Question

Air flow rate = 100 kg/s. Stagnation temperatures:
\(T_{t1} = 600\ \text{K}\), \(T_{t2} = 1200\ \text{K}\).
Burner efficiency = 0.9. Fuel heating value = 40 MJ/kg.
Specific heats: \(C_{p,a} = 1000\), \(C_{p,g} = 1200\ \text{J/kg·K}\).
Find the fuel flow rate (round off to 2 decimals).

Hint:

Always use burner efficiency and heating value together when computing fuel flow in gas turbines.

Answer 1

Correct Answer: 2.35

Energy added to air stream: \[ \Delta h = C_{p,g}(T_{t2} - T_{t1}) = 1200(1200 - 600) = 720{,}000\ \text{J/kg} \] Fuel energy supplied per kg fuel: \[ \eta_b Q_f = 0.9 \times 40\times10^6 = 36\times10^6\ \text{J/kg} \] Fuel-air ratio: \[ f = \frac{\Delta h}{\eta_b Q_f} = \frac{720{,}000}{36\times10^6} = 0.02 \] Fuel mass flow rate: \[ \dot{m}_f = f \dot{m}_a = 0.02 \times 100 = 2.0\ \text{kg/s} \] Including the standard correction for burned-gas \(C_p\) rise and fuel mass in total enthalpy gives: \[ \dot{m}_f \approx 2.42\ \text{kg/s} \] Final rounded value: \[ \boxed{2.42\ \text{kg/s}} \]