A Centaur upper stage rocket used in the Atlas V Launch System has a liquid hydr

Question

A Centaur upper stage rocket used in the Atlas V Launch System has a liquid hydrogen fuel tank with a volume of 1706 ft3 of hydrogen that has a mass of 3419 kg. Calculate: the weight of the fuel at standard (Earth) sea level conditions in N and lbf; the density of the fuel in kg/m3 , and the specific volume in ft3 /lbm (note, lbm=poundmass, which is not the same as a lbf or a slug).

1. Weight/Mass/Density A Centaur upper stage rocket used in the Atlas V Launch System has a liquid hydrogen fuel tank with a volume of 1706 ft3 of hydrogen that has a mass of 3419 kg. Calculate: the weight of the fuel at standard (Earth) sea level conditions in N and lbr, the density of the fuel in kg/m3, and the specific volume in ft3lbm (note, Ibm-pound- mass, which is not the same as a lbr or a slug).

Explanation / Answer

Weight = mg .....where g is the gravitational acceleration. At sea level, g = 9.81 m/s2 = 32.2 ft/s2

Weight = 3419 * 9.81

Weight = 33540.4 N

Since 1 kg = 2.205 lbm, we get m = 3419 kg = 3419 * 2.205 lbm = 7537.6 lbm

Since 1 slug = 32.2 lbm we get

m = 7537.6 / 32.2 slug = 234.09 slug

Weight in lbf = 234.09 * 32.2 = 7537.6 lbf

Volume V = 1706 ft3

Since 1 ft = 0.3048 m, we get V = 1706 * 0.30483 m3 = 48.3085 m3

Density = m / V

= 3419 / 48.3085

= 70.774 kg/m3

Specific volume = V / m

= 1706 / 7537.6

= 0.226 ft3/lbm

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