Name: turbine work from energy changes
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

High School

Chemistry

Energy

C-PS3-4

Conservation of Energy in Control Volume

The first law of thermodynamics states that the rate of change of total stored energy in a system equals the net rate of heat and work transferred into a system.
For a control volume that coincides with the system at a given moment, the net heat and work entering the system equal the net heat and work entering the control volume.
For this system and coincident control volume, the Reynolds Transport Theorem is applied.
The total rate of energy change within the control volume is determined by both the time rate of change in stored energy and the net energy flow through the boundary.
The energy flowing across the boundary includes contributions from heat and work, such as shaft work and pressure work.
Shaft work results from rotating components like turbines, while fluid stresses produce pressure work.
The general energy equation combines all elements: stored energy, heat, shaft work, and pressure work due to normal stresses.
This equation represents energy conservation in fluid systems, incorporating heat transfer, shaft work, and pressure forces at the control surface.

conservation of energy in control volume

Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
<img alt="Thermodynamic process equation, integral form, fluid flow energy balance, engineering formula." src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Since we focus on work done by the turbine shaft and assume negligible heat transfer, Q&#775; &#8776; 0. Therefore, the energy equation simplifies further to:
<img alt="Thermodynamics equation, shaft work integral, W&#775;shaft = &#8747;epV&#183;n&#770; dA, energy analysis diagram." src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
The flow is divided into two components: the fluid entering the turbine (inlet) and exiting the turbine (outlet). The mass flow rate at both points is constant, and the energy flux at the inlet and outlet is given by:
<img alt="Thermodynamics; shaft work equation, energy balance; thermodynamic process analysis." src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;" data-altupdatedat="1762173717000" data-alt="Equation 3" />
Where:
-&#7745; is the mass flow rate,
- &#361;1, V1, and z1 refer to the internal energy, velocity, and height at the inlet,
- &#361;2, V2, and z2 refer to the internal energy, velocity, and height at the outlet,
In a typical turbine, the fluid's internal and kinetic energy decreases as it passes through the turbine, which results in useful shaft work being done. Suppose a turbine operates with an inlet velocity of V1=50&#8201;m/s, an outlet velocity of V2= 20&#8201;m/s, an inlet height z1=100&#8201;m, and an outlet height z2=90m. Assume the internal energy change is small compared to the kinetic and potential energy changes, and the mass flow rate is 10&#8201;kg/s.
<img alt="Shaft work equation diagram: \( \dot{W}_{shaft} \) calculation, 11481W, energy transfer formula." src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;" data-altupdatedat="1762173717000" data-alt="Equation 4" />
As a result, the turbine produces approximately 11.48 kW of mechanical power by extracting energy from the flowing fluid.

The first law of thermodynamics states that the rate of change of total stored energy in a system equals the net rate of heat and work transferred into a ...

Education

JoVE Core

Civil Engineering

Unit 1

Finite Control Volume Analysis

KEY TERMS AND CONCEPTS

turbine work from energy changes

A turbine can turn fluid energy into shaft work when flow passes through a control volume. The fluid enters the turbine at one point and leaves at another. Under steady-flow conditions, there is no energy buildup inside the control volume, so the stored energy does not change with time.

This steady-flow setup makes the energy equation simpler. The turbine is treated as doing mechanical work, and heat transfer is taken as negligible, so Q̇ is approximately zero. The flow at the inlet and outlet is then described by the mass flow rate and by the fluid’s internal energy, velocity, and height at each location.

For the inlet and outlet, the mass flow rate is constant. The energy flux depends on ṁ, u1, V1, and z1 at the inlet, and on ṁ, u2, V2, and z2 at the outlet. Here, u is internal energy, V is velocity, and z is height.

In a typical turbine, the fluid loses internal energy and kinetic energy as it moves through the device. That energy loss becomes useful shaft work. For example, if V1 = 50 m/s, V2 = 20 m/s, z1 = 100 m, z2 = 90 m, and the mass flow rate is 10 kg/s, with a small internal energy change, the turbine produces about 11.48 kW of mechanical power.

Turbine Work from Energy Changes

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Wind Turbine Torque and Angular Momentum

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A turbine can turn fluid energy into shaft work when flow passes through a control volume. The fluid enters the turbine at one point and leaves at another. Under steady-flow conditions, there is no energy buildup inside the control volume, so the stored energy does not change with time. This steady-flow setup makes the energy equation simpler. The turbine is treated as doing mechanical work, and heat transfer is taken as negligible, so Q̇ is approximately zero. The flow at the inlet and outlet...

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key terms and concepts

Learn how a steady-flow turbine uses changes in velocity, height, and internal energy to produce shaft work, with a worked 11.48 kW example.

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Turbine Work from Energy Changes

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