Question

A modern-day zeppelin holds 7,490 m3 of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.)

Answer 1

The buoyant force is

$$F_b=\rho_{air} g V$$

The weight of the helium:

$$W=\rho_{He} g V$$

The maximum payload at sea level:

$$F=F_b-W=(\rho_{air}-\rho_{He}) g V$$

$$F=(1.22-0.18)(9.81)(7490)=76400N=76.4 kN$$