Blimps Ahoy! A blimp\'s and it\'scargo have mass m = 780 kg. Lift for the blimp

Question

Blimps Ahoy! A blimp's and it'scargo have mass m = 780 kg. Lift for the blimp is provided by gas inside the blimp's envelope(the baloon part). Assume the gas in the baloon is at the samepressure at the air outside (atmospheric pressure). And the blimp is flying very close to sea level. The density of air is p_air = 1.22 kg/m^3 What volume of hydrogen gas(pH_2 = 0.09 kg/m^3) would provide the buoyant force required to maintaine a constant altitude? Recall that hydrogen forms a diatomic molecule. What volume of belium gas(pH_e = 0.178kg/m^3) would provide this buoyant force?

Explanation / Answer

THe force needed is 780*g N

F = 780 * 10 = 7800 N

we know that the buoyant force is given by the weight of the displacecd air.

THe differential density of air and filled gas be

Density difference = 1.22 - 0.09 = 1.13 kg/m^3

Hence the the volume be

V *density = 780

V = 780 /1.13 = 690 m^3

And for helium

Difference = 1.22 - 0.178 = 1.042 kg/m^3

Hence the volume for He will be

V = 780/1.042 = 748 m^3

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