Consider the well insulated turbine sketched in the figure. 15 kg/s of steam ent

Question

Consider the well insulated turbine sketched in the figure. 15 kg/s of steam enters at 3MPa, 400°C. Some steam is extracted from the turbine at apressure of 0.5 MPa and a temperature of 180°C. The rest expands to a pressure of 6 kPa and a quality of 90%. The total power developed by the turbine is 12000 kW. Kinetic energy and potential energy can be neglected. Determine the mass flow rate of the steam at each of thetwo exits, in kg/s.

Exaclty like the turbine problem 5-29 in the introduction to thermal systems egineering book, just different values.

Explanation / Answer

State 1: P1=3MPa, T1=400C ---> h1=3231.57 kJ/kg

State2: P2=0.5MPa, T2=180C --->    h2=2812.45 kJ/kg

State3: P3=6kPa, x3=0.9  ---> h3=2325.15 kJ/kg

Let x be the portion of the mass flow rate extracted in state 2

First law at the turbine,

15h1 - xh2 - (15-x)h3 = 12000 kW

15(3231.57)-x(2812.45)-(15-x)2325.15 = 12000

x = 3.275 kg/s --> exit at state 2

15-x = 11.725 kg/s --> exit at state 3

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