GATE 2023 AE – Question 61
A methane–air combustor operates at equivalence ratio $\phi=(F/A)/(F/A)_{stoich}=0.5$, with air flow 20 kg/s. Methane flow (kg/s, two decimal places) is _____.
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Correct answer: 0.57 to 0.59
Explanation
**Stoichiometric methane-air combustion** (air as $O_2+3.76N_2$):
$$CH_4+2(O_2+3.76N_2)\to CO_2+2H_2O+7.52N_2 .$$
**Stoichiometric air-fuel ratio by mass.**
- Fuel: 1 kmol of $CH_4$ is 16 kg.
- Air: $2$ kmol of $O_2$ is 64 kg, and $7.52$ kmol of $N_2$ is $7.52\times28=210.6$ kg; total 274.6 kg.
$$\left(\frac AF\right)_{st}=\frac{274.6}{16}=17.16 .$$
**Equivalence ratio.** $\phi=\dfrac{(F/A)}{(F/A)_{st}}=0.5$, so $F/A=0.5/17.16=0.02913$.
**Fuel flow** for 20 kg/s of air:
$$\dot m_f=0.02913\times20=\mathbf{0.58\ kg/s}.$$