Question

Water vapor enters a turbine operating at steady state at 500 degrees C, 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 9.48 cubic meters per second.

The power developed by the turbine, in kW, is approximately:

A. 3500

B. 3540

C. 3580

D. 7470

Answer 1

correct option is C. 3580

Step-by-step explanation:

given data

temperature = 500 degrees C

steady state at = 40 bar

velocity = 200 m/s

saturated vapor = 0.8 bar

velocity = 150 m/s

volumetric flow rate = 9.48 cubic meters per second

solution

we use here steam tables for temp 500 deg C, 40 bar

we get h1 = 3445300 J/kg and 0.8 bar

we get hg = h2 = 2665800 J/kg

and vg = v2 = 2.087 m³/kg

and

we know power that is express as

Power = w × (Q ÷ v2) ....................1

and

here

`h1 + (V1^2)/(2) = h2 + (V2^2)/(2) + w`

so

w =
`(h1 - h2) + (V1^2-V2^2)/(2)`

put here value and we get

w = (3445300 - 2665800) +
`(200^2 - 150^2)/(2)`

w = 788250 J/kg

so put value in equation 1 we get

Power =
`788250* (9.48)/(2.087)`

Power = 3580551 W

Power = 3580 kW