# Sample Problems on Jet Propulsion with Solutions

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#### Sample Problems on Jet Propulsion with Solutions

Problem 1:

A German turbo-jet uses petrol having a calorific value of 4.184 x 104(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 CVf = 4.184 x 104 kJ/kg

Thrust Force TF = 8829 N

Thrust Specific Fuel Consumption = 0.1427 kg/N

Velocity of the aircraft Vaircraft = 425 m/sec

Mass flow rate of air ṁa = 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 ṁf (kg/hr)/Thrust force TF(N)

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

f (kg/hr) = 1259.89

f = 0.35 kg/sec

Air to fuel ratio = ṁa/ ṁ= 19.5/0.35 = 55.71

Overall efficiency η0 = propulsive efficiency ηP x thermal efficiency ηth

Propulsive efficiency ηP = Thrust Power TP/ Propulsive Power PP

Thrust Power TP = Thrust Force TF x Velocity of the aircraft Vaircraft

Thrust Power TP = 3752325 W

Propulsive Power PP = ṁa*(V2jet – V2aircraft)/2

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

TF = ṁa(Vjet – Vaircraft)

Vjet = 878 m/sec

Now using the value of Vjet we can find the propulsive power PP

PP = 5751076.5 W

Propulsive efficiency ηP = TP/PP

Propulsive efficiency ηP = 65.24 %

Thermal Efficiency ηth = Propulsive Power PP/(fuel flow rate f x Calorific Value CVf)

Thermal Efficiency ηth = PP/f x CVf

Thermal Efficiency ηth = 47.39 %

Overall efficiency η0 = propulsive efficiency ηP x thermal efficiency ηth

Overall efficiency η0 = 30.91 %