A rocket engine is tested on a test bed under the ideal condition of fully expended jet. The exhaust velocity is \(2\; km/s\) through a nozzle of area \(2.5\;m^{2}\). The mass flow rate is \(200 \;kg/s\). What is the specific impulse of the propellant and the thrust developed?
A rocket engine is tested on a test bed under the ideal condition of fully expended jet. The exhaust velocity is \(2\; km/s\) through a nozzle of area \(2.5\;m^{2}\). The mass flow rate is \(200 \;kg/s\). What is the specific impulse of the propellant and the thrust developed?
We need to find here thrust of the rocket engine and specific impulse.Thrust of the rocket engine is given as\[ T=\dot{m}V_{e}+\left ( P_{e}-P_{a} \right )A_{e} \]
Since the the rocket is tested under ideal condition of fully expanded jet the exhaust pressure will be equal to the ambient pressure that is \(P_{e}=P_{a}\)
\[\Rightarrow T=\dot{m}V_{e}\]
\[\\\Rightarrow T=200\times 2\]
\[\\\Rightarrow T=400\;kN\]
Specific impulse is given as \[I_{_{sp}}=\frac{T}{\dot{m}g}\]
\[\\\Rightarrow I_{_{sp}}=\frac{400\times 10^{3}}{200\times 9.81}\]
\[=203.87\;s\]
Therefore thrust and specific impulse are 400 kN and 203.87 s.
