# Calculating State of Steam and Mass Flow Rate in a Steam Turbine

## What are the state of the steam at discharge and the mass rate of flow of the steam in a steam turbine?

## Answer:

## State of the Steam at Discharge:

Pressure, P2 = 10 kPa

Specific Enthalpy, h2 = 3446.9 kJ/kg

## Mass Rate of Flow of the Steam:

m = 31.21 kg/s

## Explanation:

**A steam turbine with a rated capacity of 56,400 kW(56,400 kJ⋅s−1) operates with steam at inlet conditions of 8600 kPa and 500 °C, and discharges into a condenser at a pressure of 10 kPa. Assuming a turbine efficiency of 0.75, let's determine the state of the steam at discharge and the mass rate of flow of the steam.**

Given Data:

Rated Capacity of Steam Turbine, P = 56,400 kW (56,400 kJ/s)

Turbine efficiency, η = 0.75

Steam Inlet Conditions:

Pressure, P1 = 8600 kPa

Temperature, T1 = 500 °C

Steam Discharge Conditions:

Pressure, P2 = 10 kPa

Let's determine the specific enthalpy of steam at the turbine inlet condition:

At pressure 8600 kPa and temperature 500 °C, the specific enthalpy of steam is obtained from the Steam Tables:

Specific Enthalpy at 8600 kPa and 500 °C, h1 = 3522.1 kJ/kg

Now, let's determine the specific enthalpy of steam at the turbine discharge condition:

The work done by steam in the turbine is given by: Wt = P / η = 56,400 kJ/s / 0.75 = 75,200 kJ/s

The specific enthalpy at the turbine discharge condition can be calculated as: h2 = h1 - Wt = 3522.1 kJ/kg - 75.2 kJ/kg = 3446.9 kJ/kg

Next, let's determine the specific volume of steam at the turbine inlet condition:

From the Steam Tables, the specific volume at 8600 kPa and 500 °C is: v1 = 0.097 m^3/kg

Finally, let's determine the mass flow rate of steam flowing through the turbine:

Using the equation P = m(h1 - h2), we can solve for the mass flow rate:

m = P / (h1 - h2) = 56,400 kJ/s / (3522.1 kJ/kg - 3446.9 kJ/kg) = 31.21 kg/s