. Let the temperature at any intermediate distance r from the axis be t. When the temperature is steady the same amount of heat must flow through each cylindrical surface, i.e. : — K 2-rrr.l — = —. = constant ; d r time where I is the length of the pipe, whence H t K 2ttI X time log r + constant. Putting r successively equal to a and b and t equal to t x and t 2 , and subtracting H 1 2 " K2ttI x time ■1 b When the pipe wall is thin log = nearly a a I 16288 HEAT TRANSMISSION so that k k-- H (b-a) K 2-na. I x time where 2na.l. is the area of the surface of the pipe. Hence H = _ A (t t — 1 2 ) x time. The flow of heat is therefore proportional to the difference of temperature, inside and out, to the time, area, and to the quantity Kj(b — a). This last quantity is the coefficient of transmission. It is the amount that flows through each area in unit time when unit difference of temperature exists between inside and outside. It is measured in Centigrade-heat-units (C.H.U.) per hour per square foot per degree centigrade difference of temperature. If the temperature of the pipe wall, at inside and outside surface, were known it would be a very easy matter to calculate the flow. All that is usually known, in practice, is the average temperature of the liquid flowing. There is, necessarily, a gradient of temperature across the liquid when heat is being transmitted, and this is often very great near the metal surface. Practically the whole of the difficulty of the problem is concerned with this fact; because it becomes necessary to calculate the distribution of temperature across the liquid or gas on each side of the pipe wall. This distribution varies very much from one case to another. If the fluid is moving very fast, all except a very thin film is stirred up by the eddies that arise and is practically at one temperature. In the film the heat is transferred, not by motion of the fluid, but by thermal conduction alone ; and since most liquids are very bad conductors, even a thin film introduces great resistance to the heat transfer. The thickness of the non-eddying film depends upon the velocity of flow; it diminishes as the velocity increases, and there is a corresponding increase in transmission. We can define the coefficient of transmission for the fluid on each side of the pipe wall in the same way as for the pipe itself. Calling the coefficients k, k and k', and the temperatures t, t lt t 2 , t' , as shown in the figure ; then, if H is heat flowing per unit ^.#time, and A is the area through which it Fluid. Wall. Fluid. I. II. 1 h h f k R k' >* H_ Ak whence flows. = t — t 1 Ak' ~ h H Ak -t' t-i ta A\k + k + VJ ~ t ~ t ' and X r + + i coefficient of transmission. If this is known, and t - heat transfer can be calculated. The calculation is the reciprocal of the effective or over-all ■ t' is known, the of the effective THEORETICAL SECTION coefficient from the separate values k, k , k' can be easily made by means of an alignment chart. (Fig. i.) Usually (i.e., for metal pipes) k is very large compared with k and k', and, consequently, ■=- has a negligible effect, and can therefore be left out of account altogether. Fig. i Alignment Chart for Resultant Coefficient of Transmission To find res. coeff. of trans. Join Scales. Intersecting. AandB C C and D E 1 = 1 +1 + K t 600- J00- 800- 900- IO0(H 1200- M00- 1600 1800- 2000- 3000-^ AO00-= When calculations are required for much smaller coefficients the scale values on A and B can be divided by any factor such as ioo. The scale value of C must then be_ divided by the same factor. Scale D cannot be used with these altered scales. G £ 300-- 350- - 400- J- 4SQ-} 500- =• 600- - 900 -f- 100 1500 700 -- -J0P- 8oo«f ~" -8oo -900 -300 -350 J-400 1500 -600 Scale A represents k x B Scale B represents k 2 Scale C represents k= , , , ', AT. or if thickness of pipe is 2 -600 -1000 :: 1 1500 -700 -800 : 900 -1000 : J£00' -1400 -1600 -1800 -2000 "-ieoo Laooo pipe allowed for Scale E represents k where r is as given above. b — a Thickness Brass Tube -•06 m«l» .-•05 .<&' 10 A2 4 HEAT TRANSMISSION Criterion for Turbulence .—When the velocity of the fluid is small enough, it moves without turbulence. In such a case k has a very small value. It was shown by Osborne Reynolds, by experiment on cylin- drical tubes, that in such tubes turbulence does not begin until the velocity reaches a particular critical value depending upon the viscosity and density of the fluid and the diameter of the pipe. The equation determining this critical velocity is — feet\ v viscosity in Brit, units (ft. lb. sec) t(m sec. 400 X specific gravity X diameter of pipe in inches. The viscosity varies very fast with temperature; the following tables are useful; they give the viscosity in British units. Water Nitric Acid Temp. Viscosity. .C 40 80 100 •001250 •000441 241 192 HN0 8 Viscosity at Per cent. io° C. 20° C. 53-9 0-00198 0-00I56 61-56 232 175 71-24 221 156 100 152 II 9 Sulphuric Acid Wt. per cent. H 2 S0 4 Grms. H 2 S0 4 per 1,000 c.c. of Solution. Viscosity. 3-3 33-o 0-00712 at 20 U C. n-4 114-2 813 t) 36-5 458-4 •00155 ,, 52 748-3 267 ,, 60 922-6 407 »> 75 1240-4 950 )t 100 1840 ■ •01454 >j 100 1840 • •0215 at II°-2C. The viscosity of all liquids diminishes with rise in temperature. For rough purposes, when the true variation is not known, it may be taken as following an exponential law, i.e., equal rises in temperature produce equal ratios of fall in viscosity. THEORETICAL SECTION Determination of coefficient of Transmission. — The case of non- turbulent motion in a cylindrical tube can be worked out exactly. The velocity follows the law, V = V a (' - 5) where a is the radius and r is the distance from the axis of the point whose velocity is V. The distribution of temperature across the pipe is given by the curve shown below — the ordinates being excess temperatures above that of the inside of pipe wall. I'U ,/ ? / 3 ■3-6 £ .A. t 'Z. 1-0 Fig. 2. The coefficient of transmission 4 C.H.U. /deg.C./ft. 2 /hour for a pipe of smaller pipes it is higher. •4- -6 -8 1-0 Distance from eixis in this case is only about i foot inside circumference; for When the velocity is great enough to ensure decided turbulence, much greater coefficients are obtained, especially for gases at high pressures and velocities. Unfortunately the case of turbulent motion cannot, in general, be solved completely and recourse must be made to such experimental results as exist, together with such additional aid as can be obtained from dimensional considerations. It is still more unfortunate that the details of experiments are often so incomplete that rio general law can be deduced with certainty. The controlling factor is the non-turbulent film of flowing fluid which is in contact with the wall of the pipe. The coefficient of transmission for the fluid on one side of the pipe is if/film-thickness. For. any given fluid, therefore, the thickness of film necessary to reduce the coefficient to any stated value can be calculated. For example, for water the following values have been calculated; in making the calculation the logarithmic formula has been used instead of the approximate one. HEAT TRANSMISSION Coefficient of Film thickness, in inches, for the stated value of /c. Transmission. K 5 10 20 50 100 500 1000 Radii of pipe in inches. o-6 i-93 •61 •26 ■092 045- 1-2 1-23 •52 •24 •090 •045 2-4 1-04 47 •23 •089] 3-6 1-01 46 •23 •087 >■ • 0089 •0044 4-8 ■96 46 •22 •086^ •043 6-o •92 45 •22 •086 7 -2 . •91 45 •22 •086 J J In order that the coefficient may be 1000, the thickness must be only -0044 inch; whereas a thickness of -045 inch reduces the coefficient to 100. It will be seen, therefore, how exceedingly important this film is, and how advantageous any circumstance will be that tends to reduce its thickness. This is also an appropriate place to point out how influential will be a thin film of any poorly conducting deposit in the pipe in regard to heat transmission. Such a deposit may easily have a thermal conduc- tivity only of the same order as that of water, and it will form an absolutely stagnant layer. This must be well borne in mind. The data that are deduced later all refer to clean pipes of the sizes given ; no general rule can be given of the amount of deposit to expect. Unless the pipes can be frequently cleaned out, or unless the process is unfavourable to the formation of a deposit, the behaviour may often be very spasmodic, owing to temporary depositions. Application of method of dimensions. — In order to find the influence of the various factors concerned upon the coefficient of transmission, the only feasible way is by the method of dimensions. This method consists in utilising the fact that the fundamental physical quantities of mass, M, length, L, and time, T must enter in the same way in the case of any two quantities that can be equated one to the other. Now k = 2£/thickness. We may assume that k is proportional to K, and find how the film- thickness depends upon the physical data, viz., density, D, of fluid, viscosity,^, of fluid, diameter, d, of pipe, and the mean velocity of flow, v. The simplest assumption to make is that each of these enters as a power of itself, and we write — thickness is proportional to D^dV. THEORETICAL SECTION Now the dimensions of the several quantities are thickness L density = mass vol. M ' L 3 viscosity M LT diameter L velocity L T' Because the mass must enter to the same power on both sides of the equation o = x -\- y. Similarly for length — I = — 3* — y -\- z -{- n. Similarly for time o = — y — n. Hence y = — n x = n z = — i -f- 3« — n — n — n — i . ihus rr-^-5 vanes as thickness (fJ and the coefficient of transmission is this multiplied into the thermal conductivity of the fluid. This is as far as the method carries one. The value of n and the factor of proportionality require to be found by experiment. Stanton (Phil. Trans. A (1897), p. 67) experimented with a copper tube, 48 cms. long, the outer diameter of which was 1-47 cms., inner diameter 1-39 cms., containing water raised throughout to 47!° C. It was surrounded by a jacket, the jacket space being 0-165 cms., containing running water. When the velocity of the water was 69 cms. /sec (about 135 feet/min.) the rise of temperature was 6-47 C. This is equivalent to a coefficient of transmission of -061 cal./cm. 2 /deg.C./sec./, or 450 C.if. Lr./foot 2 /deg.C./hour. With increased velocity the coefficient increases less fast than the velocity, i.e., n < 1. Stanton's experiments on the flow of water give n = o • 73 for smooth glass pipes, and o-86 for smooth copper, increasing to ro as a limit for rough metal. An examination of Joule's condenser experiments lead to a value about 0-75. Experiments made by Greenwood, Acland and Nobbs 8 HEAT TRANSMISSION give 0-71 for the case of compressed gases. It is probable that it will not be far wrong to take n = 0-75, so that „ /vD\* 1 k vanes as K I — I -^ • In the case of liquids, K may be taken as independent of temperature, so that for any particular substance its value can be included in the factor of proportionality. This formula is represented by the accompanying alignment charts, by which the coefficient can be calculated for a wide range of conditions. Fig. 3 is where water is the flowing liquid, and Fig. 4 is for hydrogen, specially at high pressures. Factors are given on the charts to adapt them to other fluids. The values given apply to circular pipes. If the outer fluid is in an annular space surrounding the pipe, it would seem to be fair to treat it as equivalent to a pipe of diameter equal to the difference of the diameters of its outside and inside surfaces. The value of #c' can then be found from the appropriate chart on this assumption, and then the over-all coefficient is given, as we have said, by Reciprocal of over-all coefficient = r + -r,- The following tables are calculated as examples ,on the assumption that the equivalent diameters, inside and out, are about the same. They can be used to estimate, roughly, the values appertaining to not very widely different circumstances from those specified. Over-all coefficient of transmission k for water expressed in C.H.U./it. 2 /deg. C./hour. Pipe i-in . diameter. 20° C. Velocity inside. 100 200 300 400 500 Velocity outside. 100 160 185 224 240 251 200 185 220 277 302 318 300 224 277 375 421 454 400 240 302 421 480 523 500 251 318 454 523 570 Pipe 6-in . diameter. 20° C. Velocity outside. 100 97 123 137 146 152 200 123 168 195 214 228 300 i37 195 232 250 280 400 146 214 260 294 320 500 152 228 280 320 352 Velocities are in feet per min. To fa.ee 7>cM? e ® o O o 1- < LU =c u. o (X z LU o 1- < CO $■ en o s z CO >- Z a: < VL < O o; 1- en ij_ UJ O U. 0. 1- tr z o LU u. CO o I* • -ft t cu. && 3an±v«3dW3x aavaoiiNia o © 3inNIW W3d 133d Nl A1I0013A ?"§ c= ^ <*5 l| 1- 2>. ^ «^ "^ "J ^0 LiJ 3 HO .^P «XO 00 < ft §-§< CD 3 "5 s =» — "^I^S O ft fe^C/) ■^ 8-SZ >- ^ ft< cc *4. r "i CO UJ n. Q. "Sp cu C fO 1 — .ft t)<^_ i. i t Q — o Ll. e inter :t/on & f Jfiin G fficient FFIC .ft £ 9UJ ^ O «o.„ "*>■£ ft (B-J; "^ i 05 0, 1) CO ft ,C> ,ctj ^ .C.^ -s e> - fhj Mtyiioj ox THEORETICAL SECTION g All data are for perfectly clean pipes. For ordinary pipes 30-50 per cent., or even more, must be deducted to allow for incrustations. Hausbrand's tables give values considerably different from these ; but they are based on an imperfect interpretation of Joule's experiments on the surface condensation of steam, and make no allowance whatever for the influence of the size of pipe. Application of the coefficient of transmission to specific problems. — There are three specific types of interchange which we will specially consider. Type I. — A coil of pipe carrying circulating fluid is placed in a tank or vat, in which the fluid to be cooled (or warmed) is kept well agitated. We shall call this Tank interchange. A pipe of inner radius a, and outer radius b, of overall coefficient of transmission C, carries liquid of specific heat c, density D, velocity v, entry temperature t , temperature at distance x along its length, t x exit temperature after travelling a length / of pipe, t,. Temperature in tank, t' (supposed uniform throughout owing to efficient stirring). Consider a length Ax of the pipe. If C be written for the overall coefficient, then we have seen that TJ TiEe~ = C ^ a (t-i'), where H is the heat that flows through unit length of wall in the given time, the area of this unit length being 277a. The heat that is brought in by the flowing fluid in unit time is ira?.D.cvt, and that similarly carried out is ir J. It is clear from this equation that the amount of heat transferred is not proportional to the length of the pipe. If the length of pipe is found which would transfer just half of the maximum quantity corresponding to an infinite length (viz., -n-a 2 Dcv(t — t'), then twice that length would transfer - - | four times „ ,, | eight times „ „ f§ and so on. It follows at once that additional lengths of pipes are not so effective as the first one. In other words, let us suppose that, in a particular installation, 20 feet of piping are found not to be sufficient — merely changing the temperature of the hot fluid from ioo° to 8o°, instead of to 6o°, as desired. Then another 20 feet will not change the temperature through the remaining 20 , but only to 70 . A further 20 feet would change it to 65 ; and so on. The, explanation, of course, lies in the simple fact that the transfer per unit length is proportional to the temperature difference on the two sides of the pipe wall (t — t'), and this gets less as the length of pipe is increased. To cool the stuff in the tank to the temperature of the water in the pipe would require an infinite length of pipe. This is impossible, and even a great length is economically wrong. It is not possible to give any general rule as to the length that should be taken. If the piping is fairly cheap and indestructible in the process for which it is used, then it will pay to put in a long length once for all, and thus gain in efficiency of transfer of heat. But if the pipe is liable to quick corrosion, the cost of replacement might easily swamp the advantage otherwise gained from increased transfer. We may introduce the term economic factor to stand for the total fraction of transferable heat (proportional to t — t') which the V-l S o z o ul a a LU a. Q u. z o ll. X o J- h- o 7 k: uJ < _i OH o < a OLJ 3 So to - Solving these two equations gives f -t = (V - t )e- in - 1)K *- where n is written for qjq' and A for ; thus A is the heat transmitted by unit length of pipe divided by the thermal capacity per unit time flowing in pipe. By substitution the following useful alternative forms are obtained : I —t = f °' ~ l ° (i — e -<"- »>*) n — i V -t'= ^ (V - to) (i - s-'- 1 ^). The values t t and t\ at the cold end are obtained by putting x = I. It will be seen that (/„' — t')j(t ' — t) —n everywhere, and, therefore, as a particular case *°' ~ tl ' =». t t t This can be seen also from elementary considerations, for the ratio of the changes of temperature of the two fluids must be inversely proportional to the thermal capacities of the amounts flowing in the two spaces in equal times. The quantity of heat transferred per unit time by the entire Dipe (length, /) is — -^-(t '-t Q )(i-e-«-»») time n — i THEORETICAL SECTION 13 This equation is of the same general character as that obtained for Type I. The remarks that were made about the economic factor apply, therefore, to this case also. In the most important case for which n — 1 (i.e., q — q') Time T +AZ- (N.B. — A little care is necessary in obtaining this special result, as the equation for H takes an " indeterminate " form when n = 1.) It is to be noted that the exponential term has disappeared, but the general character of the variation is much the same; i.e., as I increases — changes from zero up to unity as before. This case is important, because in common practice the available waste liquor and liquor to be heated are, on the average, about equal in amount ; though, of course, a great variety of cases arises. Determination of \l for various Values of the Economic Factor (/). — The value of / being the fraction of the heat entering (with incoming liquid), which is actually transferred in the installation, we have n ■ (» - 1) w n ,-(»-!)«' which determines XI for various values of / and n. Solving for XI we get XI = log. l-fjn n — 1 1 — / " The following table gives values in various cases : — Values of XI for various values of n and/. / 0-9 o-8 0-7 o-6 n = 1 9 4 2-33 1-50 n = 1-5 2-77 1-69 i-i5 o-8i n = 2 1-71 1 -io 0-77 0-56 n = 3 0-97 0-65 0-47 0-36 The value of XI is therefore determined when the permissible value of the economic factor has been fixed from experience; usually from 0-7 to o-8 is a suitable value. The length of pipe is then calculated by dividing the number in the table by A, i.e., by coefficient of transmission X circumference of pipe thermal capacity of fluid flowing in pipe per unit time* These calculations are made by means of the alignment charts. 14 HEAT TRANSMISSION Type III. — Co-current {or parallel current) interchange. — In this case the flow of both currents is in the same direction; it can be depicted graphically, thus : — V Hot t' ; ► Cold // t Cold t * Hot /, t ' Hot t' r * Cold t( -x- Both the fluids enter at the left and travel along the system. The temperature t' must be greater than t. The problem is to express the total flow in terms of t ' and t . Proceeding on similar lines, and putting i. = p. q JL = __£_ (t'-t ) (x-e-^ + w). time p + i v ° °' K ' The difference of temperature between outside and inside diminishes along the pipe according to an exponential law. The final temperature of the inside fluid is given in terms of the initial values by *'-*<> = t 4r : v^ (i-e- ( * + 1)W ). p + I Co-current transfer is not nearly so important as counter-current. It will not be discussed further. The discussion, in any case, would be conducted on the same lines as in the previous case. Chart for Liquids (Fig. 3.) Construction of Alignment Charts. — Scale A is a uniform scale of (velocity)*. Scale B is a uniform scale of (viscosity of water) l . The viscosity of water depends upon the temperature. The scale is labelled, not with the numbers giving viscosities, but with the temperature C, to which the points on the scale correspond. This is done because the temperature will be the actual datum. The intersection of the support C by the line joining A to B therefore represents (vel./viscy.) J on a scale which is non-uniform. By projection from P it is translated into a uniform scale on the support D. Scale £ is a uniform scale of (diameter of pipe) 1 . The intersection of the diagonal F by the join from D to E gives, therefore, / vel. \« r Vvisc./ (diam) 1 which is proportional to the coefficient of transmission. The support F is so labelled. THEORETICAL SECTION 15 Both the thermal conductivity and density of water are taken as constant. This is a near-enough approximation in practice. The absolute values of the coefficient marked on support F have been chosen to suit experimental data. The values of the viscosity of water which have been made use of are given below. Viscosity of Water. Temperature C. C.G.S. units Ft. lb. sec. units. 0-01793 ' 0-0012 10 1311 • 00082 20 1006 67 30 800 53 40 657 5i 50 550 37 60 469 3i 70 406 27 80 356 24 90 316 21 100 284 18 Directions for using the chart are given upon it. It is to be used successively to determine the coefficient for each side of the pipe, the appropriate data being utilised (see p. 8). The over- all coefficient is then to be obtained by the relation already given E = Z -+ J - over-all coefficient k k' The value of k for the material of the pipe- wall is here omitted from the expression because, in practice, it makes a negligible contribution. Charts for Gases (Fig. 4.) Scale A is a uniform scale of (velocity) 1 . Scale B is a uniform scale of (diameter) 1 . Scale D is a uniform scale of ' viscosity at f C. Therm, cond. of gas at t° C. x .]' Ldensity at t° and 1 Atm. The numbers labelling this scale are the temperatures to which the points on the scale correspond. Scale £ is a uniform scale of (pressure of gas) 1 . The intersection of C by the line joining A and B gives (vel.^diam.)*. By projection from P its scale is translated into a uniform scale on support G. The intersection of F by the line joining D to E gives (press. X dens, at 1 Atm.^/Oviscosity) 1 . By projection from Q its scale is translated into a uniform inverse scale on H, l6 HEAT TRANSMISSION The temperature varies along the length of the pipe and the coefficient of transmission varies with it. The problem becomes intract- able if this variation is taken into account. It is necessary to take a mean value of the temperature as giving a mean value of the coefficient. The mean value may often be taken as the arithmetic mean of the extreme values; it is more nearly (t — t e )/log e (t /t[).' Since G and H are parallel scales, the diagonal scale I represents the ratio GjH or [- press, x dens, at i atm. X vel.h i L ' viscosity -I (diam.) 1 which is proportional to the coefficient of transmission. Directions for using the chart are given upon it. It is to be used successively to determine the coefficient for each side of the pipe, the appropriate data being used. The over-all coefficient is then to be obtained by the relation already given i i T+-r over-all coefficient k ' k The value of the coefficient for the material of the pipe-wall is here omitted from the expression because, in practice, it makes a negligible contribution to the value of the over-all coefficient. When the pipe has gas flowing on one side, and water on the other, the coefficients for the two sides must be obtained from the gas chart and water charts respectively. When the gas is a condensable gas, like steam (as in steam condensers), the question is very much complicated by the amount of condensation which occurs and the chart must not be used for such cases. EXPERIMENTAL SECTION The large number of coolers actually in use in various factories provided the means of ascertaining what the efficiency of different forms is in actual practice. A number of data is given in the accompanying tables (Figs. 6 and 7). Although these tables do not contain full particulars, yet they may be taken as showing the kind of efficiency that is obtainable in practice. Extensive investigations were made at Gretna on an acid cooler, in which water flowing over the pipes cools their contents by evaporation. This is quite a distinct problem from those heretofore described. The cooler was used in connection with a mixer, which was employed to break down oleum, or 98 per cent, sulphuric acid, to make feed acid for a Grillo plant. The mixer consisted of a pottery-lined iron cylinder, set about 10 feet above the ground, into which oleum, or 98 per cent, acid and water, are fed simultaneously in the proportions necessary to form the acid required. This acid was then fed into the cooler proper through a z\ in. pipe. H.M. Factory. FIG. 6. Heat exchangers and coolers Queen's Ferry. To fact page 16 Tem- Cooling pera- ture Tem- Capacity pera- Mean Cooling in Plant. Heat Exchanger. Material. Surface, Sq. ft. Range of Cooled Sub- stance. ture Range of Cooling Medium. Cooling Medium. Water Consumption, Tons per hour. .UCaJ.1 Tem- perature Gradient . Capacity in C.H.U. Sq.ft./hr. C.H.U.s Sq.ft./hr./ i°C. tem- perature difference. °C. °C. °C. Mixers 10 ft. x 5 ft. mixer. M.S. 3i6 42-5-4I 6 Air — 35-7 68-9 1-9 Coils Lead 70 per coil 42-30 11 Water 3-2 34-o II20-0 33-o >> M.S. 80 per coil 42-30 19 » 1-7 34-0 88o-o 25-9 Deni- Outer D.N.A. Lead 78-3 150-68 15-45 Water 3'33 94 3,064 3T3 trators. cooler. Inner D.N.A. ,, 78-3 6S-40 15-30 „ 3-33 39 2,090 74-0 cooler. D.N.A. >t 224-6 60-52 18-20 8-33 41 2-870 2-109 Launder, 2 half-full. Harts Glass 166 no-55 15-43 1-0 68 702 13 Condensers, 3 headers. Hart's Acid Narki 77-0 8o-35 15-27 ,, 1-25 43 540 12 Cooler. D.N.A. Lead 928 including surface of liquid. 50-40 15 (air) Air — 35 52 10 Pre-heating ,, 245 15-60 200-60 Steam 23-7 tons H,0 — 4,860 — coils. at 35° C. in 24 hours. N.C. Coils Silica 38-9 117-20 — Water — 9 1 3.473 38-2 Stills. Still C.I. 143-0 — — Air — Launder Lead 74 water and 82 air-cooled 185-112 28-52 Air and water. 8-o no 5,820 10% allowed for radia- tion. 53 Mann- Mixer C.I. 229 Water _ heim. i and 2 oxide coolers. M.S. 375 365-159 — " — — 513 — 3 oxide 71 187 159-65 — ,, — — 47 1 cooler. Pt. cooler ,, 187 230-80 — „ — — 722 Heat ,, 495 480-230 15-240 S0 2 &c. — 165 400 2-4 exchange. ■ Superheater " — — — — — — — — Retorts Retort C.I. I4-3 — Air , _ Hart's Glass 202 — — Water — 420-600 condenser. N.A. cooler Pb. 34-6 80-12 10-30 i% — — — — Gaillards Main tower cooler. C.I. Pb. coils. Coils, 107-7 C.I. water, 33-4 C.I. air, 15-5 Surface, 9-2 210-30 8-35 Water 7-0 100 2,850 28-5 Recuperator Pb. 157-8 130-45 8-25 ) j — 60 — . cooler. Gilchrist Cooler Pb. 153-5 250-27 8-35 Water 6-7 115 2,637 22*9 x 1628 To follow Tig. 6 facing p.16. -p o o en :*: cc <: LU III o~S 5. Is? 5 J •§■ Iggj §1 1 * Hi S -u.y £3 <0 S ID -3 y> ^ j+J U) UJ tr. z q- LU UJ — 2 _i a. < a u_ -■5-S *■*} toss § s BIO 5-t; V.cf) _. tD £ S5 Ovo (Deo K} CVl o o 5 ^*- O O r — . u ^ CVl <£> At- 5S = S£ t0 LU ^ °- ^ 0= iS f -r U> C- "- ■ Q ^ o- CO CO -a 1 «> 9 S CO cJ2 co-s; C\l Cvi^: 10 cm CM CM < S E UJ lu S 2J Lu S Lu >J 55 CM o R 00 o o o -i CO < QC 8 2 C 5 I ~0 1U <3 t 1 to 'o CO t, ° 00 (U ^^ O -P u U 0} -otf ra CO 1^ -u ( f> \ t ^ «z: > JO u \ a < O n •«• SO cn rS K (5 . O ■,**• ^ .:< ^ V H ,5 +J V <, r o Q. UJ ' c - -** """? <— / H > E o U *' X — < r/ £=• ■ ~—~ 1.1 5-5! CO 6 a. < tr to EXPERIMENTAL SECTION 27 If one is content with an 80 per cent, transmission, the length of the pipe need only be 143 feet. Acid Coolers at Queen's Ferry (Grillo Plant). — The following tests were made at Queen's Ferry on the acid coolers in the Grillo plant there. This cooler had nine straight pipes, each 8 feet long. All the straight lengths and four of the bends were under water. Internal diameter of pipes 5 inches, and external diameter 6 inches. External cooling area = 126 square feet. The specific heat of 20 per cent, oleum is ■ 33 ; the quantity dealt with, 22,400 lb. per hour. Holes were drilled in the pipes leading to and from the cooler, and pockets put in so that the temperatures could be determined. The temperature on entering from the towers was 65-68 C. ; that on leaving the cooler 48-49 C. ; so that the average cooling is about 18 C. The total heat transferred is, therefore, ' 22400 X 0-33 x 18 = 134388 C.H.U./hour, and the amount per square foot of surface 22400 X 0-33 X 18 H/;rU TT/win, ^ = 1056 C.H.U./ft. 2 /hour. The temperature of the water was not given in the report. Water Economy and Efficient Cooling Nitro-Cotton Spent Acid Stills. — The rate of delivery of both sprays and sprinklers was carefully measured under similar conditions. The graphs (Fig. 8) show cooling curves plotted from readings made simultaneously with a sprinkler, using what common practice required, i.e., 10 gallons per minute. The keys to the graph show the sprays used in each experiment. Graph I gives the results of one inverted 60-spray, and the cooling was not efficient. Water consumed = 2 gall, per min. on spray. Water consumed = 10 gall, per min. on sprinkler. Graph II was much more satisfactory, for here, taking 10 gall, per min. as standard, the two cooling curves approximate — Water consumed = 3-5 gall, per min. on sprays. Water consumed = 10 gall, per min. on sprinkler. Experiments were then repeated with double sprays, starting with 35. 4°> 5°. an d then 60-sprays, and the results were plotted. Two 35-sprays consume 2 gallons per min. Two 40-sprays consume 2 • 5 gallons per min. Two 50-sprays consume 3 ■ 2 gallons per min. Two 60-sprays consume 3 • 6 gallons per min. So that, using two 60-sprays, which appear to give satisfactory results, one saves per coil at least 6 gall, per min., which is equivalent to 362,880 gallons per day. 28 HEAT TRANSMISSION Lead Coolers in Denitration Plant. — In a report entitled : Notes on the DNA (denitrated acid) coolers (T.N.T. denitrators), particulars are given of the performance of D.N. A. coolers which had newly been installed at Queen's Ferry. The only advantage these coolers have over the old type, and the only way in which they differ, is in the water jacket, which now extends to the base of the cooler and is not only a shallow cup, as was previously the case. Measurements. — Each cooler is 2 ft. 6 in. in diameter and is 3 ft. 6 in. high. It is surrounded by a water jacket 2 ft. io in. in diameter, so that there is a jacket of water 2 in. thick encircling the cooler. The lead sheeting of the coolers is about y& in. material, weighing 12 lb./sq. ft. Coils. — Inside each cooler are two coils — 22 in. and 15 in. diameter respectively — the latter coil fitting comfortably inside the former. The larger coil has 10 turns of 22 in. each ; the smaller has 10 turns of 15 in. each. Both coils are of 2 in. lead pipe. There are three coolers for every two columns. Each column feeds directly into its own cooler — these two coolers feeding into a third common cooler — and from here to the acid main and storage. Cooling surface. — -The total cooling surface offered by unit cooler is the surface offered by the lead coils, added to that offered by the superficial surface of lead in the water jacket. ( z ) 39 ' 3 Iee t length of 2-in. lead = 20-6 square feet surface in small coil. (2) 57-6 feet length of 2-in. lead = 30-2 square feet surface in large coil. (3) - • — • - — 27-5 square feet in water jacket. Total surface offered per coil = 78-3 sq. ft. The D.N. A. issues from the columns at a temperature, approximately, 150° C. The maximum production of D.N. A. per column was about 58 tons daily. Over an experimental run of two columns the following data were obtained : Rate of production of D.N. A. = 58 tons/day /column. Temperature of D.N. A. in boot, 150 C. Temperature of D.N. A. leaving 1st cooler, 68° C. Loss of temperature in 1st cooler, 150-68 = 82 C. Temperature of D.N. A. leaving middle cooler = 40 C. Loss of temperature in middle cooler = 28 C. Temperature of water from 1st cooler = 45° C. Amount of water used in cooler per day = go tons. Temperature of water from middle cooler = 30 C. Amount of water used in middle cooler per day = 80 tons. To faee COEFICENTS OF HEAT TRANSMISSION IN SURFACE CONDENSERS : : ( STEAM. TO WATER ) RELATION OF Us Vu, (AVERAGE EXPERIMENTAL-VALUES) UJ a. < CC a 1000 UJ 1- F DIFFERENCE 00 CO o o o o o a. UJ CL 70O CC 3 O I CC uj 600 a i- o o "" 500 uJ CC < 3 o- en 400 CC UJ a. «<$// ^fr . f // Ss t / / j/y 3 h* 300 CD n 9nn 3 10 12 3 4-5 Mm -VELOCITY OF WATER IN FEET PER SECOND /. 2. 3. 4. S. Ser 6. Stanton Josse 7. Joule Weigh ton 8. Allen Hepburn 9. Clement & Garland Hageman. 10. Orrok FIG. 9 53 • w £c/> oa o w _J 0- UI 10-3 9-1 8 7-E 6-^ 10-^= 5 £ o = - 8 = : 9-fll2 o_|Lu 7#" r5- 6 : =- = 9 -: E 5- = 7 .: CO UJ Q- Q- z Z =3 o ac QC i- "~— UJ UJ h- u. < o O U CC X o UJ a r> $ O q o z o a o 0£ Q. Q < ui I •7— _ 6 — CD < _l i X Q. o ui Z O UJ •5- •4— •3 — < CO O Q CJ d u. UJ o <£ CD o a To face p. 34- foTZowi^ Kg.21. EXPERIMENTAL SECTION 35 feet per second. This is a very important contributing factor, but it is not the only one. A large number of other factors enter : temperature of water, diameter of tubes, velocity of steam, &c. The large difference, shown in the chart, between the results for different observers, must be attributed to these causes. Heat interchange in a cylinder in which a heat-producing reaction takes place. (Fig. 10.) , Tempi V* Fig. io. The kind of case referred to is that in which gas is continuously delivered into a reaction bomb, and passes along an inner cylinder which contains a catalytic agent, which causes chemical action to occur. In this reaction a certain amount of heat, h, is set free per unit length of the reaction cylinder. Similar considerations to those entertained before show that the temperatures, in the steady state, are given by the formulae 2na.Ch 2 j _ t i 2ira.Ch 2 ^2~ t' = T — „ 2-na.Ch , (x\ 2q" 2q* \q) where q is the thermal capacity of the flowing gas per unit time [ assumed to be the same before and after reaction), and C is the coefficient of transmission. It follows that the difference between the outlet and inlet temperatures is hl/q, where / is the length of the cylinder. This last result is somewhat unexpected, because it shows that the difference between outlet and inlet temperatures is independent of the conductivity and dimensions of the wall of the cylinder when the steady state is reached. The explanation is that any heat that is conducted through the cylinder is brought back again by convection. The problem is different from that of ordinary interchange, because in the present case the identical material flows through both outer and inner cylinders in succession. Surface loss. — No allowance is made in the above theoretical reports for the loss of heat from the outside surface of an interchanger. This allowance is best made separately, especially as in most cases it can only be made in a very approximate way, because of the great influence played by draughts over the surface. The loss is partly due to D 2 36 HEAT TRANSMISSION radiation, the relative importance of which is greater at high tempera- tures; and partly due to conduction and convection through the air. The accompanying chart represents experiments conducted at the National Physical Laboratory, Teddington. It gives the heat loss arising from all causes per square foot of large surfaces under ordinary conditions, at various excess temperatures above the surroundings. Alignment Chart for flow of Water in Pipes. In Fig. 12 an alignment chart is given for calculating the flow of water in cylindrical pipes in gallons per minute and also the head required (in fractions of a foot per hundred foot run) when the data are the diameter of the pipes in inches, and the linear velocity in feet per second. The appropriate diameter (scale E) and velocity (scale G) being joined, the intersection of the join with scale F gives the gallons per minute and with scales A, B, C, D the head according to four different authorities. Example : When the diameter is 10 inches and the velocity is 6 feet per second, the number of gallons per minute is 1,180, and the heat, according to Goodman, i-6 feet per ioo feet. According to Unwin this value should be 1-36 feet per 100 feet. Application of the principle of Quinan's bubbler-scrubber to the cooling of condenser water. — In this system the gas or air is forced upwards through a layer of liquid supported on a perforated diaphragm, the velocity of the air or gas being sufficiently great to prevent the liquid from passing downwards through the small perforations. Intimate contact is thus effected between the liquid and the gas. The liquid is circulated by means of a pump. In the cases under consideration the holes are \ in. in diameter, spaced | in. centre to centre. Analysis of cooler required to reduce the temperature of 1,000 lb. of water per hour from 98 F. to 8o° F. Air temperature 6o° F. and 70 per cent, saturation, on the assumption that holes in plates are \ in. diameter. Amount of air passed through \ in. diameter hole for various pressure differentials The velocity of efflux from short cylindrical tubes may be calculated from the following formula. {See Kent's Pocket Book, page 485.) Ih V = 363 c. ^Jpin which V = velocity in feet per second. c = a co-efficient = 0-83 for short tubes. h = difference in pressure at each end of tube in inches of water. p = barometric pressure in inches of mercury. Assuming p = 30 ins., then formula becomes f~h V = 203 \ — ' yo V30 QUINAN S BUBBLER-SCRUBBER Velocities for various pressure differentials Table No. i. 37 h = inches water. h 30 fl V 30 29 V- + y •\ 30 Feet per second. i 00833 0913 27-2 i 01666 129 38 4 i 02500 158 47 1 i 0333 181 54 ii 0417 204 61 7 ii 0500 223 66 5 if 0583 242 72 2 0666 258 76 9 2} 0833 288 85 8 3 1000 316 94-3 sq. ft. Area of \ in. diameter hole = 0-01227 square inches == 0-0000882 Cubic feet of air passed through 1 hole per second. Table No. 2. h i in. Jin. | in. 1 in. ij in. i£in. if in. 2 in. 2|in. 3 in. Cubic feet •0024 •00338 •00415 • 00476 •00543 •00586 • 00634 • 00678 •00756 •00831 Volume of air which will pass through plate. 38 HEAT TRANSMISSION Assuming holes to be spaced f in. centre to centre in each direction. Area of triangle A B C = « ^ AD BC x — _ 3_ 2 A D = AB x AD .-. —— = A B X 3 4 = o-375 x o-43 — 0-1628. And area of triangle ABC = 0"375 X 0-1628 = 0-061 square inches From sketch we see that triangle ABC contains one-half of a I in. hole. /. area of plate per hole = -061 =0-122 square inches and number of holes per square foot of plate 144 0-122 = Il80. Volume of air passed through one square foot of plate for various pressure differentials. Table No. 3. h 1 in. i in. | in. 1 in. ii in. ii in. if in. 2 in. 2f in. 3 in. Cubic feet air per sec. 2-83 3-99 4-90 5-61 6-41 6-92 7-48 8-oo 8-92 9-80 Weight of water passed over one foot length of plate at a velocity of 1 foot per second for various depths of liquid on plate. Table No. 4. h i 1 I 1 li i| if 2 2 * . 3 Pounds water passing per sec. 1-30 2- 6l 3-9 1 5-21 6-51 7-82 9-ii 10-42 13-03 I5-63 UJ > a. O ' 5-S O nl o t— < a a. < < >- - oc m o UJ U_ in o ^ CD t— UJ m ■3\ 3: 1— a: LU 1- / % < y ^\ Q u_ ^7 . •■A X "/ c\ 2 Sc */ <\ en UJ UJ i 7 Q z UJ 0/ d\ U_ H- _j VI t.\ 1 MOUNT Q Z < z 7 - UJ 1 z h- ^y 1 I j T - ■■^ SO Co "~" ^ 1 j co z n ■> j I 0/ UJ > 1— z Q^ • ! J to/ o 1]/ 7 o a. .">/ / > rr V ?/ r if 3 J X J U . o/ V 7 CU 4-> CO (0 a ^ 4- o 6 _c u. ■p m -o 5 u. !i_r lO D o o o CO o a> o in oo o oo IT) o j saad?3a — J^I-B/iA j,o diuai > QUINAN S BUBBLER-SCRUBBER 41 From Fig. 14 (Curve No. 2) we have width of plate required to cool from 98 F. to 8o° F. for the three velocities taken, to be — ( a ) 5 '55 feet for V = 1 foot per second. (b) 8 • 45 feet for V = 1 • 5 feet per second. (c) 11 -io feet for V =2-0 feet per second. Therefore the area of plate required per 1,000 lbs. of water cooled per hour in the three cases becomes — / \ r, n 5'5 X 1,000 (a) 5-55 sq. ft. per 3-91 lb. per sec. =, ygi x 6o x 60 = 0-394 square foot. (6) 8-45 sq. ft. per 5-86 lb. per sec. = J^£^^~ (c) 11 • 10 sq. ft. per 7 • 92 lb. per sec. = o • 400 square foot. 11 -io x 1,000 7-92 X 60 x 60 - 0-394 square foot. From these results it is apparent that, as far as area is concerned, the velocity of flow is of no consequence, the only effect of change of velocity being that a different width of plate is required, that is, the faster the flow, the wider the plate required to cool to equal temperature. Air efficiency. From Table 5 we have B.Th.U. abstracted in passing over first foot of plate = 18 -ii, which is equivalent to 100 per cent, efficiency over that part of the plate. If, therefore, the air through each successive square foot of plate subtracted the same amount, we should have : — Heat abstracted over 10 feet width of plate = 18 -ii x 10 = 181 • 1 B.Th.U. From the same table, however, we have the total heat abstracted = ioo-io B.Th.U. .-.volumetric efficiency of air used = o — 55*3 per cent. Air required to cool 1,000 lb. water per hour. We have already found that to cool the above amount of water we require 0-394 square feet of plate, whilst from Table No. 3 we see that each square foot of plate (under f inch head of water) will pass 4 • 9 cubic feet per second. .•. air required per 1,000 lb. of water per hour = 4-9 cubic feet x 0-394 x 60 = 116 cubic feet per minute. Power required. If we have § inch water over the plates we shall probably require about ij inch water pressure at the fan to overcome pipe friction, &c. HEAT TRANSMISSION 27-6 inches water press = 1 pound per square inch. 1 X I2 '5 TU ~^6~ = 0-0454 lb- 6 • 53 lb. per square foot 1 • -,' 1 X 12-5 „ ... ij inches water press = — 2 7-6 = °'°454 b- P er S( l uare lnc "- and theoretical power of fan 6-53 x 116 _ T = — — = 0-02204 H.P. 33,000 ^ Assuming efficiency of fan to be 65 per cent., then actual power required 0-02294 x 100 TT _, = ^ = 0-0353 H.P. Summary. To cool i.ooo lb. water per hour from 98° F. to 8o° F. with air at 6o° F. and 70 per cent, saturation, we require 0-394 square feet of f-in. plate perforated with | in. diameter holes spaced § in. centre to centre, 116 cubic feet of air per minute at a pressure of ij in. of water, and 0-0353 horse power at the fan shaft. Example. 1,000-k.w. generator set. Steam consumption, 15 lb. per k.w. hour. Circulating water entering cooler, 98 F. Circulating water entering condenser, 8o° F. Ratio of cooling water to steam condenser. 60 : 1 ; air temperature, 6o° F., and saturation, 70 per cent. Water to cooler = 1,000 k.w. x 15 lb. per k.w. x 60 = 900,000 lb. per hour. Area of bubbler plates required = 0-394 x 900 = 354*6 sq. ft. Plates may be 5-5 ft. wide x 64 feet long, 8 • 45 ft. wide x 42 feet long, or n-oft. wide X 32 feet long. Volume of air required = 116 x 900 = 104,400 cubic feet per minute. Power required = 0-0353 X 9°° — 3 I- 77 H.P. = 3-177 per cent, of power of generator set. Velocity, 1 foot per second. From Table 2 we have water passing = 3-91 lb. per sec. From Table No. 3 we have air passing through 1 square foot of plate = 4-9 cubic feet per second. = 0-408 lb. per second. 1st foot of plate : — Temperature of water =^ 98 F. Temperature of air = 6o° F. Saturation of water =50 per cent. 1 lb. of air at 6o° F. and 100 per cent, saturation holds -on lb. water • 408 lb. of air at 6o° F. and 100 per cent, saturation holds — ^ , r 100 = • 002244 lb. water. 'do «J31BM JO doi91 QUINAN S BUBBLER-SCRUBBER 43 ■ 408 lb. air at 98 F. and 100 per cent, saturation holds • 0415 — o ■ 408 = ■ 017 lb. water. .'. water taken up by -408 lb. air — 0-017 — 0-002244 = 0-14756 lb. = 1,035 B.Th.U. per lb. = -014756 = 1035 = 15-27 B.Th.U. = 38° F. = 0-408 x 38 XO-24 = 3-73 B.Th.U. = 15-27 +3-73 = 19 B.Th.U. -r- 1, - , 19-00 B.Th.U. c . ro „ Fall in temperature of water = ,, = 4-80 b. Temperature of water after passing over 1 foot of plate = 98 — 4-86 = 93-14° F. Table 5a. Velocity of water, 1 foot per second. Depth of water, f in. Latent heat of water at 98° F. Heat taken from water by evaporation Rise in temperature of air passing through water Sensible heat taken up by air Total heat abstracted from water At end of Heat abstracted Water evaporated, Temperature. (Total), B.Th.U. lb . Total. F. 1st foot 19-00 014756 93-14 2nd „ 34-46 026412 89 19 3rd „ 47-63 036328 85 82 4th „ 59-10 044904 82 89 5th „ 69-35 052560 80 27 6th „ 78-89 059316 77 83 7th „ 87-03 065422 75 75 8th „ 94-57 071 158 73 82 9th „ 101-28 076274 72 11 10th „ 107-33 080900 70-60 Table 6a. Velocity of water 1 • 5 feet per second. Depth of water, f in. At end of Heat abstraced Water evaporated, Temperature. (Total),*B.Th.U. It ). Total. F. 1st foot 19-00 014756 94-76 2nd „ 35 33 027232 91-97 3rd „ 5o 16 038488 89-44 4th „ 63 44 078524 87-18 5th „ 75 48 057530 85-13 6th „ 86 72 065930 83-19 7th „ 95 86 072506 81-63 8th „ 105 48 079662 79-99 9th „ 114 50 086418 78-45 10th „ 122 • 98 092774 77 , 44 HEAT TRANSMISSION Table ya. Velocity of water, 2 feet per second. Depth of water, § in. Heat abstracted Water evaporated, Temperature. (Total), B.Th.U. lb . Total. F. 1st foot 19-00 014756 95-57 2nd „ 35 80 027602 93-42 3rd „ 5i 35 039458 91-45 4th „ 65 73 050314 89-62 5th „ 79 03 060350 87-92 6th „ 9 1 86 069976 86-28 7th „ 103 73 078882 84-76 8th „ 114 69 097058 83-36 9th „ 124 88 094514 82-06 10th „ 134-54 101770 80-82 From Fig. 15 (Curve No. 3) we have width of plate required to cool from 98 F. to 8o° F. for the three velocities taken and 50 per cent, saturation. {a) 5-1 feet for V = 1 foot per second. (b) 7-9 feet for V = 1 • 5 feet per second. (c) 10-75 feet for V = 2 feet per second. .-. the area of plate required for 1,060 lb. of water cooled per hour in the three cases becomes (a) 5-1 square feet per 3-91 lb. per second 5 • I X IOOO = 3-19 X60X60 = °'3 6 3 sq- ft. (b) 7-9 square feet per 5 • 86 lb. per second 7-9 X 1000 = 5-86 x6o x 60 =0 '374 sq-ft. (c) 10 • 75 square feet per 7 • 82 lb. per second 10-75 x 1000 -^-60 = 0-379 sq ft. ""7-82 X 60 Air efficiency. From Table 5a we have B.Th.U. abstracted in passing over first foot of plate = 19 which is equivalent to 100 per cent, efficiency over that part of the plate. If, therefore, the air through each successive square foot of plate abstracted the same amount, we should have Heat abstracted over 10 feet width of plate = 19 X 10 = 190 B.Th.U. From the same table, however, we have total heat abstracted = I0 7"33 B.Th.U. . . volumetric efficiency of air used = IQ7-33 190 = 56-4 per cent. quinan's bubbler-scrubber 45 Air required to cool 1,000 lb. water per hour. We have already found that to cool the above amount of water we require o • 374 sq. ft. of plate, whilst from Table 3 we see that each square foot of plate (under f in. head of water) will pass 4-9 cubic feet per second. .•. air required per 1,000 lb. water per hour = 4-9 cubic feet x ■ 374 x 60 = no cubic feet per minute. Power required. If we have f in. of water over the plates we shall probably require about i| in. water pressure at the fan to overcome pipe friction, &c. 27-6 inches water pressure = 1 lb. per sq. in. ■, ■ -, 1 XI -25 1 J inches water pressure = <■ = 0-0454 1°- P er S( h m - and theoretical power of fan 6-53 x no 6-53 lb. per sq. ft. = 0-0218 H.P. 33000 Assume efficiency of fan to be 65 per cent., then actual power required •0218 x 100 , TT _ = ^ = 0-0336 H.P. Summary. To cool 1,000 lb. of water per hour from 98 F. to 8o° F., with air at 6o° F. and 50 per cent, saturation, we require 0-374 sq. ft. of f in. plate perforated with J in. diameter holes spaced f in. centre to centre, no cubic feet of air per minute at a pressure of i£ in. of water and o ■ 0336 horse power at fan shaft. Example. 1,000 k.w. generator set. Steam consumption, 15 lb. per k.w. hr. Circulating water entering cooler at 98 ° F. Circulating water entering condenser at 8o° F. Ratio of cooling water to steam condensed 60 : 1, air temperature 6o° F. and 50 per cent, saturation. Water to cooler = 1,000 k.w. X 15 lb. x 60 = 900,000 lb. per hour. Area of bubble plates required = 0-374 X 900 = 336 sq. ft. Plates may be 5-1 feet wide X 66 feet long. 7 • 9 feet wide = 42-6 feet long. 10-75 feet wide x 31-3 feet Jong- Volume of air required = 110x900 = 99,000 cubic feet per min. Power required = 0-0336 x 900 = 30-2 h.p. = 3-02 per cent, of power of generator set. 4 6 HEAT TRANSMISSION Velocity, i foot per second. Depth of water, f in. ; saturation, 80 per cent. 1 lb. of air at 6o° F. and 100 per cent, saturation holds -on lb. water •408 lb.of air at 6o° F. and 80 per cent, saturation holds ' oiix8oX ' 4 ° 8 100 = * 00359 lb- water. •408 lb. of air at 98 F. and 100 per cent, saturation holds -0415 X -408 = • 017 lb. water. , " . water taken up by 0-48 lb. air = -017 — -00359 = -01341 lb. Latent heat of water at 98 F. = 1035 B.Th.U. Heat taken from water by evaporation =-01341 x 1035— 13-88 B.Th.U. Rise in temperature of air passing through water = 38 ° F. Sensible heat taken up by air = -408 X 38 x -24 = 3-73 B.Th.U. Total heat abstracted from water = 13-88 + 3-73 = 17-61 B.Th.U. 17-61 4-5^ Fall in temperature of water 3 -9i -°F. Temperature of water after passing over 1 foot of plate = 98° - 4 -5 u F. = 93-5° F. Table No. 56. Velocity, 1 ft. per second. Depth of water, | in. At end of Heat abstracted (Total), B.Th.U. Water evaporated, lb. Total. Temperature, ° F. 1st foot 17 61 •013410 93-5 2nd „ 3i 77 •02389 89-88 3rd „ 43 74 •03258 86-82 4th „ 54 27 •04023 84-12 5th „ 63 57 •04686 81 -74 6th „ 7i 80 •05269 79-64 7th „ 79 24 •05795 77-74 8th „ 85 96 •06271 76-00 9th „ 9i 9i •06689 74-48 10th „ 97 28 • 07066 73-10 QUINAN S BUBBLER-SCRUBBER Table No. 6b. Velocity, 1-5 feet per second. Depth of water, f in. 47 At end of Heat abstracted Water evaporated, Temperature, (Total), B.Th.U. lb. Total. F. 1st foot 17-61 013410 94-93 2nd „ 32-65 02462 92 36 3rd „ 46-23 03463 90 04 4th „ 58-44 04354 87 97 5th „ 69-60 05162 88 06. 6th „ 79-80 05895 84 32 7th „ 89-18 06566 82 72 8th „ 97-93 07191 81 23 9th „ 106 -ii 07774 79 84 10th „ 113-21 1 08266 78-63 Table No. 76. Velocity, 2 feet per second. Depth of water, f in. At end of Heat abstracted Water evaporated, Temperature, (Total), B.Th.U. It ). Total. F. 1st foot 17-61 013410 95-75 2nd „ 33-n 02496 93 79 3rd „ 47-44 03557 91 95 4th „ 60-87 04548 90 21 5* „ 73-13 05443 88 64 6th „ 84-65 06278 87 16 7th „ 95-52 07066 85 77 8th „ 105-54 07777 84 49 9th „ 115-14 08466 83 26 10th „ 124-02 09097 82 13 Width of plate required (from Curve No. 3) — (a) 5 • 85 feet for V =1 foot per second. (b) 8-9 feet for V = 1-5 feet per second. (c) 12 feet for V = 2 feet per second. Areas of plate required per 1,000 lb. of water cooled per hour (a) 5 • 85 sq. ft. per 3 • 91 lb. per second 5-85 X 1000 3-91 X 60 x 60 (b) 8-9 sq. ft. per 5 • 86 lb. per second 8-9 X 1000 5-86 x 60 x 60 0-41 sq. ft. = 0-41 sq. ft. 48 HEAT TRANSMISSION (c) 12 square feet per 7-82 lb. per second 14 X 1000 = 0-41 sq. ft. 7-82 X 60 x 60 Air efficiency. B.T.U. abstracted over 1st foot of plate = 17-61 equivalent to 100 per cent, efficiency. Heat abstracted over 10 feet of plate = 17-61 x 10 = 176-1 B.T.U. Total heat abstracted from Table 56 = 97-28. 07-28 Volumetric efficiency = 'c. T =55-1 per cent. Air required to cool 1,000 lb. water per hour. We require 0-41 square feet of plate. From Table 3 each square foot of plate will pass 4-9 cubic feet per second. .". air required per 1,000 lb. of water per hour = 4-9 X 0-41 x 60 = 120 cubic feet per minute. Power required. 6 - ^^ x 120 Theoretical power of fan = — = 0238 h.p. rr ■ 1 0-0238 X 100 and at 65 per. cent, efficiency actual power = -rz = 0-0367 h.p. Summary. To cool i.ooo lb. water per hour from 98 to 8o° F., air at 6o° and 80 per cent, saturation, we require o • 41 square feet of f in. perforated plate \ in. diameter holes and f in. pitch. 120 cubic feet of air per minute at a pressure of ij in. of water and -0367 h.p. at the fan shaft. Example. Taking the same example as before — Water to soaker = 900,000 lb. per hour. Area of bubbler plates = 0-41 x 900 = 369 sq. ft. Plates may be 5-85 feet wide X 63-2 feet long. 8 • 9 feet wide X 41 • 5 feet long. 12 feet wide x 30 • 75 feet long. Volume of air required = 120 x 900 = 108,00 cu. ft. per min. Power required = 0-0367 x 900 = 33 h.p. = 3-3 per cent, of power of generator set. Printed under the authority of His Majesty's Stationery Office By Eyrejand Spottiswoode, Ltd., Bast Harding Street, B.C. 4, Printers to the King's most Excellent Majesty, To be purchased through any Bookseller or directly from H.M. STATIONERY OFFICE at the following addresses: Imperial House, Kingsway, London, W.C. 2, and 28, Abingdon Street, London, S.W. i ; 37, Peter Street, Manchester ; 1, St. Andrew's Crescent, Cardiff; or 23, Forth Street, Edinburgh. Price 55. od. Net.