Formulæ for Flow of Compressed Air in Pipes.-The formulæ on pages 486 and 487 are for air at or near atmospheric pressure. For compressed air the density has to be taken into account. A common formula for the flow of air, gas, or steam in pipes is = difference of pressure in which Q = volume in cubic feet per minute, p in lbs. per sq. in. causing the flow, d = diameter of pipe in in., L = length of pipe in ft., w density of the entering gas or steam in lbs per cu. ft., and ca coefficient found by experiment. Mr. F. A. Halsey in calculating a table for the Rand Drill Co.'s Catalogue takes the value of c at 58, basing it upon the experiments made by order of the Italian government preliminary to boring the Mt. Cenis tunnel. These experiments were made with pipes of 3281 feet in length and of approximately 4, 8, and 14 in. diameter. The volumes of compressed air passed ranged between 16.64 and 1200 cu. ft. per minute. The value of c is quite constant throughout the range and shows little disposition to change with the varying diameter of the pipe. It is of course probable, says Mr. Halsey, that c would be smaller if determined for smaller sizes of pipe, but to offset that the actual sizes of small commercial pipe are considerably larger than the nominal sizes, and as these calculations are commonly made for the nominal diameters it is probable that in those small sizes the loss would really be less than shown by the table. The formula is of course strictly applicable to fluids which do not change their density, but within the change of density admissible in the transmission of air for power purposes it is probable that the errors introduced by this change are less than those due to errors of observation in the present state of knowledge of the subject. Mr. Halsey's table is condensed below. Diameter of Pipe, in inches. Cubic feet of free air compressed to a gauge-pressure of 80 lbs. and passing through the pipe each minute. 50 100 200 400 800 1000 1500 2000 3000 4000 5000 Loss of pressure in lbs. per square inch for each 1000 ft. 0.20 1.05 4.30 0.12 0.35 1.41 5.80 0.14 0.57 2.28 0.26 1.05 4.16 6.4 8 10 12 14 0.14 0.54 2.12 3.27 7.60 10.7 2.59 To apply the formula given above to air of different pressures it may be given other forms, as follows: = Let Q: the volume in cubic feet per minute of the compressed air; Q1 the volume before compression, or "free air," both being taken at mean atmospheric temperature of 62° F.; w1 = weight per cubic foot of Q1 = 0.0761 lb.; r = atmospheres, or ratio of absolute pressures, (gauge-pressure +14.7) 14.7; w = weight per cu. ft. of Q; p= difference of pressure, in lbs. per sq. in., causing the flow; d = diam. of pipe in in.; L = length of pipe in ft.; c= experimental constant. Then The value of c according to the Mt. Cenis experiments is about 58 for pipes 4, 8, and 14 in. diameter, 3281 ft. long. In the St. Gothard experiments it ranged from 62.8 to 73.2 (see table below) for pipes 5.91 and 7.87 in. diameter, 1713 and 15,092 ft. long. Values derived from D'Arcy's formula for flow of water in pipes, ranging from 45.3 for 1 in. diameter to 63.2 for 24 in., are given under "Flow of Steam," p. 671. For approximate calculations the value 60 may be used for all pipes of 4 in. diameter and upwards. Using c = above formulæ become 60, the Loss of Pressure in Compressed Air Pipe-main, at St. Gothard Tunnel. (E. Stockalper.) Equation of Pipes.-It is frequently desired to know what number of pipes of a given size are equal in carrying capacity to one pipe of a larger size. At the same velocity of flow the volume delivered by two pipes of different sizes is proportional to the squares of their diameters; thus, one 4-inch pipe will deliver the same volume as four 2-inch pipes. With the same head, however, the velocity is less in the smaller pipe, and the volume delivered varies about as the square root of the fifth power (i.e., as the 2.5 power). The following table has been calculated on this basis. The figures opposite the intersection of any two sizes is the number of the smaller-sized pipes required to equal one of the larger. Thus, one 4-inch pipe is equal to 5.7 2-inch pipes. 10 316 55.9 20.3 9.9 5.7 3.6 2.4 1.7 1.3 1 13 609 108 14 733 130 15 871 154 181 211 316 115 39.1 19 10.9 7.1 4.7 3.4 2.5 1.9 1.2 47 22.9 13.1 8.3 5.7 4.1 3.0 2.3 1.5 1 55.9 27.2 15.6 9.9 6.7 4.8 3.6 2.8 1.7 1.2 65.7 32 18.311.7 7.9 5.7 4.2 3.2 2.1 1.4 1 76.4 37.2 21.3 13.5 9.2 6.6 4.9 3.8 2.4 1.6 1.2 243 88.243 24.6 15.6 10.6 7.6 5.7 4.3 2.8 1.9 1.3 1 278 101 49.1 28.1 17.8 12.1 8.7 6.5 5 3.2 2.1 1.5 1.1 55.9 32 20.3 13.8 9.9 7.4 5.7 3.6 2.4 1.7 1.3 1 70.9 40.6 25.7 17.5 12.5 9.3 7.2 4.6 3.1 2.2 1.7 1.3 88.250.532 21.8 15.6 11.6 8.9 5.7 3.8 2.8 2.1 1.6 1 609 221 108 61.7 39.1 26.6 19. 14.2 10.9 7.1 4.7 3.4 2.5 1.9 1.2 733 266 130 74.247 32 871 316 154 88.2 55.9 38 499 243 130 88.260 733 357 205 130 88.2 63.2 47 499 286 181 123 88.2 62.750.5 32 670 383 243 165 118 88.2 67.843 871 499 316 215 154 115 88.255.9 22.9 17.1 13.1 8.3 5.7 4.1 3 2.3 1.5 27.2 20.3 15.6 9.9 6.7 4.8 3.8 2.8 1.7 43 32 24.6 15.6 10.6 7.6 5.7 4.3 2.8 36.2 19 15.6 11.2 8.3 6.4 4.1 21.8 15.6 11.6 8.9 5.7 23.220.9 15.6 12 7.6 27.2 20.3 15.6 9.9 38 Measurement of the Velocity of Air in Pipes by an Anemometer.-Tests were made by B. Donkin, Jr. (Inst. Civil Engrs. 1892), to compare the velocity of air in pipes from 8 in, to 24 in. diam., as shown by an anemometer 234 in. diam. with the true velocity as measured by the time of descent of a gas-holder holding 1622 cubic feet. A table of the results with discussion is given in Eng'g News, Dec. 22, 1892. In pipes from 8 in. to 20 in. diam. with air velocities of from 140 to 690 feet per minute the anemometer showed errors varying from 14.5% fast to 10% slow. With a 24-inch pipe and a velocity of 73 ft. per minute, the anemometer gave from 44 to 63 feet, or from 13.6 to 39.6% slow. The practical conclusion drawn from these experiments is that anemometers for the measurement of velocities of air in pipes of these diameters should be used with great caution. The percentage of error is not constant, and varies considerably with the diameter of the pipes and the speeds of air. The use of a baffle, consisting of a perforated plate, which tended to equalize the velocity in the centre and at the sides in Bome cases diminished the error. The impossibility of measuring the true quantity of air by an anemometer held stationary in one position is shown by the following figures, given by Wm. Daniel (Proc. Inst. M. E., 1875), of the velocities of air found at different points in the cross-sections of two different airways in a mine. DIFFERENCES OF ANEMOMETER READINGS IN AIRWAYS. Force of the Wind.-Smeaton in 1759 published a table of the velocity and pressure of wind, as follows: VELOCITY AND FORCE OF WIND, IN POUNDS PER SQUARE INCH. The pressures per square foot in the above table correspond to the formula P = 0.0052, in which V is the velocity in miles per hour. Eng'g News, Feb. 9, 1893, says that the formula was never well established, and has floated chiefly on Smeaton's name and for lack of a better. It was put forward only for surfaces for use in windmill practice. The trend of modern evidence is that it is approximately correct only for such surfaces, and that for large solid bodies it often gives greatly too large results. Observations by others are thus compared with Smeaton's formula: Old Smeaton formula. P= As determined by Prof. Martin.. Whipple and Dines.. .005Ꮴ .004V P = .0029 .P= At 60 miles per hour these formulas give for the pressure per square foot, 18, 14.4 and 10.44 lbs., respectively, the pressure varying by all of them as the square of the velocity. Lieut. Crosby's experiments (Eng'g, June 13, 1890), claiming to prove that PfV instead of P = fV2, are discredited. A. R. Wolff (The Windmill as a Prime Mover, p. 9) gives as the theoretical dQv pressure per sq. ft. of surface, P = in which d= density of air in pounds " g .018743(p+P) per cu. ft. = ; p being the barometric pressure per square t foot at any level, and temperature of 32° F., t any absolute_ temperature, Q = volume of air carried along per square foot in one second, v = velocity dva of the wind in feet per sec., g = 32.16. Since Q = v cu. ft. per sec., P= g' Multiplying this by a coefficient 0.93 found by experiment, and substituting the above value of d, he obtains P = 0.017431 x p t x 32.16 .018743 and when p =2116.5 lbs. per sq. ft. or average atmospheric pressure at the sea-level, an expression in which the pressure is shown to vary P= 36.8929 tx 32.16 v2 -0.18743 with the temperature; and he gives a table showing the relation between velocity and pressure for temperatures from 0° to 100° F., and velocities from 1 to 80 miles per hour. For a temperature of 45° F. the pressures agree with those in Smeaton's table, for 0° F. they are about 10 per cent greater, and for 100° 10 per cent less. Prof. H. Allen Hazen, Eng'g News, July 5, 1890, says that experiments with whirling arms, by exposing plates to direct wind, and on locomotives with velocities running up to 40 miles per hour, have invariably shown the resistance to vary with V2. In the formula P = .005SV2, in which P = pressure in pounds, S = surface in square feet, V velocity in miles per hour, the doubtful question is that regarding the accuracy of the first two factors in the second member of this equation. The first factor has been variously determined from .003 to .005 [it has been determined as low as .0014.-Ed. Eng'g News]. The second factor has been found in some experiments with very short whirling arms and low velocities to vary with the perimeter of the plate, but this entirely disappears with longer arms or straight line motion, and the only question now to be determined is the value of the coefficient. Perhaps some of the best experiments for determining this value were tried in France in 1886 by carrying flat boards on trains. The resulting formula in this case was, for 44.5 miles per hour, p = .00535SV2. Mr. Crosby's whirling experiments were made with an arm 5.5 ft. long. It is certain that most serious effects from centrifugal action would be set up by using such a short arm, and nothing satisfactory can be learned with arms less than 20 or 30 ft. long at velocities above 5 miles per hour. Prof. Kernot, of Melbourne (Engineering Record, Feb. 20, 1894), states that experiments at the Forth Bridge showed that the average pressure on surfaces as large as railway carriages, houses, or bridges never exceeded two thirds of that upon small surfaces of one or two square feet, such as have been used at observatories, and also that an inertia effect, which is frequently overlooked, may cause some forms of anemometer to give false results enormously exceeding the correct indication. Experiments of Mr. O. T. Crosby showed that the pressure varied directly as the velocity, whereas all the early investigators, from the time of Smeaton onwards, inade it vary as the square of the velocity. Experiments made by Prof. Kernot at speeds varying from 2 to 15 miles per hour agreed with the earlier authorities, and tended to negative Crosby's results. The pressure upon one side of a cube, or of a block proportioned like an ordinary carriage, was found to be .9 of that upon a thin plate of the same area. The same result was obtained for a square tower. A square pyramid, whose height was three times its base, experienced .8 of the pressure upon a thin plate equal to one of its sides, but if an angle was turned to the wind the pressure was increased by fully 20%. A bridge consisting of two plate-girders connected by a deck at the top was found to experience .9 of the pressure on a thin plate equal in size to one girder, when the distance between the girders was equal to their depth, and this was increased by one fifth when the distance between the girders was |