Hydrogen Rocket

The reaction chamber of a rocket engine is supplied with a mass flow rate m of hydrogen and sufficient oxygen to allow complete burning of the fuel. The cross section of the chamber is A, and the pressure at the cross section is P with temperature T. Calculate the force that this chamber is able to provide.

SOLUTION

Find the amount of water vapor produced in the reaction

(1)

One mole of hydrogen yields one mole of water, or in mass

(2)

Since m is the mass of fuel intake per second, m' = 9m is the mass of water ejected from the engine per second. If the water vapor density is ρ, this rate may be expressed as

(3)

where v is the velocity of the gas ejected from the engine. Therefore,

(4)

Express the density as

(5)

From (4) and (5), we then have

(6)

The mass ejected per second from the engine provides the momentum per second m'v, which will be equal to the force F_r = m'v supplied by the engine. Apart from this reactive force, there is a static pressure from the engine providing a force F_s = PA, so the total force

(7)

In real life the second term is usually small (P is not very high), so the force by an engine is determined by the reactive force.