HEAT TRANSFER AND PRESSURE DROP IN
Rectangular Air Passages The wall thermocouples were calibrated in place, first at room temperature and then (except couples 1 and 6) with saturated steam in the jacket a t atmospheric pressure. The air thermocouples were in the design of certain comm&ial heat WILLIAM M. MARKS also calibrated at two temperatures, by exchangers, such as air preheaters for immersion in a water bath a t room temStandard Oil Go. of California, steam boilers. In a search for such perature and in a steam bath a t atmosLa Habra, Calif, data the authors found only the papers Dheric uressure. All thermocouples were connected to a of Cope ( 5 ) and of Bailey and Cope ( 2 ) . Leeds & Northrup type K otentiometer, Cope cooled air in rectangular ducts; with type R galvanometer. The voltage of t>hekeston model although he varied the air temperatures widely, he kept the 4 standard cell was checked at intervals. The cold junction flow rate nearly constant and did not measure duct-wall tem(common to all couples) was immersed in an ice-water mixture. The inlet and outlet air chambers, made of galvanized iron, peratures. The data of Bailey and Cope, who heated and were 12 inches in diameter and 18 inches long. Each chamber cooled water in ducts, are replotted below. contained a flat vertical baffle, 4 inches wide and placed about 6 Fairly extensive information on air flowing over a single inches from the inlet end. The inlet chamber was insulated with plate is available (9, IS, 16) but is useful here only for very two la ers and the outlet chamber with four layers of corrugated widely spaced plates or very short passages. The data reair-celypaper. Loss of heat from the ends of the steam jacket was reduced by the placing of a layer of l/s-inch sheet cork on the ported here are offered with the hope that they will meet, at face of each air chamber opposite the end of the jacket. Also, least partially, the existing need. each 1-inch air space between chamber and jacket end plate was subdivided by the insertion of two circular sheets of I/la-inch asbestos paper. The air spaces were enclosed by wrapping the Apparatus flanges with air-cell paper. Compressed air was throttled and then passed through one of Calibrated etched-stem thermometers were used to measure three horizontal, steam-jacketed, copper-walled ducts, all of the the temperatures of inlet steam, jacket, condensate, room, and same height and length but each having a different gap between air ahead of the metering orifice. The inlet-steam, condensate, the side walls. The dimensions are given in Table I; for conand air thermometers were placed in wells, and the jacket thervenience the ducts will be designated as the 1/~-, 1 / ~ , and */lemometer was inserted directly through a packed gland. inch ducts. All pressure-measuring instruments are shown in Figure 2. The air flowed successively through a sharp-edged metering When the over-all drop was less than 1 inch, it was measured by orifice, an inlet chamber, the test duct, and an outlet chamber. means of the Ellison inclined draft gage; when it exceeded 1 inch, In order t,o include entrance effects, as in commercial equipment, the pressure taps were connected to the 30-inch U-type mano calming section was used. The abruptness of entrance, hownometer. The four Bourdon gages were used only for control purever, was reduced by the use of an entrance cone (Figure l),made poses. of two curved strips of copper ribbon. Pressure taps on the inlet and outlet chambers were connected to a differential manometer. Temperatures along one wall of TABLE I. DIMENSIONS OF DUCTS the duct were measured by thermocouples 1 to 6 (Figure 1). '/s-In. l/eIn. #/ls-In. The inlet-air temperature was determined by means of three Symbol Duct Duct Duct soldered-joint, copper-constantan couples which were suspended Gap between side walls, in. b 0 . 1 2 5 0 . 2 5 0 0 .562 in the inlet chamber about 1inch from the mouth of the duct, each Height inside, in. 5.00 5.00 5.00 opposite the center of one-third of the cross section of the duct. Length, ft. % 4.00 4.00 4.00 Equivalent diameter This method was also used to determine the outlet-air tempera0.0203 0.0397 0,0842 [Qab/(a ,+ b ) I, ft. ture. Cross-sectional area, sq. ft. 0.00434 0.00868 0,0195 The duct walls were made of l/ls-inch, smooth-rolled cop er 3.33 3.33 3.33 Total heating surface,(2aN),sq. f t . Length/diameter ratio 101 47.5 197 plates and were separated at the edges by strips of Transite. 8e0.00130 Seotion/surfaoe ratio 0.00260 0 .00585 cause of their low conductivity, as compared to copper, the sepa0.1125 0.0250 0.0500 Breadth/height ratio rating strips were assumed to transmit no heat. Steam was admitted on both sides of the jacket, and was deflected to prevent direct impingement on the duct. The jacket was tilted slightly towards the condensate connection. Air was The ends of the duct passed through slotted brass plates; vented from the jacket a t two points; the bleeder valve and a pet these were fastened to the duct by means of soldered strips of cock tapped into the drain pipe. copper ribbon, shaped to form crude expansion joints. A slight The ends of eleven Leeds & Northrup constantan thermoleakage of condensate from the joints was caught in small troughs couple wires were imbedded in the plates; thus, the duct walls and led to the main weighing tank. were used as the copper element of the thermocouples. The The air-metering orifice was mounted between flanges in a run of wires were No. 28 B & S gage, enameled and doubly covered with 3-inch standard pipe, with pressure taps at two and a half diamecotton. The grooves for the junctions were cut in the outer surters upstream and seven and a half diameters downstream from faces of the plates, and after the wires were soldered in place the the orifice plate. For the five sizes of orifice that were used, disexcess solder was scraped away in order to restore the original charge coefficients were taken from Figure 15 of an A. S. M. E. rethickness of the plates. The junctions were about * / 8 inch long. port ( I ) , and were later checked by calibration against flow nozThe wires were carried upward from the junctions and under the zles. The air temperature was taken a t eleven diameters ahead edge of the upper copper-ribbon sealing strip, a t which points of the upstream pressure tap. The flow was calculated by an Permatex rather than solder was the sealing medium. As shown appropriate equation of Moss (17). in Figure I, the wires were formed into a cable and were brought The specified gaps between duct walls were checked by miout along the upper edge of the duct. Thence they passed crometer measurement, and the flatness of the plates was tested through the air-discharge chamber into the room. before and after the ducts were assembled. 337
ATA on the heating and pressure drop of a fluid between two parallel flat plates may be used
D
LAWRENCE WASHINGTON Stanford University, California
338
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 29, NO. 3
TABLE11. HEATINGDATA Temp. Temp. Net of Air of Air Heat Ab- Heat Av. Surface Over-All Approx. Mass into from sorbed from Av. Wall Cpeffi- Nusselt Pressure Friction cient, No., Drop, Gradient, Run Velocity, Duct, Duct, by Air, Steam, Reynolds No. Velocity, Temp., No. G 20 ta qa qs DG/r DQ/rt. V tw h h D / k PO -pa 4pr/N B. t. u./(hr.) B. t . u./ B. t . u./ O F aF hr. hr. Ft./sec. F. ( s q . f f . ) ( O F . ) In. Ha0 In./ft. '/a X 5 X 48 Inch Duct; Heat Loss qr = 1455 B. t. u. per Hour 985 940 9.8 209.5 0.98 1.33 0.413 0.096 90.0 178.0 215 225 13 2,330 1.43 1.94 1,280 1,220 12.7 210.5 0.544 0.124 85.0 182.5 310 350 19 3,020 1,435 1,370 14.3 209.0 1.69 2.28 360 0.621 0.140 86.5 184.0 346 12 3,390 1,695 17.7 210.5 2.24 3.03 455 1,780 0.788 0.174 187.0 459 83.0 18 4,210 1,970 20.3 211.0 2.61 3.54 80.0 187.0 550 605 2,070 0.950 0.207 8 4,880 3.29 4.45 2,525 2,410 25.1 210.0 1.25 0.266 655 655 83.6 188.0 11 5,980 3,100 2,940 29.8 21O:O 3.78 5.16 1.57 0.325 975 74.0 184.0 835 7 7,270 3,320 34.7 4.34 5.88 3,490 210.5 1.86 0.376 900 885 82.5 186.5 10 8,250 5.b8 7.58 2.50 0.508 3.860 39.6 1035 4,050 209.5 189.0 1110 78.0 6 9.550 4;OlO 41.7 210.0 5 . 8 4 7.90 1140 1140 4;210 2.73 0.552 80.5 190.0 9 9[950 4,740 7.68 48.8 209.5 10.4 3.86 1455 4,970 0.782 193.0 1420 77.5 5 11,740 5,380 55.4 209.0 12.7 5.11 1.04 9.40 195.0 1650 1675 5,640 4 13,350 77.0 6,000 11.0 62.0 208.0 14.9 6.18 1840 6,270 1.25 195.5 1840 17 14,830 77.5 6,560 68.3 208.5 1 2 . 6 17.0 7.38 1.49 2000 1970 6,860 80.5 197.5 14 16,320 7,290 14.9 75.7 207.5 20.1 8.51 2285 2250 7,620 1.69 77.5 198.0 2 18,070 7,310 14.15 75.2 208.5 19.1 8.74 2310 2230 7,660 1.74 76.0 197.5 3 18,150 1 8 . 7 2 5 . 4 9,360 8 9 5 0 92 2 205.5 12.35 2.40 2850 2740 7 4 . 5 196.5 1 22,200 11:800 119:4 201.0 26.3 35.5 19.56 3.75 194.0 3590 3260 12,300 16 29,000 76.0 13,000 131.8 30.9 41.5 201.5 22.92 4.34 3305 13,500 196.0 3780 16 32,100 83.5 x 5 X 48 Inch Duct: Heat Loss 4,. = 1450 B. t. u. per Hour 1400 7.46 211.0 1.68 4.46 0.100 0.0207 84.5 183.0 367 505 1,470 1 1775 2.02 5.38 1:690 8.88 211.0 0.130 0.0268 80.0 182.0 457 560 1,780 18 2:140 2.42 6.44 2070 10.9 211.5 0.170 0.0337 81.5 181.0 547 590 2,180 19 2,620 2:340 1 2 . 4 211.0 2.60 6.92 0.200 0.0387 601 640 2,460 82.0 179.6 2 2960 2.71 7.22 2,560 13.5 212.0 0.230 0.0440 645 690 2,700 83.0 178.5 20 3:250 3.02 8.05 2,910 15.3 212.0 0.270 0.0502 83.5 177.0 725 700 3,070 21 3,690 3,150 16.7 211.0 3 . 1 6 8 . 4 5 0.300 0.0545 8 1 . 5 174.0 773 850 3,330 3 3990 3,430 18.0 212.0 3.56 9.51 0.350 0.0635 81.5 176.0 859 840 3,620 22 4'340 3.86 10.3 0.400 3,900 3,700 19.5 211.0 0.0720 940 975 80.5 176.5 4 4'670 4 120 4.61 21.8 211.0 12.3 0.500 1070 4,350 0.0900 179.5 1090 79.5 5 5'210 4:510 23.9 211.0 5.19 1 3 . 8 0.600 0.108 1210 1210 4,750 79.0 180.5 6 5:710 4,930 2 5 . 9 211.0 5 . 8 1 15.6 0.700 0.125 7 5 . 0 179.5 1365 1530 5,210 7 6,230 5,290 6.30 16.8 0.800 0.142 27.9 211.0 1540 5,590 181.0 1470 76.5 8 6,700 6.85 0.900 0.160 18.3 5,590 29.6 211.0 182.0 1550 1580 77.5 5,900 9 7080 7.15 19.1 1.00 0.177 5,940 31.3 210.0 77.0 181.0 1630 1560 6,270 12 7'510 210.5 9.00 24.0 1.50 0.260 7,440 39.2 1910 7,850 181.5 2050 77.5 13 9:410 8780 45.6 210.0 10.66 28.6 2.00 0.341 71.0 180.0 2520 2565 9280 14 11,070 13.16 35.2 3.00 10:950 57.0 210.5 0.503 72.5 180.0 3110 3065 11:550 15 13,820 16.93 45.6 5.06 14,700 75.9 209.0 0.819 68.5 176.5 4200 4070 15,600 10 18550 19.45 6.50 1.10 16,900 84.7 52.0 4480 17,800 209.5 178.0 4530 76.0 17 21:250 21.0 8.00 1.26 19,000 97.8 56.5 209.0 4960 20,100 71.5 175.0 5210 11 23,900 23.5 63.2 10.00 1.55 21,600 111.1 208.5 5510 22,800 73.5 174.5 5740 16 27.200 D/la . - - X 5 X 48 Inch Duct: Heat Loss OI = 1470 B. t. u. oer Hour 1 903 ... 87.0 171.0 356 340 1,600 1,530 3.76 212.0 1.41 7.99 . 2 1,060 79.0 165.0 429 530 1,890 1,780 4.37 212.0 1.56 8.92 3 1400 80.0 160.5 529 560 2,500 2,360 5.73 212.0 1.85 10.6 ... 4 1:675 81.0 158.0 606 530 2,995 2,820 6.89 212.0 2.09 12.0 5 1,920 83.0 157.0 667 590 3,430 3,240 7.89 212.0 2.30 13.2 0.'050 0.0080 3,630 212.0 2.50 14.4 8.84 0.060 83.0 155.5 655 3,850 6 2,150 2.72 15.6 3,950 212.0 9.60 0.070 82.0 155.0 670 4,190 7 2 340 2.87 4,260 211.0 10.3 0.080 16.6 151.0 870 4,540 76.0 8 2:510 4,550 211.0 3.02 0.090 17.5 11.0 151.0 870 4 850 78.0 9 2,690 4,800 211.0 3.19 0.100 18.4 11.7 5:llO 151.5 940 78.5 10 2,840 3.99 23.1 6,040 14.6 211.0 0.150 149.5 1150 6,440 77.0 11 3 560 4 . 4 8 25.9 211.0 0.200 7,070 17.1 148.0 1350 7,540 76.0 12 4:170 5.57 32.4 21.5 211.0 0.300 8,980 1720 146.0 9,590 74.0 13 5290 6.30 37.0 0.400 10 500 24.9 210.5 141.0 67.5 2130 11 260 14 si160 7.05 41.3 0.500 12:ooo 28.5 210.6 2410 12:SSO 140.0 67.5 15 7,050 7.64 44.6 0.600 0.0785 31.1 210.5 70.5 141.0 2570 2730 16 7;760 8.27 48.4 0.0897 0.700 34.0 210.5 70.0 140.0 2795 2690 17 8 500 8.72 51.2 0.101 0.800 36.6 209.5 2960 2930 69.0 138.0 18 9:140 9.33 0.112 3 9 . 1 209.5 0.900 54.7 69.5 138.0 3150 3050 19 9,770 0.126 1.00 56.7 41.0 209.5 9.66 3230 69.5 137.5 3280 20 10260 5 9 . 6 0.240 2 . 0 0 76.4 204.5 13.0 4100 72.0 133.0 4280 21 14:920 a These are values of jam, ~~
~~
~~
After the heat transfer tests of the l/s-inch duct were completed, the outlet chamber was removed and a vertical velocity traverse across the end of the duct was made. For this purpose an impact tube made of 0.052-inch brass tubing was used. The tube was moved along the vertical center line with its tip about inch inside of the duct mouth. The impact pressure was read on an Ellison inclined gage.
Experimental Procedure Each duct was tested through a wide velocity range, under both isothermal and heating conditions. In the isothermal tests, the air temperature (approximately room temperature) was measured only in the metering pipe. Two sets of readings a t each flow rate were taken, and if these agreed the next rate was established. The controlled variables in the heating tests were the rate of air flow and the steam pressure and inlet temperature. The
~
~
.. ...
~~~
.... .... .... ....
Approx. Friction Factor,
I
Heat Transfer Faqtor, 1
0.0257 0.0198 0.0175 0.0142 0.0128 0.0108 0.0091 0.0080
0,00133 0.00146 0,00148 0,00156 0,00156 0,00159 0,00154 0.00190
0.0081 0.0083 0.0086 0.0083 0.0081 0.0075 0.0078 0.0071 0.0066 0.0063
0,00212 0,00235 0.00264 0,00267 0.00278 0,00298 0,00281 0,00303 0.00325 0.00346
0.0187 0.0168 0.0141 0.0126 0.0120 0.0106 0.0098 0.0096 0.0094 0.0094 0.0094 0.0092 0.0091 0.0091 0.0090 0.0084 0.0081 0.0076 0.0069 0.0071 0.0064 0.0061
0,00291 0.00291 0,00284 0,00276 0,00265 0.00259 0,00286 0.00297 0,00298 0,00319 0,00328 0,00337 0,00339 0,00349 0,00344 0,00345 0,00348 0.00344 0.00330 0,00331 0.00318 0,00312
....
0.00510
0.0082 . ...-
O:Oi34 0.0124 0.0121 0.0120 0.0118 0.0117 0.0102 0.0103 0,0092 0.0090 0.0083 0.0082 0.0078 0.0076 0.0074 0.0076 0.0068
0.00211
0
0.00427 0.00435 0.00431 0.00431 0.00417 0.00409 0.00409 0.00408 0.00392 0.00384 0.00374 0.00366 0.00360 0.00356 0.00349 0.00349 0.00319 0.00345
incoming steam was superheated- not to exceed 50" F., in order that its enthalpy might be determined without the use of a calorimeter. No run was star td until the air-outlet temperature and the condensate flow rate had been approximately constant for 10 minutes. The te& were from 25 to 60 minutes long, the length depending t % the constancy of condensate rate: Thermocouples were read every 10 minutes and all other instruments every 5 minutes. The anticipated symmetry of heating was so completely attained that thermocouples 9, 10, and 11 agreed with the corresponding couples 2, 3, and 5 within 0.5' F.; hence, after preliminary runs, couples 9 to 11were not read. Further, the regular reading of couples 7 and 8 proved unnecessary, since they agreed with couple 2 within 0.5' F. Before each duct was tested, several blank runs were made a t different room temperatures in order to find the mean heat
INDUSTRIAL AND ENGINEERING CHEMISTRY
MARCH, 1937
.
LACQUER
THE,RMOCOUPLE LEAD
BRASS PLATE LEADS
TAPE
COPPER P L A T E /
339
PERMATEX
COPPER RIBBON
%
--
LEAD
SOLDERED JOINT
TRANSITE STRIP
COPPER PLATES
B R A S S PLATE
1
ENTRANCE
CONE.
CONDENSATE DRAIN
DETAILSAND ASSEMBLY OF APPARATUS FIGURE1. CONSTRUCTION Figures in parentheses denote thermocouple junotions. Junctions 1 to 8 are in one wall, junctions 9 to 11 in the other.
loss to the surroundings. The effect of a change of room temperature from 69"to 80" F. was negligible. In the blank runs, as in the heating tests, the steam-jacket pressure was held a t about 1 inch of water.
Precision of Measurements and Accuracy of Results All thermometer readings were estimated to 0.1" F., but averages were recorded only to the nearest 0.5O F., as were the averages of thermocouple observations. The draft gage with which orifice pressure drop was measured was scaled to 0.OJ inch of water in the range 0 to 3 inches, and to 0.1 inch frog; 8.0 to 8 inches. Readings were estimated to one-tenthiof a division. Duct pressure drop was estimated to 0.1 inch,on the vertical manometer and to 0.001 inch on the inclined &aftgage. The condensate scales were scaled in 0.05-pound divisions and their readings were estimated to 0.01 pound. Orifice diameters were measured to 0.0001 inch, but, in view of possible variations in the inside diameter of the metering pipe, the orifice diameters were taken only to 0,001 inch in the computations. All computations were made on 10-inch slide rules. It is estimated that the average error in the heat transfer coefficients is * 5 per cent. Because of the assumptions necessary to their calculation from over-all pressure drop data, the friction factors are probably not as accurate as the heat
FIGURE2. GENERAL VIEWOF APPARATUS transfer coefficients-hence the label "approximate." the average, they may be off as much as * 10 per cent.
On
Test Data and Results The data and results of the heating runs are summarized in Table 11, and those of the isothermal tests in Table 111. The range of the principal variables is given in Table IV.
VOL. 29, NO.3
INDUSTRIAL AND ENGINEERING CHEMISTRY
340
Discussion of Results
0.07
As shown in Figure 3, there are pronounced discontinuities in both the h a02 and A p p / N curves for the l/8and ‘/4-inch ducts a t 0.01 velocities of 35 and 17 feet 0.007 p e r s e c o n d , respectively. This would indicate that 0.00f heated air experienced an 9 ,cons,stent on& abrupt transition from visFIGURE4. APPROXIMATE FRICTIONFACTOR cous to turbulent flow at FOR I / g I DUCT ~ ~ ~ t h e critical velocity. In i s o t h e r m a l flow, on the For use in Fanning equation: other hand, the transition * F = zfc2 Ib./(sq. ft.)(ft.) N ODP’ Curve for smooth, round tubes taken from McAdams a p p e a r 8 t o h a v e been (16,Figure 40). gradual. A discontinuity Theoretical isothermal line: in the h curve for the 9/ls4P f = inch duct, a t about 8 feet where n, a function of b / a , IS taken from iMoAdams per second, is a t least sug(16,Figure 45). gested. That the friction loss in isothermal viscous flow at a given velocity wa5 less than the loss during heating a t the same velocity, as shown in Figure 3, is in accord with the flow theory of Keevil and McAdams (14). They predicted that a gas in viscous flow would show a higher friction loss when heated, because of the increase in viscosity with rise of temperature near the wall. But the very nature of turbulent flow is such as 0.01
f
/o
5
20
50
/oo
V, fusec. FIGURE 3
The wall temperature, t,, used in the computation of heat transfer coefficients, is an average of the readings of thermocouples 1 to 6, weighted on the basis of area. Thus, from the dimensions given in Figure 1, couples 1 and 6 were weighted a t two each and couples 2 to 5 a t eleven each. Air temperatures to and ta are arithmetic averages. The heat balances were made on the assumption that the heat loss was constant. The air properties, p and k , were taken at t, = t3) and were obtained from the International Critical Tables (11). The film viscosity, pi, was taken at tf = (l/Z) (t, t,). In the calculation of inlet and outlet velocities, a gas constant, R, of 54.1 foot-pounds per (pound x O F.) was used, on the assumption that the incoming air was saturated with water vapor because of the previous compression and cooling. For the sake of simplicity, the hydraulic radius, m, appropriate for the friction calculations was used also in the heat transfer calculations. Thus, the equivalent diameter, D , was taken as 2ab/(a b), and not as 2b asrecommendedbythose writers who interpret Liwetted’fperimeter as “heated” perimeter. The method of correcting the over-all pressure drop, PO p 3 , for duct-end losses and for expansion due to heating, in order to arrive at the friction gradient in the duct ApF/N and the friction factor, f, is described in the appendix. The heat transfer factor, j , developed by Colburn (4) from a modified Reynolds analogy between friction and heat transfer, is defined-as follows:
+
+
+
The factor j,, is similarly defined in terms of ha, and A,,,,.
TABLE111. ISOTHERMAL DATA Temp. Mass Over-All VeRe nolds Av. Pressure Read- of in@: Air, locity, Go., Velocity, Drop, No. ta 0 Da/p V PO ~3 F . L b . / ( h r . ) ( s q .ft.) Ft./sec. In. HnO 1/8 X 5 X 48 Inch Duct 59 73, 895 412 3.38 0.099 0.129 525 4.31 57 58 73.0 1,260 1.140 0.141 580 4.75 56 73.0 1,380 635 5.20 0.156 725 5.96 0.180 E5 73.0 1,575 778 6.40 0.194 54 73.0 1,690 53 73.0 1,820 838 6.87 0.210 877 7.18 0.219 52 72.5 1,900 910 7.37 0.230 20 69.0 1,960 51 72.5 2,070 955 7.80 0.239
-
290
a;:
4s 47 46
72.5 72.5 72.0 72.0
45
21 44
69.0
72.0
2,640 2840 3:150 3,450 3,490 3,840
2; a: 2;;;; 23 70.0 4,980 2: ;:: $;$; 24 25
6,080 7,000 7,960
29 27 28 30 31 32 33 34 35
70.0 71.0 72,0 74.0 72.0 74.0 74.0 74.0 74.0 72.0 67.0 67.0
8,130 8,550 9,300 11,400 14,100 18,000 22,300 25,600 36,600
44 43 47
63.0 63.0 63.0
1,140 1,590 1,825
1 45 2 26 41 25 40
66.5 62.5 66.5
26
i;
65.0 65.0
65.0 65.0
i:!: 2,450 2.640 2 850 3:lOO 3,370 3,660 3,820
0.0165 0.0153 0.0136 0.0127 0.0124 0.0114
0,680
0.146
o.0095
22.8 0.880 26.4 1.10 30.1 1,37 30.8 1.60 32.2 1.65 35.2 2.05 42.9 3.05 53.2 4.87 68.0 7.04 83.2 10.02 94.2 12.80 134.1 23.10 48 Inch Duct 4.19 0,040 5.85 0.060 6.70 0.070
0.184 0.227
o.0081 0.0076
0.335 0.340 0.427 0.635 1.02 1.43 2 01 2.55 4.41
o.008z 0.0075 0.0079 0.0083 0.0071 0.0066 0.0065 0.0055
0.0087 0.0125 0.0142
0.0218 0.0160 0.0138
18.70
:!:$
:$:: it:!!
2,230 2,410 2,600 2,830 3,080 3,340 3,490
0,0259
0,0240 0,0230 0,0226 0.0210
0.0710 0.0763 0.0833 0.0933 0.0930 0.104
2,300
;;Ti:
0,0483 0.0385 0,0342 0.0316 0.0276
~:~~~~
9.95 10.75 11.90 13.00 13.20 14.60
2,810 3,240 3,680 3,740 3,950 4,290 5,250 6,500 8,300 10,290 11,900 17,000 1/1 X 5 X 1,040 1,450 1,670
0.0240 0.0310 0.0338 0.0372 0.0425 0.0457 0.0492 0.0512 0.0537 0.0555
0.311 0.337 0.372 0.419 0.420 0.473
1,220 1,310 1,450 1,590 1,620 1,770
8;y:g
In./ft.
8:;;;
9;:”
:;$;
Appro*. Approx. Friction Friction Gradient, Factor, APF/N f
::::: g:; : ;;:it$ gi: ;: :$: : :z
::$; E:?g:
9.20 9.77 10.70 11.63 12.50 13.76 14.16
0,100 0.115 0.130 0.150 0.175 0.200 0.225
o,280
:$:E 0.0192 0.0220 0.0245 0.0282 0.0327 0.0370 0.0422
o,oo71
o.ooso
g:0.0102 ;::: 0.0102 0.0096
0.0094 0.0093 o.0088 0.0093
INDUSTRIAL AND ENGINEERING CHEMISTRY
MARCH, 1937
341
to minimize the effect of heating or cooling on fluid friction, since there can be no pronounced viscosity gradient across a mass of t u r b u l e n t l y moving fluid. This explains the coincidence of the Ap,/N curves for heating and isothermal turbulent flow. Theoretically t u r b u lence is incipient a t the point where %he rate of shear, and therefore the too0 zoo0 sooo iaooo 20.000 5ooc velocity gradient, is a ,consstant units maximum. I n isotherFIGURE5 (Top). APPROXIMATE FRICTION mal flow the v e l o c i t y FACTOR FOR INCH DUCT parabola is, of course, FRICTION FIGURE6 (Bottom). APPROXIMATE FACTOR FOR ’/ia-INCH DUCT “steepest” at the wall. /om Pow 5wQ /o,ooo 29000 S0,WO During the heating of a consishnt unth and McAdams, the velocity is less gas, according to Keevil FIGURE 7. NUSSELT NUMBERvs. REYNOLDS near the wall and greater near the center of the passage than NUMBER it is in isothermal flow. This reduction of velocitv gradient Dashed line for turbulent flow in straight round pipes: near the wall may account for the fact t h a t viscoui flow was h D / k a 0.0203(DU/s)0.8derived from McAhams (16, page 169, Equation 11). maintained up to higher average velocities during heating than it was during isothermal flow. that all of the reliable friction data for the 9/1~-inchduct lay All of the effects just discussed are shown with equal clarity in the turbulent zone. The position of the theoretical line in the friction-factor plots (Figures 4 and 5 ) . Figure 6 shows for the 1/8-inch duct is somewhat uncertain, because the b/a ratio of 0.025 was so small as to make it difficult to read McAdams’ Figure 45 with any degree of accuracy. TABLE111 (Continued) In isothermal flow through the l/8- and l/d-inch ducts the Temp. Mass Over-All Approx. Approx. transition from streamline t o turbulent flow began a t Re = Read- of VeReynolds Av. Pressure Friction Friction ing Air, locity, No., Velocity, Drop, Gradient, Factor, 2300, approximately, as noted by McAdams for the results of NO. ta G DG/s V PO - PJ APFIN f others. But when the air was heated, streamline flow was F. L b . / ( h r . ) ( s q .ft.) Ft./sec. In. Hz0 In./ft. maintained up to a Reynolds number of about 3400, which 1/4 X 5 X 48 Inch Duct (Cont’d) corresponds to the critical velocities shown in Figure 3. 15.32 0.250 0.0462 0.0089 24 65.0 4,060 3,710 15.60 0.275 0.0517 0.0094 39 65.0 4,200 3,830 I n turbulent flow, a t a given value of Re, the friction factor 16.64 0.300 0.0560 0.0091 65.0 4,420 4,030 23 increased with the gap b between the walls. This may have 16.93 0.320 0.0600 0.0093 65.0 4,560 4,160 38 22 66.0 0.0652 0.0090 4790 4,360 18.02 0.350 been due in part to the greater opportunity for the formation 66.0 19.50 0.400 0.0737 0.0087 5:180 4,720 21 66.0 5,820 5,300 21.9 0.500 0.0920 0.0086 19 of eddies as b was increased. Flow through the l/s-inch duct 5,850 24.2 0.600 66.0 0.110 0.0084 6,420 17 was almost two-dimensional, since the proximity of the walls 66.0 6,740 6,140 25.3 0.650 0.118 0,0082 16 66.0 7,050 6,420 26.5 0.700 0,127 0,0081 15 tended to minimize velocity components normal to the walls. 66.0 7,520 6,850 28.3 0.800 0.145 0,0081 13 I n turbulent flow, a large part of the pressure drop is caused 11 65.0 8,010 29.9 0.900 0.163 7,310 0,0081 0.171 o.onso 65.0 8.260 10 7.540 30.9 0.950 . ..-. by eddy formation, and anything which tends to reduce these 65.0 9 8,460 31.7 1.00 0.180 7,720 0.0080 formations should act also to reduce the friction loss. (A 8,870 33.2 0.198 65.0 8,100 1.10 8 0.0080 65.0 8,880 9,730 36.3 1.30 0.233 7 0.0079 similar effect of wall spacing on free-convection currents is 39.4 65.0 10,560 9,640 0.0076 1.50 0.266 6 11,300 46.3 64.0 1” 400 2.00 0.350 29 0.0073 discussed below.) n.no7i 52.3 0.434 64.0 1z:ooo 12.780 2.50 28 . The heterogeneous character of the duot walls, too, may 66.0 16;lOO 3 14,730 60.2 3.20 0.548 0.0067 65.0 18,500 30 16,900 68.2 4.00 0.669 0.0063 have been partly responsible for the increase off with b in the 65.0 20,900 32 19,060 76.9 5.00 0.827 0.0061 turbulent zone. The Transite strips a t the top and bottom 65.0 23,000 34 21,000 84.7 6.00 0,987 0,0061 65.0 27,000 36 24,600 99.1 8.00 1.29 0.0058 were rougher than the copper plates, and, as the gap was in65.0 30.600 37 28,000 112.3 10.10 1.61 0.0056 creased, they formed a greater percentage of the total wall g / i ~ X 5 X 48 Inoh Duct 66.0 1,850 3,570 6.90 0.040 0.00670 0.0134 surface. This may account for the fact that the curve for the 13 14 66.0 2,090 47O4O 7.82 0,050 0,00827 0,0129 9/16-inch duct lies above the curve for smooth, round tubes. 66.0 2,350 15 4,540 8.77 0.060 0.00965 0,0119
p,
O
~
16 17 18 19 20 28 21 29 22 23 1 2 3
4 5 6 7 8 9
66.0 66.0 66.0 66.0 66.0 59.0 65.8 59.0 65.5 65.5 67.0 67.0 67.0 67.0 67.0 67.0
2,570 2,800 2,980 3,180 3,970 4,370 4,630 5.350 5,850 6,950 7,640 8,500 9,230 9,950 10,640 11 150
67.0 67.0 67.0
13:840 16,200 20,150
4,960 5,410 5,770 6,140 7,670 8,530 8,960 10,450 11,300 13,430 14,730 16,400 17,800 19,200 20,500 21,500 26,700 31,200 38,800
9.60 10.46 11.15 11.90 14.82 16.05 17.30 19.69 21.8 25.9 28.6 31.8 34.6 37.3 39.8 41.7 51.7 60.5 75.2
0.070 0.080 0.090 0,100 0.150 0.175 0.200 0.250 0.300 0.400 0.500 0.600 0.710 0.800 0.910 1.01 1.50 2.00 3.01
~
0 0111 0.0124 0.0139 0,0152 0.0222 0.0256 0.0232 0.0350 0.0417 0.0532 0.0682 0.0795 0.0945 0.104 0.117 0.132 0.188 0.243 0.356
0,0114 0,0107 0.0106 0.0102 0.0096 0,0092 0,0093 0.0084 0.0083 0.0075 0,0079 0.0074 0.0075 0.0071 0.0070 0.0072 0.0066 0.0063 0.0060
TABLEIv. RANGE OF PRINCIPAL VARIABLES IN HEATING RUNS Symbo1
V
Av‘ velocitypft’@c* to F* 13 Air Outlet F* tw temp’9a. F‘ A e&zr$mp* diff’v F* DG/s viscosity ib.,(hr.)(ft.) s Thermal Lonductivity (E. t. u.)(ft.)/(hr.)&q. ft.)(’ F.) k Sp. heat, B. t. u./(lb.)(” F.) CP Sp. vol cu. ft./lb. 21 Equivaiknt diam., ft. D Over-all pressure drop, in. HzO PO - pa
Maximum 131.8 90.0 198.0 212.0 102.5 27,400 0.0484
Minimum 3.76 67.5 133.0 201.0 36.7 985 0,0459
Ma.x./ Min. 35.0 1.33 1.49 1.05 2.79 27.8 1.05
0.01503 0.2417 15.15 0.0842 22.92
0.01433 0.2414 14.41 0,0203 0.050
1.05 1.001 1.05 4.15 458
INDUSTRIAL AND ENGINEERING CHEMISTRY
342 b.O/O
0.008 (0
u
s
*.r
0.006 OJOf
C
2 .$
s
\-0.002 Yu
‘i 0.001
a, consistent
umts
Pf
FIGURE 8. HEATTRANSFER FACTOR, AND FRICTION FACTOR FOR TURBULENT FLOW, us. FILMREYNOLDS NUMBER Equations of Colburn ourves for round tubes having same N / D as these ducts: curve D : 0.0007 4- 0.066 (DG/9f)-O az j = f!2 Curves B , B’, and B”. (“)-“a((”) -1’8 j a m = 1.5 DQ Pf where Q = f (1 f 0.015 Grl /a)* and
a,. -
“p2gAum
Asymptotes A , A’, and A ” :
TPfZ
jam =
;(y,)Z‘’
and g/~-inchducts are The turbulent f curves for the nearly parallel with the curve for round tubes, but the curve for the l/s-inch duct is steeper. This is believed to be due to the fact that a t high rates of flow the l/s-inch duct was overloaded; that is, the high pressure within the duct probably caused its walls to bulge slightly, particularly near the inlet end. The resulting increase in cross section tended to reduce the observed pressure drop and, therefore, to reduce the calculated friction factor. As would be expected from previous analysis of the friction data, the Nu-Re curves (Figure 7) are discontinuous at Re = 3400, approximately. The data are correlated only above Re = 13,000, from which point on they tend to follow closely the line for round pipes. Below Re = 13,000 the increasing steepness of the curves with decrease of gap is believed to be due to a dampening of the free-convection currents as the walls are brought closer together. The curve for the ’ / ~ i n c h duct approximates that for round pipes throughout its length, probably because its proportions are such as to encourage free convection a t low values of s k,o Re, as in round pipes. Further explanation of the steepness of the 6 Nu-Re curves for the I/*- and 1/4-inch ducts is 4 found in a comparison with a similar curve for the heating of hydrocarbon oils in horizontal pipes, .r‘ given by McAdams (16, page 194, Figure 74). Here Nu/h4.4 is plotted against Re, and the kind of flow a t a given value of Re is determined by reference to the friction factor curves, plotted above the NuIPrQ.4 curve to the same abscissa scale. I n fully turbulent flow, the heat transfer curve approximates the anticipated slope of 0.8, but in the (‘dip region,” between Re = 2300 and Re = 3000, the slope greatly exceeds 0.8. In oils free convection is hindered by viscosity; in the present tests, as already noted, i t must have been hindered in the narrower ducts by the retarding influence of the walls. That most of the turbulent flow data for the two smaller ducts lay in the dip region is well shown by Figure 8. As the ratio p/p,, throughout the tests, deviated only slightly from a mean value of 0.95, the value of Re, that corresponds to Re,,rt. 5 3400 is 3200. Below this critical value of Re, the ordinate of the plotted points in Figure 8 is jam; above the
VOL. 29, NO. 3
critical value the ordinate is j . Although this change of ordinates produces “breaks” in the curves, the use of the arithmetic mean temperature difference in the viscous region is desirable in order that the resulting curves may be comparable with Colburn’s theoretical curves for round tubes. I n the fully turbulent region, on the other hand, the modified Reynolds analogy indicates that, a t a given value of Re,, the logarithmic factor, j , should be equal to the corresponding value of f/2. Above the dip region for each duct the agreement between j and f/2 is excellent for the l/~- and l/4inch ducts. The exact location of the dip region for the s/lainch duct is difficult to determine, but above Re, = 15,000 a good agreement is noted. The “rise” lines, C, C‘, and C“, for which simple equations are lacking, Were located by interpolation between corresponding lines on Colburn’s “resum6 chart” (4). They start a t Re, = 2200, rather than a t the critical value of Re, indicated by the present data, because, in the data for round tubes which Colburn studied, the bottom of the dip occurred, on the average, a t Re, = 2300 p/p,. For the l/~-, and 9/16-inch ducts, average values of the Grashof number for viscous flow during heating were 790, 6230, and 69,400, respectively. I n a comparison of the plotted data with Colburn’s predicted lines, it must be borne in mind that these lines were based on a study of heat transfer in round tubes, and that in rectangular passages additional factors must be considered. One such factor is the shape of the cross section, as evaluated by the ratio b/a. The importance of this ratio is indicated in McAdams’ equation (Figure 4) for the theoretical friction factor in isothermal viscous flow. It must influence heat transfer also, because of its bearing on the ease of formation and propagation of free-convection currents. I n addition to the ratio b/a, the orientation of the cross section should affect the surface coefficient a t low gas velocities. If the 5-inch side of these ducts had been horizontal rather than vertical, it seems reasonable to suppose that in the larger sizes the effect of free convection would have been much reduced, if not eliminated. Hence, free convection in rectangular passages can be accounted for only partially by the in-
0
Ap,
, in. water
FIQURE
9
troduction of a function of Grashof’s number, as in Colburn’s equation. Consider, for example, two rectangular passages whose b and a dimensions are 0.125 X 5 and 0.5 X 0.161 inch, respectively, (The a sides are vertical.) For both passages D = 0.244 inch, and therefore under like conditions of average pressure, temperature, and temperature difference, Gr would be the same for both. But it is improbable that the effects of free convection would be the same in both. I n the transitional or rise region, the plotted points for the and ‘/(-inch ducts lie close to the corresponding lines,
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
343
Figure 12. Their experiments differed from the writers' in that all four walls of their ducts were of copper, l/32inch thick. They used a calming section a b o u t 3 f e e t long; their temperature changes and differences were comparatively minute, none exceeding 18" F. and some being as small as 1.8' F. They took no heat balance data, and they made only four runs a t Re, less than 2500. Throughout the recalculation of their data, the arithmetic mean temperature difference was used, because it differed negligibly from the logaM M PPRESSURE ~ - INCHES WATER rithmic mean, FIGURE11. VELOCITYTRAVERSES In each figure the dashed line is a ALONG VERTICAL AXIS AT OUTLET OF plot of Colburn's equation for fully tur~/S-INCH DUCT bulent flow. Despite the scattering of >. 3 s d 4 the points and the scarcity of data a t low Thermocoup/e position pIGURE T~~~~~~~~~~ G~~~~~~~~ C and C'. But Reynolds number, a few general conclusionsmay be drawn: (1) The agreement betweenj andf/2 is fairly good for the square lf the lines B and ALONG WALLOF 1 / 8 - 1 ~DUCT ~ ~ duct but progressively poorer as the section becomes narrower. B' had been ex(2) Except for the square section, no SWWation of the Points tended to the critical Ref of about 3200 for these ducts, and the for heating and for coolingis discernible. (3) In all of the plots lines C and C' had been started therefrom, the latter lines the start of a dip region is a t least suggested, and in Figure 12 would have fallen considerably below the plotted points. C and D the points below Re, = 2500 are probably in the However, as Colburn indicated in his paper, the rise lines viscous region. I n Figure 1.20 the bottom of a dip in j for must be located empirically and, from the limited data availheating is suggested somewhere between 2500 and 3000 on able, their position is by no means finally established. the Ref scale. (4)Except for the 0.126 X 0.995 inch duct, The approximate coincidence of all of the j and f/2 points the friction data agree fairly well with the dashed line, but with line D a t high Reynolds number indicates that the proportions of a duct exert a negligible influence in fully turbulent flow. Agreement between the B lines axid the corresponding points is poor, but again we have Colburn's statement that his equation "represents only an approximation based upon the few data a t present available." For the l/s-inch duct, the rise of j in the viscous region, between Re, = 940 and Re, = 1700, is contrary to theory and suggests the possibility of error in air-temperature measurements in this region. Radiation errors in thermocouple readings were discounted, since they were estimated to be less than 0.5 per cent. It was finally concluded that the error lay principally in the outlet temperature and that it was due to heat loss from the outlet chamber, which would have the greatest effect a t the lowest rates of flow. A study of Figure 9 suggested a correction. On the assumption that all points for the I/S-inch duct should have fallen on a straight line, values for h, hD/k, and j,, for runs 13, 19, 12, and 18 were redetermined from this line and are given as dotted lines in Figures 3, 7, and 8. The temperature-gradient curves of Figure 10 show that, as the air velocity was increased, the walls of the l/*-inch duct were cooled considerably below the steam-jacket temperature, especially near the inlet end. The difference was much less in the larger ducts. At the maximum rate of air flow in the 1/4-inch duct, couple 2 read 3.0" F. below the jacket temperature, and in the g/le-inch duct, 6.5" F. below this temperature. The complete data on wall temperatures justify, except for a few of the high-velocity runs, the assumption of a uniform wall temperature in the calculation of A. The velocity-traverse data (Figure 11) were taken only to justify the use of the arithmetic mean of the three outlet-air thermocouple readings as temperature t8. That this procedure was satisfactory is shown by the flatness of the velocity 5000 /O~oW P G W a 30wO curves. consistent units FIQURE12. DATAOF BAILEYAND COPE Data of Bailey and Cope
e,
The data of Bailey and Cope (9)on the heating and cooling of water in square and rectangular ducts are replotted in
A. B.
Water in 0.561 X 0.551 X 72 inch duct Water in 0.354 X 0.748 X 72 inch duct
D.
Water In 0.126 X 0.996 X 72 inch duct
C. Water /n 0.248 X 0.873 X 72 inoh duct
INDUSTRIAL AXD ENGINEERIKG CHEMISTRY
344
for this duct they average about 25 per cent above the line, as was noted by Bailey and Cope when comparing their data with the line of Stanton and Pannell (19). This is in marked disagreement with the results of the writers’ tests of the l/s x 5 inch duct, whose friction factors fell about 12 per cent below the line of Drew, Koo, and McAdams (8). Because of the lack of data with which to compare them, it did not seem worth while t o calculate and plot the Colburn lines for the dip and viscous regions. It is regrettable that more data were not taken in these regions.
Summary and Conclusions As in round pipes, the isothermal flow of air in rectangular passages is viscous only if Reynolds number is less than 2300. When heat is applied the flow is viscous up to Re = 3400. The flow is fully turbulent only if Re exceeds 13,000, in which case the present data are represented fairly well b y the equations :
The factor K , a function of the smoothness of the entrance as well as of the ratio &/So, is given for sudden contractions in McAdams’ Figure 47. Neglecting for the moment the effect of smoothness, we see from this figure that, because SI/SO was practically zero for all of the ducts tested, K would be practically 0.5 for a sharp-edged entrance. If the entrance were perfectly smooth and frictionless, K would be zero. As the actual entrance was neither sharp-edged nor frictionless, the true value of K must have been somewhere between zero and 0.5. A value of 0.25 was assumed. Equation 3 then becomes: po
- pl
= 1.25
Appendix
The first right-hand term is the pressure increase caused by the decrease in kinetic energy, and the second term is the pressure decrease caused by fluid friction. Substituting V S = 0 in Equation l, we see that p z - p3 = 0. The pressure drop at a sudden contraction is:
Again, the first term accounts for kinetic energy change and t h e second term for friotion. If VOand (VO - v,) are neglected, Equation 2 becomes: (3)
(4)
Pressure drop within the duct was caused by friction ( A p p ) , and by expansion as a result of heating. That is, expansion within a assage of uniform cross section must result in an in. crease of tinetic energy and, therefore, in a decrease of pressure. Calling t’hepressure drop that is due to expansion A p ~ n we , have from McAdams (16, Equation 35, page 130): APKE =
FRICTIOW GRADIENTAND FACTOR. The measured pressure drop, PO - p3, was an algebraic summation of the pressure changes that were caused by friction, expansion, and chan e of kinetic energy: (1) at the entrance, (2) in the duct, and F3) a t the exit To approximate the unmeasured entrance and exit effects, the following method, based upon McAdams’ analysis of gas flow (15,pages 121-134), was employed. The cross-sectional areas of the inlet and outlet chambers were so large compared to the duct cross sections that the chamber velocities, Voand Va, were taken as zero. The pressure drop at a sudden enlargement of cross section is given approximately by the hydraulic equation:
2gvo
Va
+
CALCULATION O F
V2
2, lb./sq. f t .
= 0.00374 2, in. HzO vo
j = f/2 = 0.007 O.O65(DG/p~)-O*~* hD/k = 0.0203(DG/p)0*8
Within the limits of the data, a t a given velocity in viscous flow a n increase in gap b between walls produces a n increase in the surface coefficient, h, and a decrease in the friction gradient, App,”. I n turbulent flow also, App/N decreases as b is increased, but the relation between hand b is indeterminate. I n both types of flow, friction factor f increases as the gap is increased. Heating increases the friction factor in viscous flow but does not affect it appreciably in turbulent flow. Supplemented by theory, the data indicate that at low air velocities the heat transfer is influenced b y the aspect ratio bja, by the length-diameter ratio hT/D,and by the orientation of the cross section. For horizontal exchangers, if a choice between placing the plates “flat” or “on edge” is possible, freeconvection theory favors the on-edge position. Further study is needed in order to determine: (1) which ratio, b/a or N / D , has the greater effect on heat transfer; ( 2 ) the relative advantages of horizontal and vertical flow; and (3) the quantitative effect of temperature difference on friction factor in both heating and cooling.
VOL. 29, NO. 3
=
(go)’ -,
w,
(3600 2)’
+
therefore p l - p , = A p p
The measured drop (pa pa
- p3 =
- PI)
(Po
+
0.00374 VI Va
lb./sq. f t .
g
in. H ~ O
(5)
APKE
- p 3 ) may therefore be expressed as:
(Pi
- Pz) -1- (pz -
P3)
+ [APF + (go)’ + 0 , in. HzO (7)
Since all quantities but A p p were known, Equation 7 was solved
for A p p , and friction factorfwas then calculated from the Fanning
equation.
Nomenclature (Consistent Units’) area of heat-transfer surface, sq. ft. height, of cross section of air duct, ft. = width of cross section of air duct, ft. = sp. heat at constant pressure, B. t. u./(lb.) (” F.) = equivalent diam. = 4m, f t . = friction factor in Fanning equation = standard acceleration of gr. = 4.18 X lo8, ft./(hr.)(hr.) G = mass veIocity = M / S = Vp, Ib./(hr.)(sq. ft.) Gr = Grashof No. = ____ D3p2PgA
A
a b cp D f g
= =
P2
h = surface coefficient of heat transfer, B. t. u./(hr.) (sq. ft.) /o
T? \
I’.)
(y)
2 13 h = Colburn heat transfer factor = CPG k . = thermal conductivity, (B. t. u.) (ft.)/(hr.) (sq. ft.) (” F.) M = rate of flow, lb./hr. m = hydraulic radius = ah/2(a b), f t .
j
N = length of duct, f t .
+
N u = Nusselt No. = hD/k p = pressure, Ib./ sq. ft. Pr = Prandtl No. = c+/k = rate of heat flow, B. t. u./hr. = gas constant = p v / T , ft.-lb./(lb.) (” F.) Re = Reynolds No. = D G / p S = oross-sectional area, sq. f t . t = temp., F. T = abs. tem ., ’ F. 460 V = linear verocitv, ft./hr.
%
+
O
v
= sp. vol., CU.
p
=
460)
A = ,u
4 p
ft.’/lb.
thermal coefficient of expansion
=
I / T for gases, I/(” F.
mean temp. difference (or, as prefix, increment of),
+
F.
= abs. viscosity, lb./(hr.) (ft.) = ( ~ / p y )(1 0.015 Gr”3)3 = density, lb./cu. ft.
+
1 In Tables I to I%’, some of these quantities are given in “practical” units.
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
Subscripts: a = air f = film temp. F = friction r = room s = steam w = wall am = arithmetic mean temp. difference 0 = conditions in inlet air chamber 1 = conditions in duct at inlet 2 = conditions in duct at outlet 3 = conditions in outlet air chamber m = mean condition
Acknowledgment The experiments were made in the mechanical engineering laboratory of Stanford University, whose research fund met the ~~t~ on the i/s-inch duct were taken by the authors, and the other ducts were built and tested by K. c. Burch and F. H. Taylor (3).
Bibliography (1) Am. SOC.Mech. Engrs., “Fluid Meters-Their Theory and Application,” research pub., 3rd ed., 1931. (2) Bailey and Cope, Aeronaut. Research Comm. (Gr. Brit.), Tech. R e p t . 43, 199 (1933). (3) Burch and Taylor, engineer’s thesis, Stanford Univ.. 1935.
345
(4) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29, 174 (1933). (5) Cope, W. F., Aeronaut. Research Comm. (Gr. Brit.), Tech. Rept. 37, 384 (1930). (6) Davies and White, Engineering, 128, 69 (1929). (7) Drew, T. B., Am. Inst. Chem. Engrs., preprint, 1931. (8) Drew, Koo, and McAdams, Ibid., advance paper, 1932. (9) Elias, F., Natl. Advisory Comm. Aeronaut., Tech. M e w . 614 (1931). (10) Fishenden and Saunders “Calcuiation of Heat Transmission,” H. M.Stationery Office, London, 1932. (11) International Critical Tables, McGraw-Hill Book Co., 1929. (12) Jordan, Proc. Inst. ilfech. Engrs. (London), 1909, 1317. (13) Jurges, Gesundh.-Ing., Appendix 19, Series 1, 1 (1924). (14) Keevil and McAdams, Mass. Inst. Tech., Pztb2. 65, No. 79 (1929). (15) McAdams, W. H., “Heat Transmission,” New York, McGrawHill Book Co., 1933. (16) Marks, W. M., engineer’s thesis, Stanford Univ., 1934. (17) Moss, 8 . A., Trans. Am. 8 O C . Me&. Engrs., Applied Mechanics, 50 (3), 1 (1927). (18) Schack, A., “Industrial Heat Transfer,” tr. by Goldschmidt and Partridge, New York, John Wiley & Sons, 1933. (19) Stanton and Pannell, Trans. Roy. SOC. (London), A214, 199 (1914). RECEIVED August 10, 1936. Presented as part of t h e Heat Transmission Symposium held under the auspices of the Division of Industrial and Engineering Chemistry of the American Chemical Society at Yale University, New Haven, Conn., December 30 and 31, 1935.
THE ALCHEMIST
BY Dav,id Tei .em, the Y CDun er
Again we are privileged t o present a painting by David Tgniers, the Younger (1610-1690). The original is located in the John G. Johnson Art Collection, Philadelphia, Pa., and our thanks are extended t o the Curator of the Collection for permission t o print this picture. This painting, 33 by 23 inches, completed in 1649, is one of the seventeen alchemical paintings by the David Teniers, father and son, and is one of the few originals
by these artists in this country. It was formerly in t h e collection of the Chevalier Evard, Paris. This is No. 75 in the Berolzheimer Series of Alchemical and Historical Reproductions. In its general composition, the furnace and laboratory equipment shown, it closely resembles some of the earlier Teniers’ paintings in the series, particularly Nos. 2, 6, 14, 30. and 47.
A detailed list of Reproductions Nos. 1 to 60 appeared i n our issue of January 1936 page 129, and the list of Nos. 61 t o 72 appeared in Januar;, 193f age 74 where also will be found Reproduction No. 73. Reprb$uction’No. 74 appears on page 166, February issue.
