The Altas V rocket has been used by NASA to launch important payloads such as th

Question

The Altas V rocket has been used by NASA to launch important payloads such as the Mars Science Labratory in Novemeber 2011. The first-stage engine of the Atlas V rocket is usually fueled by Rocket-Propellant-1 (RP-1) which is a highly refined form of kerosene. Kerosene, a mixture of hydrocarbons, has a density between 0.78 to 0.81 g/mL, and a fuel ranging from 43.1 kJ/g to 46.2 kJ/g, depending on the exact composition.

At full throttle, the Atlas V engine must generate 20 gigawatts (2.0x 1010 J/s) of powerr. If a kerosene-based fuel has a density of 0.80 g/ML and a fuel value of 45.2 kJ/g, how rapidly must the kerosene be supplied to and completely burned in the engine? Aussme the engine is 50% efficient at converting the chemical energy available from the comvustion into the mechianical energy associated with the thrust lifting the rocket into space.

____ L/s

Explanation / Answer

Density of kerosene = 0.8 g/ml= 0.8*1000 g/Liter =800 g/L=

let the flow rate of Kerosene = x l/s

Mass flow rate= 800 g/L * x L/s =800x g/s =(800/1000) kg/s *x=0.8 kg/s x

Power to be generated by Engine = 20 gigawatts= 2*1010 J/s

But the engine is 50% efficient hence power to be generated = 2*1010/0.5= 4*1010 J/s

calorific value = 45.2 J/kg

Required flow rate of Kerosene = 4*1010 j/s / 45.2 j/kg =884955752 kg/s

but Required flow rate of kerosene =0.8x =884955752

x= 1106194690 L/s

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