# How to Find the Power Output of an Isentropic Steam Turbine.

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## Introduction: How to Find the Power Output of an Isentropic Steam Turbine.

A turbine is a mechanical machine used to produce continuous power. It is important to be able to calculate power output because it is one of America’s main sources of electricity used to light homes and businesses from major cities to small towns. Not knowing how to calculate power output from steam turbines could lead to people using electrical power faster then what is being produced from the turbine. This could lead to a power outage, leaving thousands of people without electricity.

Definition of Terms

Energy (E): Ability of system to produce change.

Adiabatic: No heat energy in the system or heat transfer to and from the surrounding.

Entropy (s): Unavailability of heat energy for conversion into work.

Isentropic: No entropy production within a system and adiabatic with its surroundings.

Heat (Q): Movement of heat energy from one temperature to another.

Work (W): Mechanical energy.

Power (P): Work per unit time.

Mass flow (m): Amount of a fluid’s mass traveling in a system per unit time.

Enthalpy (H): Total heat content of the system.

Pressure (p): Force per unit area.

Materials

· Pencil

· Paper

· Calculator

Note:

The approximate completion time of these instructions should take about ten minutes. If you do not understand the definitions and terminology, it will not hinder your from completing the task. Also, you will need to be able to organize information from reading the problem statement, and be able to read tables of information.

Problem Statement

Superheated steam enters an isentropic turbine at a temperature (T) of 700ᵒC and pressure (p) of 3.0 MPa and exits at a pressure of 0.30 MPa. The steam has a mass flow rate of 5 kg/s, find the power produced by the turbine.

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## Step 1: Draw a Picture.

For problems such as these, it is good to draw a picture so it is easy to see what is being said in the problem statement. Since the problem ask to find the power of a turbine, draw a turbine. It can be illustrated as a trapezoid with the long side facing to the right. Engineers have picked this illustration because it shows them power is being produced, which means work is coming out.

Note:

Drawing the picture is only a reminder the work is being done by the turbine so it should be a positive value. After you draw the turbine, you will not have to do anything with the picture.

## Step 2: Create a State Table.

Create a table with two columns. The first column will be for the inlet of the turbine and the second will be for the exit of the turbine. Place all given information in the appropriate column with labels and units on each numerical value so you know what values belong to what property. If you do not, you can get lost in what you are calculating.

Hint:

It is best to use subscript ‘i’ for inlet to the turbine values and use subscript ‘o’ for values at the outlet of the turbine.

## Step 3: Find All Properties for the Inlet of the Turbine.

You need to find all the properties of the inlet of the turbine. Since the problem gave you temperature and pressure, you have enough information to define all properties of that state.

1. Go to table A-1

2. Find the column T(C)

3. Travel down the rows until you find the temperature that corresponds to the inlet temperature.

4. At the inlet temperature of 700ᵒC, place all numerical values, symbols, and units in your state table of inlet values for the columns: v, u, h, and s.

Note:

Not all values will be used in the calculation of this problem but they are important to solve problems of this type in a general sense.

## Step 4: Finish Your State Table for the Outlet of the Turbine.

You know that the turbine is isentropic so the entropy remains constant through the system. The s value at the inlet of the turbine equals the s value at the exit of the turbine.

1. Go to table A-2

2. Find the s column.

3. Follow down the s column until you find the s value that equals the s value from the inlet of the turbine.

4. At an entropy value of 7.7571, place all numerical values, symbols, and units in your state table of outlet values for the columns: v, u, h, and T.

## Step 5: Use the First Law of Thermodynamics for Open Systems.

The first law of thermodynamics states Q-W=m*(hout – hin). Plug in h values you have on your state stable and solve for W knowing that Q=0 since the turbine is isentropic. You should get the answer 4000 ±10 KJ/s. This value is a standard for turbines of this size and mass flow.

## Step 6: Review

You have successfully found the work of an isentropic turbine and can know read state tables. This information can be used to find the power produced by a vapor power plant and determine how much electrical power can be supplied to homes and business in cities and small towns. You can use this Instructable to work all kinds of problems of this type if you are inclined to do so. Below are links to websites that would be beneficial to you if you want learn more about turbines.

http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?topic=th&chap_sec=06.5&page=theory

https://engineering.purdue.edu/ME200/Woodland/ME%20200%20-%20Lecture%2025_BW.pdf

http://www.learnthermo.com/examples/ch08/p-8d-3.php