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1. Consider a rocket motor equipped with a nozzle in which the stagnation conditions are 3000 K and 60 atm. The specific heat ratio is 1.25 and the molecular weight of the propellant is 18. The nozzle throat diameter is 5 cm and the nozzle exit diameter is 30 cm. a. Calculate the exit velocity b. Calculate the exit pressure c. Calculate c* for this propellant d. Calculate the mass flow rate for the rocket e. If the rocket is fired at sea level, calculate the thrust. f. If the rocket is fired at sea level, calculate the thrust coefficient g. If the rocket is fired at sea level, calculate the effective exhaust velocity h. If the rocket is fired at sea level, calculate the specific impulse. i. If the rocket is fired in space, calculate the thrust. j. If the rocket is fired in space, calculate the thrust coefficient k. If the rocket is fired in space, calculate the effective exhaust velocity I. If the rocket is fired in space, calculate the specific impulse

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The Exit velocity and Pressure in the case of a rocket motor are 1290m/s and 8.1 atm respectively. The C* and thrust propellant calculations are based on certain formulas.

  • Exit velocity is v_e = sqrt((2 * C_p * 3000 K) / (1.25 - 1)) * sqrt((1.25 + 1) /  2) * (1 - (p_e / 60 atm) ^ ((1.25 - 1) / 1.25)) = 1290 m/s.

  • Exit pressure is p_e = 60 atm * ((2 / (1.25 + 1)) * (1 - (1290 m/s / sqrt((1.25 + 1) / 2 * C_p * 3000 K)) / (1 - (p_e / 60 atm) ^ ((1.25 - 1) / 1.25)))) ^ (1.25 /  (1.25 - 1)) = 8.1 atm. This is the pressure at the nozzle exit.

  • To calculate c* for the propellant, we can use the equation c* = sqrt(1.25 * 8.314 J/mol-K * 3000 K / 18) = 654.3 m/s.

  • To calculate the mass flow rate for the rocket, we find that m_dot = 60 atm * (pi * (5 cm / 2)^2 / 4) * 654.3 m/s / sqrt(3000 K) = 4.1 kg/s.

  • To calculate the thrust of the rocket, we can use the equation that F= 4.1 kg/s * 1290 m/s + (8.1 atm * (pi * (30 cm / 2)^2 / 4) - 60 atm * (pi * (5 cm / 2)^2 / 4)) = 45600 N. This is the thrust produced by the rocket at sea level.

  • To calculate the thrust coefficient of the rocket motor, we can use the equation  C_F = (2 / (1.25 + 1)) * (1 - (1290 m/s / sqrt((1.25 + 1) / 2 * C_p * 3000 K)) / (1 - (8.1 atm / 60 atm) ^ ((1.25 - 1) / 1.25))) = 0.8. This is the thrust coefficient of the rocket motor.

  • To calculate the effective exhaust velocity of the rocket motor, we can use the equation v_e, eff = v_e + g * Isp, where v_e, eff is the effective exhaust velocity, v_e is the exit velocity, g is the acceleration due to gravity, and Isp is the specific impulse. At sea level, g = 9.8 m/s^2.

  • The specific impulse of the rocket motor is given by the equation Isp = (1.25 * 8.314 J/mol * K * 3000 K) / (9.8 m/s^2 * 18 g/mol) = 279 s.

  • The effective exhaust velocity of the rocket motor is v_e, eff = 1290 m/s + 9.8 m/s^2 * 279 s = 36660 m/s. This is the effective exhaust velocity of the rocket motor when fired at sea level.

  • To calculate the thrust of the rocket motor, we can use the equation F = 8.1 atm * 28.3 cm^2 * 1290 m/s = 3.1 * 10^6 N.

  • To calculate the thrust coefficient, we can use the equation C_F = 3.1 * 10^6 N / (8.1 atm * 0.2 cm^2) = 0.16.

  • To calculate the effective exhaust velocity of the rocket motor when fired in space, we can use the equation  v_e = sqrt((2 * C_p * 3000 K) / (1.25 - 1)) * sqrt((1.25 + 1) / 2) * (1 - (0 / 60 atm) ^ ((1.25 - 1) / 1.25)) * sqrt(1 - ((18 / 18) ^ 2)) = 1290 m/s.

  • To calculate the specific impulse of the rocket motor, we can use the equation I_sp = 1290 m/s / 9.8 m/s^2 = 131 s. This is the specific impulse of the rocket motor when fired in space.

Learn more about Stagnation Conditions here:

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