# Turbine Steam Consumption Calculations

The usual way of representing the steam consumption of a turbine is the *willans line*, for example...

Often, a willans line for a specific turbine is not available, and one only has has incomplete information about an installed steam turbine; namely the rated power and (perhaps a *guesstimate*) the isentropic efficency or specific steam consumption at full load. But what you need and don't have is the steam consumption at the turbine operating load.

## Background Information

Isentropic efficiency η by definition is given by

η = (h_{HP} - h_{LP}) / (h_{HP} - h_{LPisen})

where

- h
_{HP}is the specific enthalpy of the steam at the turbine inlet - h
_{LP}is the specific enthalpy of the steam at the turbine exhaust - h
_{LPisen}is the specific enthalpy of the steam at turbine exhaust pressure but after isentropic expansion from the HP conditions

We define the ratio

m = η_{FL}/(1 - η_{FL})

where η_{FL} is the turbine isentropic efficiency at full load

The isentropic efficiency η at load *P* can be estimated by

η = m·P / (P_{R} + m·P)

where P_{R} is the rated turbine power.

The specific enthalpy at the turbine exhaust conditions is then

h_{LP} = h_{HP} - η·(h_{HP} - h_{LPisen})

The steam consumption at operating load *P* is given by

m_{s} = P / (h_{HP} - h_{LP})

Do these calculations online