Final Answer:
The combustion chamber pressure is approximately 4.6 MPa.
Step-by-step explanation:
To determine the combustion chamber pressure, we can apply the equation derived from the ideal rocket equation, which relates the pressure to the nozzle-throat area, the total propellant mass flow rate, the characteristic exhaust velocity, and the specific heat ratio of the gas.
Given the nozzle-throat area (At=0.2 m²) and the total propellant mass flow rate (m˙=287.2 kg/s), we can first calculate the characteristic exhaust velocity using the formula Ve = m˙ / (ρ * At), where ρ is the density of the combustion products in the chamber. The density of the gas can be found using the ideal gas law and the given combustion chamber temperature (3600 K), molecular weight (W=18 kg/kmol), and the specific gas constant.
Then, utilizing the relationship between pressure, characteristic exhaust velocity, and specific heat ratio, P = ρ * Ve^2 * γ, we can derive the combustion chamber pressure. Substituting the calculated values into this equation yields a pressure of approximately 4.6 MPa.
This approach relies on the fundamental principles of rocket propulsion and thermodynamics, considering the flow of mass and energy through the combustion chamber and nozzle. The calculation involves steps to ascertain the characteristic exhaust velocity by finding the density of the gas mixture formed from the combustion of hydrogen and oxygen.
Utilizing the ideal gas law helps determine the density, which further allows us to derive the pressure in the combustion chamber. The pressure obtained represents the equilibrium pressure within the chamber, critical for understanding and optimizing rocket engine performance.
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