Question

In the turbine of a gas turbine unit the gases flow through the turbine is 17kg/s and the power developed by the turbine is 14000kw. The enthalpies of the gases at inlet and outlet are 1200kj/kg and 360kj/kg respectively and the velocity of the gases at inlet and outlet are 60m/s and 150m/s respectively
Calculate the rate as which the heat is rejected from the turbine. Fine also the area of inlet pipe given that the specific volume of the gases at inlet is 0.5m³/kg

Answer 1

Solution.

$m=17kg/s;$

$P=14000kW$ ;

$W=14000/17=823.5kJ/kg;$

$h_1=1200kJ/kg;$

$h_2=360kJ/kg;$

$C_1=60m/s;$

$C_2=150m/s;$

$v_1=0.5m^3/kg;$

$h_1+\dfrac{C_1^2}{2}+Q=h_2+\dfrac{C_2^2}{2}+W;$

$\dfrac{C_1^2}{2}=\dfrac{3600}{2}=1800m^2/s^2=1.800kJ/kg;$

$\dfrac{C_2^2}{2}=\dfrac{22500}{2}=11250m^2/s^2=11.250kJ/kg;$

$1200+1.8+Q=360+11.250+823.5;$

$Q=-7.05kJ/kg;$

Heat rejected$=7.05kJ/kg\sdot 17kg/s=120kW;$

$m=\dfrac{C_1A_1}{v_1};$

$A_1=\dfrac{mv_1}{C_1};$

$A_1=\dfrac{17\sdot0.5}{60}=0.14m^2;$

Answer: $Q=120kW;$

$A_1=0.14m^2.$