Weights of Air, Vapor of Water, and Saturated Mixtures of Air and Vapor at Different Temperatures, under the Ordinary Atmospheric Pressure of 29.921 inches of Mercury. The weight in lbs. of the vapor mixed with 100 lbs. of pure air at any given temperature and pressure is given by the formula where E = elastic force of the vapor at the given temperature, in inches of mercury; p= absolute pressure in inches of mercury, = 29.92 for ordinary atmospheric pressure. Specific Heat of Air at Constant Volume and at Constant Pressure.-Volume of 1 lb. of air at 32° F. and pressure of 14.7 lbs. per sq. in. 12.387 cu. ft. = a column 1 sq. ft. area X 12.387 ft. high. Raising temperature 1° F. expands it or to 12.4122 ft. high-a rise of .02522 foot. 1 491.2' Work done = 2116 lbs. per sq. ft. x .02522 = 53.37 foot-pounds, or 53.37÷778 = .0686 heat units. The specific heat of air at constant pressure, according to Regnault, is 0.2375; but this includes the work of expansion, or .0686 heat units; hence the specific heat at constant volume = 0.2375 .0686 = 0.1689. Ratio of specific heat at constant pressure to specific heat at constant volume = .2375+.1689 1.406. (See Specific Heat, p. 458.) Flow of Air through Orifices.-The theoretical velocity in feet per second of flow of any fluid, liquid, or gas through an orifice is v = W2gh 8.02 Vh, in which h = the "head" or height of the fluid in feet required to produce the pressure of the fluid at the level of the orifice. (For gases the formula holds good only for small differences of pressure on the two sides of the orifice.) The quantity of flow in cubic feet per seeond is equal to the product of this velocity by the area of the orifice, in square feet, multiplied by a "coefficient of flow," which takes into account the contraction of the vein or flowing stream, the friction of the orifice, etc. For air flowing through an orifice or short tube, from a reservoir of the pressure p, into a reservoir of the pressure p2. Weisbach gives the following values for the coefficient of flow, obtained from his experiments. Diameter 1 centimetre. Diameter 2.14 centimetres Diam. 1 cm., Length 3 cm. Diam. 1.414 cm., Length 4.242 cm. Diam. 1 cm., Length 1.6 cm. Orifice rounded. FLOW OF AIR THROUGH AN ORIFICE. Coefficient c in formula v = c √/2gh. Ratio of pressures p1÷p, 1.05 1.09 1.43 1.65 1.89 2.15 Ratio of pressures........ 1.05 1.09 1.36 1.67 2.01 FLOW OF AIR THROUGH A SHORT TUBE. Ratio of pressures p1+p, 1.05 1.10 1.30 Ratio of pressures. .730 .771 .830 1.41 1.69 .... .... Ratio of pressures........ 1.24 1.38 1.59 1.85 2.14 Coefficient... ........... FLIEGNER'S EQUATION FOR FLOW OF AIR FROM A RESERVOIR THROUGH AN ORIFICE. (Proc. Inst. C. E., lv, 379.) G = the flow in kilogrammes per second; P1Po the internal and external pressures in atmospheres of 10,000 kg. per sq. metre; D = diameter of the orifice in metres; Fits cross-section in sq. metres; T= absolute temperature, Centigrade, of the air in the reservoir. The experiments were made with six orifices from 3.17 to 11.36 mm. diameter, in brass plates 12 mm. thick, drilled cylindrically for about 2 mm., and conically enlarged towards the outside at an angle of 45°. Clark (Rules, Tables, and Data, p. 891) gives, for the velocity of flow of air through an orifice due to small differences of pressure, in which V= velocity in feet per second; 2g = 64.4; h = height of the column of water in inches, measuring the difference of pressure; t = the temperature Fahr.; and p = barometric pressure in inches of mercury. 773.2 is the volume of air at 32° under a pressure of 29.92 inches of mercury when that of an equal weight of water is taken as 1. For 62° F., the formula becomes V = 363C 66.35C Vh and if p 29.92 inches V = The coefficient of efflux C, according to Weisbach, is: with pressures of from .23 to 1.1 atmospheres.. Circular orifices in thin plates.. Short cylindrical mouthpieces.. ..... The same rounded at the inner end Conical converging mouthpieces.. C.97 to .99 C.56 to .79 C.81 to. C.92 to .93 C.90 to .93 Flow of Air in Pipes.-Hawksley (Proc. Inst. C. E.. xxxiii, 55) HD states that his formula for flow of water in pipes v = 48 VI may also be employed for flow of air. In this case H = height in feet of a column of air required to produce the pressure causing the flow, or the loss of head for a given flow; v = velocity in feet per second, D = diameter in feet, L= length in feet. If the head is expressed in inches of water, h, the air being taken at 62 F., its weight per cubic foot at atmospheric pressure = .0761 lb. H= 62.36 .0761 x 12 becomes v = 114.5 68.3h. If d = diameter in inches, D = Then and the formula 12' hd in which h inches of water column, d = diam. The horse-power required to drive air through a pipe is the volume Q in cubic feet per second multiplied by the pressure in pounds per square foot and divided by 550. Pressure in pounds per square foot Pinches of water column X 5.196, whence horse-power = If the head or pressure causing the flow is expressed in pounds per square inch = p, then h = 27.71p, and the above formulæ become Volume of Air Transmitted in Cubic Feet per Minute in Pipes of Various Diameters. 2 3 4 6 7 15 28 p. sec of Flow JOHURUTERA | Feet | Veloc'y 8.18 32.7 73 24 7.85 31.4 71 125 196 283 In Hawksley's formula and its derivatives the numerical coefficients are constant. It is scarcely possible, however, that they can be accurate except within a limited range of conditions. In the case of water it is found that the coefficient of friction, on which the loss of head depends, varies with the length and diameter of the pipe, and with the velocity, as well as with the condition of the interior surface. In the case of air and other gases we have, in addition, the decrease in density and consequent increase in volume and in velocity due to the progressive loss of head from one end of the pipe to the other. Clark states that according to the experiments of D'Aubuisson and those of a Sardinian commission on the resistance of air through long conduits or pipes, the diminution of pressure is very nearly directly as the length, and as the square of the velocity and inversely as the diameter. The resistance is not varied by the density. If these statements are correct, then the formulæ h = Lv2 and h = Q2L c'do and their derivatives are correct in form, and they may be used when the numerical coefficients c and c' are obtained by experiment. If we take the forms of the above formulæ as correct, and let C be a vari able coefficient, depending upon the length, diameter, and condition of sur face of the pipe, and possibly also upon the velocity, the temperature and the density, to be determined by future experiments, then for h = head in inches of water, d = diameter in inches, L= length in feet, v = velocity in feet per second, and Q = quantity in cubic feet per second: For difference or loss of pressure p in pounds per square inch, d = 1213Q2L 12130 L L (For other formulæ for flow of air, see Mine Ventilation.) Loss of Pressure in Ounces per Square Inch.-B. F. Sturte vant Company uses the following formulæ : in which p1 = loss of pressure in ounces per square inch, v velocity of air in feet per second, and L = length of pipe in feet. If p is taken in pounds per square inch, these formulæ reduce to These are deduced from the common formula (Weisbach's), p = which f .0001608. The following table is condensed from one given in the catalogue of B. F. Sturtevant Company. Loss of pressure in pipes 100 feet long, in ounces per square inch. For any other length, the loss is proportional to the length. 600 .400 200 .133 .100 1200 1.600 .800 .533 1800 3.600 1.800 1.200 3000 10. 5. 3.333 2.5 2. 3600 14.4 7.2 4.8 3.6 4200 .080 067 .057 .050 .044 .400 .320 .267 .229 .200 .178 .160 .900 .720 .600 .514 .450 .400 .360 2400 6.400 3.200 2.133 1.600 1.067 .914.800 .711 .640 1.667 1.429 1.250 1.111 1.000 2.4 2.0571.8 3.267 2.8 .909 .833 .029 .026 .020 .018 1200 .114 .100 .080 .073 1800 .257 .225 .200 .180 .164 2400 .457 .400 .356 .320 .291 3600 1.029 .900 .800 .720 .655 4200 1.400 1.225 1.089 .980 .891 4800 1.829 1.600 1.422 1.280 1.164 1.067 .914.800 .711 .640 .582 .533 6000 2.857 2.500 2.222 2.000 1.818 1.667 1.429 1.250 1.111 1.000 .909 .833 .445 .408 Effect of Bends in Pipes. (Norwalk Iron Works Co.) Radius of elbow, in diameter of pipe = 5 3 2 11% 114 1 3/4 1/2 Equivalent lgths. of straight pipe, diams 7.85 8.24 9.03 10.36 12.72 17.51 35.09 121.2 Compressed-air Transmission. (Frank Richards, Am. Mach., March 8, 1894.)-The volume of free air transmitted may be assumed to be directly as the number of atmospheres to which the air is compressed. Thus, if the air transmitted be at 75 pounds gauge-pressure, or six atmospheres, the volume of free air will be six times the amount given in the table (page 486). It is generally considered that for economical transmission the velocity in main pipes should not exceed 20 feet per second. In the smaller distributing pipes the velocity should be decidedly less than this. The loss of power in the transmission of compressed air in general is not a serious one, or at all to be compared with the losses of power in the operation of compression and in the re-expansion or final application of the air. The formulas for loss by friction are all unsatisfactory. The statements of observed facts in this line are in a more or less chaotic state, and selfevidently unreliable. A statement of the friction of air flowing through a pipe involves at least all the following factors: Unit of time, volume of air, pressure of air, diameter of pipe, length of pipe, and the difference of pressure at the ends of the pipe or the head required to maintain the flow. Neither of these factors can be allowed its independent and absolute value, but is subject to modifications in deference to its associates. The flow of air being assumed to be uniform at the entrance to the pipe, the volume and flow are not uniform after that. The air is constantly losing some of its pressure and its volume is constantly increasing. The velocity of flow is therefore also somewhat accelerated continually. This also modifies the use of the length of the pipe as a constant factor. Then, besides the fluctuating values of these factors, there is the condition of the pipe itself. The actual diameter of the pipe, especially in the smaller sizes, is different from the nominal diameter. The pipe may be straight, or it may be crooked and have numerous elbows. Mr. Richards considers one elbow as equivalent to a length of pipe. |