If the divergence angle for a conical nozzle is 30°, nozzle exit diameter is 30 cm, exit pressure is 10% more than the ambient pressure, mass flow rate is 14 kg/s and the jet exhaust velocity is 700 m/s, determine the total thrust of the engine under standard sea level operating conditions.

If the divergence angle for a conical nozzle is 30°, nozzle exit diameter is 30 cm, exit pressure is 10% more than the ambient pressure, mass flow rate is 14 kg/s and the jet exhaust velocity is 700 m/s, determine the total thrust of the engine under standard sea level operating conditions. Correct Answer 10.3 kN

Total thrust = Corrected momentum thrust + Pressure thrust Ttot = λTmom + Tpres λ = 1/2 (1 + cosα) α = 1/2 x 30° = 15° So, λ = 1/2 (1 + 0.966) = 0.983 Tpres = (Pe – Pa)Ae Since the operation is under standard sea level conditions, Pa = 101325 Pa. Pe = 110% of Pa. So Pe – Pa = 10% of Pa = 10132.5 Pa Ae = π de2/4 = 0.071 ∴ Tpres = 10132.5 x 0.071 = 719.075 N Tmom = μe = 14 x 700 = 9800 N So Ttot = (0.983 x 9800) + 719.075 ≅ 10.3 kN.