(Solved): 1. Two Pratt \& Whitney J58 turbojet engines were used to power the Lockheed SR-71 Blackbird aircr ...

1. Two Pratt \& Whitney J58 turbojet engines were used to power the Lockheed SR-71 Blackbird aircraft. Let us here consider one engine only. Suppose during take-off the engine consumes \( 31,000 \mathrm{~L} / \mathrm{h} \) (liter/hour) of JP 7 jet fuel and operates at a \( \dot{m}_{f u e l} / \dot{m}_{\text {air }} \) (fuel-to-air ratio) \( 0.034 \). The density \( \rho_{\text {fuel }} \) of JP7 jet fuel is \( 0.8 \mathrm{~kg} / \mathrm{L} \). The flight speed \( V_{\infty}=102 \mathrm{~m} / \mathrm{s} \), and the exhaust gas speed after the engine \( V_{j}=722 \mathrm{~m} / \mathrm{s} \). (1) Transfer the fuel consumption volume flow rate \( \dot{v}_{\text {fuel }}=31,000 \mathrm{~L} / \mathrm{h} \) to \( \dot{v}_{f u e l} \) in L/second (2) Calculate the fuel mass flow rate \( \dot{m}_{f u e l} \) from the expression \( \dot{m}_{f u e l}=\dot{v}_{\text {fuel }} \rho_{\text {fuel }} \) (3) Using the following equation (in which the thrust due to the change of gas pressure before and after the engine is ignored) \[ T=\left(\dot{m}_{\text {air }}+\dot{m}_{f u e l}\right) V_{j}-\dot{m}_{a i r} V_{\infty} \] Find the thrust generation given \( \frac{\dot{m}_{\text {fuel }}}{\dot{m}_{\text {air }}}=0.034 \). (4) Estimate the engine propulsive efficiency at this velocity ratio, using \[ \eta=\frac{2}{1+V_{j} / V_{\infty}} \] \[ \eta=\frac{2}{1+V_{j} / V_{\infty}}=\frac{2}{1+722 / 102}=24.8 \% \] Note this is a really low propulsive efficiency, occurs during take-off. A typical value of propulsive efficiency of a turbojet engine of an aircraft during cruising can be around 0.7.