A spherical balloon is 5 m in diameter and is filled with a noncombustible gas where R = 386 ft-lbf/lbm(deg)R. If the atmosphere is at 14.7 psia, and the gas in the balloom is at the same temperature as the atmosphere, 70 deg. F,
Work:
Ta = temperature of atmosphere = 70 deg. F
Pa = pressure of atmosphere = 14.7 psia = 2,116 lbf/ft^2
Tg = temperature of gas = 70 deg. F
Rg = 386 ft-lbf/lbm(deg)R
Lift force L = -(integral)g(ROg - ROa)*z*dV, where ROg = density of gas, ROa = density of atmosphere, V = volume of the gas, g = gravitational constant, and z = diameter of the balloom
V = (4/3)*pi*r^3 = (1.33)*(3.14)*(8.2 ft)^3 = 2,302.6 ft^3
g = 32 ft/s^2
d = diameter of balloon = 5 m = 16.4 ft
r = 2.5 m = 8.2 ft
ROa = P/RT, where P = pressure of atmosphere
ROa = (2,116 lbf/ft^2)/[R*70(deg)F]
ROg = Pg/RgTg where Pg = pressure of gas
ROg = Pb/(386 ft-lbf/[lbm(deg)R*70(deg)F]
Solution