Nozzle Theory and Thermodynamics Questions and Answers

Answer: B

The answer is combustion chamber and nozzle throat.

The static temperature is highest in the combustion chamber, where the gas is nearly at rest and holds its full stagnation temperature. As the gas accelerates through the nozzle, static temperature falls.

Heat flux to the wall is highest at the throat. The convective heat transfer coefficient scales roughly with mass flux \((\rho V)^{0.8}\), and the mass flux per unit area is greatest at the throat, the smallest cross-section, while the gas is still very hot. That is why throats need the most intensive cooling.

The nozzle exit has the lowest static temperature, and the nozzle throat is not the hottest region in the static sense, which rules out the other three pairs.

Answer: B

The thrust is highest when the rocket is operating in vacuum.

Rocket thrust is \(F = \dot{m}V_{e} + (p_{e} - p_{a})A_{e}\). For a given chamber pressure and nozzle, the mass flow, exit velocity and exit pressure are fixed, so the thrust depends only on the ambient pressure \(p_{a}\), and it is largest when \(p_{a} = 0\).

At its design altitude the nozzle is ideally expanded (\(p_{e} = p_{a}\)), which is the best that particular ambient pressure allows, but the thrust is still lower than in vacuum. At sea level the ambient pressure is highest, so thrust is lowest. A normal shock in the nozzle means a badly over-expanded nozzle with large losses.

Answer: A

The chamber pressure is 3600 kPa and the specific impulse 183.67 s, so the answer is 3600 and 183.67.

The characteristic velocity is defined by \(c^{*} = p_c A_t / \dot{m}\), so

\[ \begin{aligned} p_c &= \frac{c^{*}\dot{m}}{A_t} = \frac{1200 \times 75}{0.025} \\ &= 3.6 \times 10^{6}\ \text{Pa} = 3600\ \text{kPa} \end{aligned} \]

The effective exhaust velocity is \(c = C_F c^{*}\), and the specific impulse in seconds is that divided by g:

\[ \begin{aligned} I_{sp} &= \frac{C_F c^{*}}{g} = \frac{1.5 \times 1200}{9.8} \\ &= 183.67\ \text{s} \end{aligned} \]

The pair '3500 and 183.67' has the right impulse but a wrong pressure, '3600 and 175.23' the right pressure but a wrong impulse, and '4600 and 190.51' gets both wrong.