GATE 2021 AE – Question 58
A combustor receives 100 kg/s air at 600 K with cp=1000 J/(kg K). Exhaust is 1200 K with cp=1200 J/(kg K), fuel heating value 40 MJ/kg and combustion efficiency 0.9. Fuel flow is ___ kg/s.
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Correct answer: 2.42 to 2.44
Explanation
**Energy balance on the combustor.** The heat released by the burning fuel (times the combustion efficiency) raises the enthalpy of the gas from 600 K (air) to 1200 K (exhaust). Reference the enthalpies to 0 K using the given $c_p$ values:
$$\dot m_a\,c_{p,a}T_{in}+\eta_b\,\dot m_f\,Q_f=(\dot m_a+\dot m_f)\,c_{p,e}T_{out}.$$
**Solve for $\dot m_f$:**
$$\dot m_f\left(\eta_bQ_f-c_{p,e}T_{out}\right)=\dot m_a\left(c_{p,e}T_{out}-c_{p,a}T_{in}\right)$$
**Numbers.**
- $c_{p,e}T_{out}=1200\times1200=1.44\times10^6$ J/kg
- $c_{p,a}T_{in}=1000\times600=6.0\times10^5$ J/kg
- $\eta_bQ_f=0.9\times40\times10^6=3.6\times10^7$ J/kg
$$\dot m_f=100\times\frac{1.44\times10^6-6.0\times10^5}{3.6\times10^7-1.44\times10^6}=100\times\frac{8.4\times10^5}{3.456\times10^7}=\mathbf{2.43\ kg/s}.$$