Question

An ideal turbofan with a bypass ratio of 5 has core mass flow rate, \( \dot{m}_a,c = 100 \, {kg/s} \). The core and the fan exhausts are separate and optimally expanded. The core exhaust speed is 600 m/s and the fan exhaust speed is 120 m/s. If the fuel mass flow rate is negligible in comparison to \( \dot{m}_a,c \), the static specific thrust (\( \frac{T}{\dot{m}_a,c} \)) developed by the engine is \_\_\_\_\_\_\_ Ns/kg (rounded off to the nearest integer).

Hint:

The static specific thrust is the difference between the exhaust velocity and free-stream velocity, normalized by the core mass flow rate.

Answer 1

Given Parameters Bypass ratio (BPR) = 5 \( \dot{m}_{a,c} = 100 \, {kg/s} \) \( \dot{m}_{a,f} = {BPR} \times \dot{m}_{a,c} = 5 \times 100 = 500 \, {kg/s} \) Core exhaust speed \( V_{e,c} = 600 \, {m/s} \) Fan exhaust speed \( V_{e,f} = 120 \, {m/s} \) Inlet speed \( V_0 = 0 \, {m/s} \) (static condition) \end{itemize} Step 1: Total Thrust \[ T = \dot{m}_{a,c} (V_{e,c} - V_0) + \dot{m}_{a,f} (V_{e,f} - V_0) \] \[ T = 100 \times 600 + 500 \times 120 = 120000 \, {N} \] Step 2: Static Specific Thrust \[ \frac{T}{\dot{m}_{a,c}} = \frac{120000}{100} = 1200 \, {N·s/kg} \] Final Answer \[ \boxed{1200} \]