Answer to Question #230597 in Molecular Physics | Thermodynamics for Unknown346307

Question

9. During flight, the air speed of a turbojet engine is 250 m/s. Ambient air temperature is – 14°C. Gas temperature at outlet of nozzle is 610°C. Corresponding enthalpy

values for air and gas are respectively 250 and 900 kJ/kg. Fuel air ratio is 0.0180. Chemical energy of fuel is 45 MJ/kg. Owing to incomplete combustion 6% of chemical energy is not released in the reaction. Heat loss from the engine is 21 kJ/kg of air.Calculate the velocity of the exhaust jet.

Answer 1

Solution;

Given;

Air speed of turbo engine,$c_a=250$m/s

Ambient air temperature =-14°c

Gas temperature at outlet of nozzle=610°c

Enthalpy of air,$h_a=250kJ/kg$

Enthalpy of gas, $h_g=900kJ/kg$

Fuel air ratio =0.0180

If mass of air ,$m_a=1kg$ ,then mass of fuel,$m_f=0.018kg$ ,mass of gas,

$m_g=m_a+m_f=1.018kg$

Chemical energy of fuel=45MJ/kg

Heat loss from engine,Q=21kJ/kg

Velocity of exhaust jet;

Energy equation for turbojet engine is;

$m_a(h_a+\frac{c_a^2}{2})+m_fE_f+Q=m_g(h_g+\frac{c_g^2}{2}+E_g)$

$1(250+\frac{250^2}{2×1000})+0.018×45×10^3+(-21)=1.018(900+\frac{c_g^2}{2×1000}+0.06×\frac{0.018}{1.018}×45×10^3)$

Gives;

$1070.25=$ $1.018(947.74+\frac{c_g^2}{2000})$

$c_g=455.16m/s$

Answer;

455.16m/s