Question

. In a gas turbine unit, the gases flow through the turbine is 15 kg/s and the
power developed by the turbine is 12000 kW. The enthalpies of gases at the inlet and outlet are
1260 kJ/kg and 400 kJ/kg respectively, and the velocity of gases at the inlet and outlet are
50 m/s and 110 m/s respectively. Calculate :
(i) The rate at which heat is rejected to the turbine, and
(ii) The area of the inlet pipe given that the specific volume of the gases at the inlet is
0.45 m3/kg

Answer 1

Gives

$\dot{m}=15kg/sec \\v'=0.45m/sec\\P=12000KW$

Work done

$W=\frac{12000}{15}=800KJ/kg$

Enthalpy of gas inlet

$h_1=1260KJ/kg$

Enthalpy of outlet

$h_2=400kJ/kg$

Velocity of out let

$v_2=110m/sec$

Heat rejected

Using the folow equation

$$h_1+\frac{v_1^2}{2}+Q=h_2+\frac{v_2^2}{2}+W\rightarrow(1)$$

K.E. inlet

$$=\frac{v_1^2}{2}=\frac{50^2}{2}=1250Nm/kg=1.25KJ/kg$$

$KE=\frac{v_2^2}{2}=\frac{110^2}{2}=6.05kJ/kg$

Equation (1) put value

$1260+1.25+Q=400+6.05$

$Q=-55.2KJ/kg$

Heat rejected =$55.2\times15=828KW$

(2)

inlet area(A)

$\dot{m}=\frac{Av'}{v_2}=\frac{0.45\times15}{50}=0.135m^2$