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# Solved Problems: Jet Propulsion

Civil - Gas Dynamics and Jet Propulsion - Jet Propulsion

Problems:

1. Air is discharged from a C - D nozzle. Pilot-tube readings at inlet and exist of the nozzle ae 6.95 × 105 N/m2 and 5.82 × 105 N/m2 respectively. The inlet stagnation

temp 250oC and exit static pressure, 1.5 × 105 N/m2. Find the inlet and exit stagnation pressure, exit Mach numbers, exit flow velocity and nozzle efficiency.

Note:

i) (Pitot - tube reading gives stagnation pressure)

ii)   (Since stagnation pr. vlaues are different for inlet and exit the flow is no longer isentropic) Mach number at exist (Ma). Consider the isentropic deceleration process

shown (a - oa) 2. A converging, nozzle operating with air and inlet conditions of P = 4 Kg/cm2, T0 = 450oC and T = 400oC is expected to have an exit static pressure of 2.5 Kgf/cm2 under ideal conditions. Estimate the exit temperature and mach number, assuming a nozzle efficiency = 0.92 when the expansion takes place to the same back pressure. 3. An aircraft flies at a speed of 520 kmph at an altitude of 8000 m. The diameter of the propeller of an aircraft is 2.4 m and flight to jet speed ratio is 0.74. Find the following:

(i) The rate of air flow through the propeller

(ii)  Thrust produced

(iii)  Specific thrust

(iv) Specific impulse

(v) Thrust power Given:

Air craft speed (or) Flight speed = 520 kmph

520 103 / 3600 s

144.44 m / s Altitude z 8000 m  4.10 Tutorial Problems:

1.The diameter of the propeller of an aircraft is 2.5m; It flies at a speed of 500Kmph at an altitude of 8000m. For a flight to jet speed ratio of 0.75 determine (a) the flow rate of air through the propeller, (b) thrust produced (c) specific thrust, (d) specific impulse and

(e) the thrust power.

2. Aircraft speed of 525 Kmph. The data for the engine is given below Inlet diffuser efficience =0.875

Compressor efficieny =0.790

Velocity of air at compressor entry =90m/s Properties of air :γ =1.4, Cp =1.005 KJ/kg K

3. An aircraft flies at 960Kmph. One of its turbojet engines takes in 40 kg/s of air and expands the gases to the ambient pressure .The air fuel ratio is 50 and the lower calorific value of the fuel is 43 MJ/Kg .For maximum thrust power determine (a)jet velocity (b) thrust (c) specific thrust (d) thrust power (e) propulsive, thermal and overall efficiencies and (f) TSFC

4.A turboprop engine operates at an altitude of 3000 meters above mean sea level and an aircraft speed of 525 Kmph. The data for the engine is given below

Inlet diffuser efficience =0.875,Compressor efficieny =0.790. Velocity of air at compressor entry =90m/s Properties of air :_ =1.4, Cp =1.005 KJ/kg K

5. A turbo jet engine propels an aircraft at a Mach number of 0.8 in level flight at an altitude of 10 km .The data for the engine is given below: Stagnation temperature at the turbine inlet =1200K Stagnation temperature rise through the compressor =175 K Calorific value of the fuel =43 MJ/Kg Compressor efficiency =0.75. Combustion chamber efficiency =0.975, Turbine efficiency =0.81,Mechanical efficiency of the power transmission between turbine and compressor =0.98, Exhaust nozzle efficiency=0.97, Specific impulse =25 seconds.Assuming the same properties for air and combustion gases calculate,

i.        Fuel air ratio

ii.        Compressor pressure ratio,

iii.        Turbine pressure ratio

iv.       Exhaust nozzles pressure ratio ,and

v.       Mach number of exhaust jet

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