In a turbofan engine, the core mass flow rate is $\dot{m}_{core} = 25\text{ kg/s}$ and the bypass mass flow rate is $\dot{m}_{fan} = 150\text{ kg/s}$. If core jet exit velocity is $V_c = 450\text{ m/s}$ and bypass fan exit velocity is $V_f = 280\text{ m/s}$ at flight speed $V_0 = 180\text{ m/s}$, what is the total net thrust in kilonewtons (kN)?

Answer Key:

21.75

### Solution: Bypass ratio BPR = $150 / 25 = 6$. Core net thrust $F_{core} = \dot{m}_{core}(V_c - V_0) = 25(450 - 180) = 25 \times 270 = 6750\text{ N} = 6.75\text{ kN}$. Bypass net thrust $F_{fan} = \dot{m}_{fan}(V_f - V_0) = 150(280 - 180) = 150 \times 100 = 15000\text{ N} = 15.0\text{ kN}$. Total net thrust $F_{total} = 6.75 + 15.0 = 21.75\text{ kN}$. Correct: 21.75.

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