Chapter 7, Problem 7.26P

Interpretation Introduction

Interpretation:

In an adiabatic hydro turbine find out outlet temperature, power output of the turbine.

Concept introduction:

For a steady state adiabatic turbine, in and out pressures are fixed. Hence, an isentropic process of turbine is called idealized process. There is no heat transfer occur in the turbine, which indicates that work output is the desired power output of a turbine.

For adiabatic turbine from first law of thermodynamics:

  $\begin{array}{l}\Delta H=Q+W\\ Q=0\\ W=\Delta H\end{array}$

Where,

  $\Delta H$ = Enthalpy of the system (kJ/Kg)

Q = Heat absorbed/ released by the system (kJ/kg)

W = Work done by/on the system (kJ/kg)

Outlet temperature of water can be calculated using equation 7.25 given in book (Introduction of chemical engineering thermodynamics by smith) for incompressible liquid.

  $\begin{array}{l}\beta =0\\ \Delta T=\frac{\Delta H-V\left(P_2-P_1\right)}{C_P}\end{array}$

Where,

  $\beta$ = Volume expansivity (zero for incompressible liquid)

V = Specific volume (m³/kg)

  $P_1$ = Inlet pressure (atm)

  $P_2$ = Outlet pressure (atm)

  $C_P$ = Heat capacity