Question

An adiabatic steam turbine is fed by 2.20 lbm/s, at a velocity of 100 ft/s. The turbine generates an output of 1507 hp. The specific enthalpy of the water at the turbine outlet is 1007 Btu/lbm. The exit velocity is 600 ft/s. Determine the specific enthalpy of the steam at the turbine inlet.

Answer 1

Step 1

Let's convert horsepower to Btu/s.

\( \dot W = \rm 1507\,hp = 1065\,Btu/s \\ \)

 

Step 2

We will determine the specific enthalpy of water at the turbine inlet from the first law of thermodynamics.

\( \dot Q - \dot W = M\left[ h_2 - h_1 +\dfrac{{v_2^2 - v_1^2}}{2} \right]\ \)

 

\( h_1 = h_2 -\dfrac{\dot Q - \dot W}{M} + \dfrac{{v_2^2 - v_1^2}}{2} \ \)

 

Step 3

Recall that this is an adiabatic turbine. This means that the heat flow is zero. 

\( h_1 = {\rm 1007\,Btu/lbm - \dfrac{0 - 1065\,Btu/s}{2.20\,lbm/s} + \dfrac{(600^2 - 100^2)ft^2/s^2}{2}\times\dfrac{1\,Btu/lbm}{25037\,ft^2/s^2} = 1498\,Btu/lbm} \ \)

\( = \boxed{\rm 1498\ Btu/lbm} \) 

 

 

The specific enthalpy of the steam at the turbine inlet is about 1498 Btu/lbm.