Answer to Question #177188 in Mechanical Engineering for aakah

Question #177188

 A steam turbine operates under steady flow conditions receiving steam at following state:-Pressure =10 bar, specific internal energy = 2800kJ/kg, specific volume = 0.2 m3/kg Velocity =100m/s. The exhaust of steam from the turbine is at 0.2 bar, with specific internal energy = 2200 kJ/kg, specific volume =15 cu.m/kg and velocity = 300 m/s. The intake is 3m above the exhaust. The turbine develops 25 kW and heat loss over the surface of turbine is 30 kJ/kg. Determine the steam flow rate (kg/s) through the turbine.


1
Expert's answer
2021-04-12T01:47:23-0400

Given as,

Inlet condition of Turbine:

Pressure(P1) =10 bar=10 x 105 Pa,

Specific internal energy(u1) = 2800x103J/kg,

Specific volume (v1) = 0.2 m3/kg

Velocity(C1) =100m/s.

Height of Inlet=Z1

Exhaust condition of turbine:

Pressure (P2)= 0.2 bar=0.2 x 105 Pa,

Specific internal energy(u2) = 2200 x 103J/kg,

Specific volume (v2)=15 m3/kg

velocity (C2)= 300 m/s.

Height of exhaust(Z2) =Z1-3

Power Developed by Turbine

W=25x103 watt

Heat loss over the surface

q=30 x103 J/kg

To Find:

Steam flow rate (kg/s) through the turbine.

Solution:

By steady flow energy Equation

"\\text{Let mass flow rate be}=\\dot{m}\\\\\n\\dot{m}[h_1+\\frac{C^2_1}{2}+gZ_1]-\\dot{m}\\times q=\\dot{m}[h_2+\\frac{C^2_2}{2}+gZ_2]+W"

"\\dot{m}[(u_1+p_1\\times v_1)+\\frac{C^2_1}{2}+gZ_1]-\\dot{m}\\times q=\\dot{m}[u_2+p_2\\times v_2+\\frac{C^2_2}{2}+gZ_2]+W"

"\\dot{m}[(u_1-u_2) +(p_1\\times v_1-p_2\\times v_2)+(\\frac{C^2_1}{2}-\\frac{C^2_2}{2})+g(Z_1-Z_2)-q]=W"

Substituting the corresponding values,

"\\dot{m}\\times (430029.4)=25000\\\\\\dot{m}=\\frac{25000}{430029.4}\\\\\\dot{m}=0.0581 kg\/s"


Answer: Steam flow rate (kg/s) through the turbine=0.0581 kg/s



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