I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
248
Nomenclature a, b, c, Ao,Bo =
Beattie-Bridgeman constants, for P in atmospheres and Ti in liters/mole IC, E, m = coefficients in Equation 2, dependent only on temperature for a given gas A , B , C, D,E , P , G = coefficients in Equaiion 6, independent of T , and P , P = pressure, atmospheres P , = critical pressure P, = reduced pressure R = molar gas conEtant, liter-atmospheres/’ K. T = temperature, K. T o = critical temperature T, = reduced temperature V = volume, liters/mole
p,
Vol. 33, No. 2
virial coefficients of Beattie-Bridgeman equation which are functions of T only for a given gas y = activity coefficient of a gas = fugacity/pressure Yoalcd. = calculated activity coefficients y . ~ = activity coefficients read from Newton’s curves YB, 6 =
Literature Cited (1) Beattie, Proc. N a t l . Acad. Sci., 16, 14 (1930). (2) Deming and Shupe, J . A m . Chem. Soc., 52, 1382 (1930). (3) International Critical Tables, Vol. 111, p. 248, New York, Mc-
Graw-Hill Book Co., 1928. (4) Maron and Turnbull, IND.EKG.CHEM.,33, 69 (1941). (5) Newton, Ibid., 27, 302 (1035).
PRESENTED before t h e Division of Industrial and Engineering Chemistry a t the 100th Meeting of the American Chemical Society, Detroit, hIich.
NOMOGRAPH FOR EQUIVALENT DIAMETERS OF ANNULI
I
N CONNECTION with the design of
double-pipe coolers, calculation of the film coefficient of the fluid flowing in the annular space is made by means of the Dittus-Boelter equation1,
-’
h = 0.0225 ;(D;
)o,a(%)Q.4
intended for turbulent flow inside clean round pipes where D is the inner diameter of the pipe, in feet. I n the case of an annulus D should be the equivalent diameter, defined as 4 times the hydraulic radius, which is the area of the annulus divided by the perimeter of the heating surface. The outer surface of the inner pipe is usually the heating surface and so the equivalent diameter, D , i n feet, is given by Di - Df -~ D = 4 lr (Di - 0;) 4 T Di (12) 12 Di where Dz and D1 are the inner diameter of the outer pipe and the outer diameter of the inner pipe, respectively, in inches. Since standard iron pipe is usually used in consbructing double-pipe coolers, it is convenient t o calculate the equivalent diameter in terms of the nominal rather than the actual diameter. The nomograph facilitates this computation, and its use is illustrated by the broken lines. What is the equivalent diameter of t h e annulus between I- and 2-inch standard iron pipes? Following the key, connect 2 on the D2 scale with 1 on the left-hand D lscale and note the intersection with the a axis. Follow the guide lines t o the p axis and connect the point so found with 1 on the right-hand Dl scale, reading the equivalent diameter as 0.162 foot on the D scale. Dittus and Boeiter, Unzv Calif. Pub. Eng , 2, 443 McAdams, “Heat Tiansmission”, p 169 (1933) and “Elements of Chemical Engineering“, p. 134 (1936),New York, MoGraw-Hill Book Company 1
(1930) ;
D. S. DAVIS Wayne University, Detroit, Mich.
