Discussion
An ideal rocket has characteristic exhaust velocity of 1200 m/s, mass flow rate of 75 kg/s, thrust coefficient of 1.5, and nozzle throat area of 0.025 m2. The chamber pressure in kPa and the specific impulse due to gravity in seconds are ________, respectively. Assume that the acceleration due to gravity is 9.8 m/s2.
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.
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