#### Sample Problems on Jet Propulsion with Solutions

**Problem 1:**

A German turbo-jet uses petrol having a calorific value of 4.184 x 10^{4}(kJ/kg). The fuel consumption is 0.1427 (kg/N) of thrust when the thrust is 8829 (N). The aircraft velocity is 425 (m/sec) and the weight of air passing through the compressor is 19.5 (kg/sec). Calculate the air fuel ratio and overall efficiency.

**Given Data:**

Calorific Value of fuel CV_{f} = 4.184 x 10^{4} kJ/kg

Thrust Force TF = 8829 N

Thrust Specific Fuel Consumption = 0.1427 kg/N

Velocity of the aircraft V_{aircraft} = 425 m/sec

Mass flow rate of air ṁ_{a} = 19.5 kg/sec

**Required:**

Calculate air fuel ratio and overall efficiency.

**Solution:**

We have the following relation for thrust specific fuel consumption TSFC i.e.

**TSFC = fuel flow rate ṁ _{f} (kg/hr)/Thrust force TF(N)**

ṁ_{f} (kg/hr) = TSFC x Thrust Force TF

ṁ_{f} (kg/hr) = 1259.89

**ṁ _{f }= 0.35 kg/sec**

**Air to fuel ratio = ṁ _{a}/ ṁ_{f }= 19.5/0.35 = 55.71**

Overall efficiency **η _{0}** = propulsive efficiency

**η**x thermal efficiency

_{P}**η**

_{th}Propulsive efficiency **η _{P}** = Thrust Power

**TP**/ Propulsive Power

**PP**

Thrust Power **TP** = Thrust Force **TF** x Velocity of the aircraft **V _{aircraft}**

**Thrust Power TP = 3752325 W**

Propulsive Power PP = ṁ_{a}*(V^{2}_{jet} – V^{2}_{aircraft})/2

We can determine jet velocity from the equation for Thrust force TF

TF = ṁ_{a}(V_{jet} – V_{aircraft})

**V _{jet} = 878 m/sec**

Now using the value of **V _{jet }**we can find the propulsive power PP

**PP = 5751076.5 W**

Propulsive efficiency **η _{P}** =

**TP/PP**

Propulsive efficiency **η _{P}** = 65.24 %

Thermal Efficiency **η _{th }**= Propulsive Power PP/(fuel flow rate

**ṁ**x Calorific Value

_{f}**CV**)

_{f}Thermal Efficiency **η _{th }**=

**PP**/

**ṁ**x

_{f}**CV**

_{f}Thermal Efficiency **η _{th }**= 47.39 %

Overall efficiency **η _{0}** = propulsive efficiency

**η**x thermal efficiency

_{P}**η**

_{th}Overall efficiency **η _{0}** = 30.91 %

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Jet Propulsion complete solution (5 downloads)