Question

A steam turbine operate under steady flow conditions receiving steam at the following state: Pressure 15 bar, internal energy 2700 kJ/kg, velocity 300 m/s, specific volume 0.17 m3/kg and velocity 100 m/s. The exhaust of steam from the turbine is at 0.1 bar with internal energy 2175 kJ/kg, specific volume 15m3/kg and velocity 300 m/s. The intake is 3 m above the exhaust. The turbine develops 35 kW and heat loss over the surface of turbine is 20kJ/kg. Determine the steam flow rate through the turbine

Answer 1

Answer:

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Answer 2

Given:

Inlet condition of Turbine:

The Pressure ($P_{1}$) $=15$ $bar$$=15\times10^{5}$ $Pa$

The Specific internal energy ($u_{1}$) $=2700\times10^{3}$ $J/Kg$

Specific volume ($v_{1}$) $=0.17$ $m^{3}/kg$

Velocity ($V_{1}$) $=300$ $m/s$

Height of the Inlet$=Z_{1}$

The Exhaust condition of the turbine

The Pressure$(P_{2})$$=0.1$ $bar$$=0.1\times10^{5}$ $Pa$

Specific internal energy($u_{2}$) $=2175\times10^{3}$ $J/kg$

Specific volume ($v_{2}$)$=15$ $m^{3} /kg$

velocity $(V_{2})=300$ $m/s$

The Height of the exhaust $(Z_{2})$$=Z_{1}-3$

The Power Developed by Turbine is

$=35\times10^{3}$ $Watt$

Therefore, the Heat loss over the surface

$q=20\times10^{3}$ $J/kg$

To Find:

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

Solution:

Use steady flow energy Equation

Assume mass flow rate be$=m$

$m[h_{1}+\frac{V_{1}^{2} }{2}+gZ_{1}]-m\times q=m[h_{2}+\frac{V_{2}^{2} }{2}+gZ_{2}]+W$

$m[(u_{1}+p_{1} \times v_{1})+\frac{V_{1} ^{2} }{2}+gZ_{1}]-m\times q=m[u_{2}+p_{2}\times v_{2}+\frac{V^{2}_{2} }{2}+gZ_{2}]+W$

$m[(u_{1}-u_{2} )+(p_{1}\times v_{1}-p_{2}\times v_{2})+\left(\frac{V_{1}^{2} }{2} -\frac{V_{2}^{2} }{2} \right)+g(Z_{1}-Z_{2})-q]=W$

Substitute the values

$m[(2700\times10^{3} )-2175\times10^{3}) +((15\times10^{5})\times0.17-(0.1\times10^{5})\times 15)+\left(\frac{300^{2}}{2} \right-\left\frac{300^{2}}{2} \right)+9.8( Z_{1}-(Z_{1}-3)-20\times10^{3}]=35000$

$m=0.0014150 kg/s$

The steam flow rate through the turbine is $0.001415$ $kg/s$.