Question

A well-insulated turbine operating at steady state develops 28.75 MW of power for a steam flow rate of 50 kg/s. The steam enters at 25 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in 8C.

Answer 1

Answer:$355^{\circ}C$

Explanation:

Given

power Developed=28.75 MW

$\dot{m}=50 kg/s$

$P_1=5 bar$

$v_1=61 m/s$

Steam exit as saturated

$P_2=0.06 bar$

$v_2=130 m/s$

From saturated steam stable h2=h_g=2567.4 KJ/kg[/tex]

Applying Steady flow Energy equation

$\dot{m}\left [ h_1+\frac{1}{2}\left ( v_1^2\right )+gz_1\right ]+Q=\dot{m}\left [ h_2+\frac{1}{2}\left ( v_2^2\right )+gz_2\right ]+W$

Q=0 because of insulation and

$z_1=z_2$

$h_1=\frac{W}{\dot{m}}-\frac{1}{2}\left ( v_1^2-v_2^2\right )+h_2$

$h_1=frac{28.75\times 10^3}{50}-\frac{1}{2}\left ( 61^2-130^2\right )\times \frac{1}{1000}+2567.4$

$h_1=3149 kJ/kg$

$At P_1=25 bar h_1=3149 kJ/kg$

using steam tables

$T_1=355^{\circ}C$