Question

A spherical balloon is 40 ft in diameter and surrounded by air at 60 0F and

29.92 in Hgabs. If the balloon is filled with hydrogen at a temperature of 70

0Fand atmospheric pressure, what total load can it lift? R of hydrogen is

766.54 ft-lbf/lbm-R. (2381 lb)

Answer 1

We know that

$T=60F=60+460=520R$

$d=40ft$

$$V=\frac{4}{3}\times\pi r^3=\frac{4}{3}\times3.14\times20^3=33510.32ft^3$$

$P=29.92 inHg abs$

$PV=mRT$

$m_{air}=\frac{PV}{RT}$

$$m_{air}=\frac{29.92\times33510.32}{766.54\times520}=2557.4201lb$$

Pul value solve it

$$m_{air}=2557.4201lb$$

$M_{H}=174.6014lb$

Now $M_{lift}=m_{air}-M_{H}$

$$M_{lift}=2557.4201-174.6014=2382.8187lb$$