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