GATE 2022 AE – Question 34
In a static test, a turbofan engine with bypass ratio of 9 has core hot exhaust speed 1.5 times that of fan exhaust speed. The engine is operated at a fuel to air ratio of f= 0.03. Both the fan and the core streams have no pressure thrust. The ratio of fan thrust to thrust from the core engine is _____ (round off to one decimal place).
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Correct answer: 5.77 to 5.83
Explanation
**Thrust from each stream** with no pressure thrust: $F=\dot m\,V_{exit}$ (static test, so the incoming velocity is zero). Let the core air mass flow be $\dot m_a$.
- **Bypass ratio 9:** the fan air flow is $9\dot m_a$.
- **Fuel-air ratio 0.03:** the core gas flow is $(1+0.03)\dot m_a=1.03\dot m_a$ (air plus fuel).
- **Speeds:** the core exhaust speed is 1.5 times the fan exhaust speed, $V_c=1.5V_f$.
**Fan thrust:** $F_f=9\dot m_a\,V_f$.
**Core thrust:** $F_c=1.03\dot m_a\,(1.5V_f)=1.545\,\dot m_aV_f$.
$$\frac{F_f}{F_c}=\frac{9}{1.545}=5.83\approx\mathbf{5.8}.$$