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I am studying rocketry and am currently learning about pump fed vs gas pressure fed propulsion systems.

Upon reading about gas pressure systems, I googled the formula to find the chamber pressure for gas pressure fed systems but did not find the formula. What is it?

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Unfortunately there is no simple equation to calculate the chamber pressure.

One major complication is that the chamber temperature depends on the chemical reaction rate of the propellants, which is a function of the temperature, making it an iterative process. See How do you determine what the temperature will be in the combustion chamber of a rocket engine?

Sutton, 4th edition, p.181 sums up the process as follows

The combustion chamber conditions (such as chamber temperature and gas composition) can be calculated by using the conditions of mass balance (Equation 6-9), the pressure balance (Equation 6-10), several chemical equilibrium conditions (Equation 6-8), and the energy balance (Equation 6-11) and by simultaneously solving these equations (see Reference 6-2, 6-3, or 6-4). The assumptions listed in Chapter 3 for an ideal rocket apply here also. Complete combustion is postulated, that is, all the propellant is reacted into suitable products, The materials introduced as propellant are transformed adiabatically and irreversibly to certain presumed reaction product constituents in the amounts fixed by equilibrium coefficients, total pressure, and mass balance at a temperature fixed by the available energy of reaction. The unknowns in these equations are the chamber temperature T, and the molar fractions n, of each of the f constituents in the reaction product gases: thus the number of independent equations must equal f + 1.

This process is fundamentally the same regardless of whether the engine is pump- or pressure-fed.

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