Sites:

## 9.2 Euler's Turbomachinery Equations

In turbomachinery, power is added to or removed from the fluid by the rotating components. These rotating components exert forces on the fluid that change both the energy and the tangential momentum of the fluid. In this section, we will develop Euler's equations for turbomachinery that relate the change in energy to the change in tangential momentum.

Consider the adiabatic flow of a fluid as shown in Fig. 9.1. The fluid in a stream tube enters a control volume at radius r i with tangential velocity v i and exits at r e with tangential velocity v e. For a compressor or pump with steady flow, the applied torque ? A is equal to the change in angular momentum of the fluid, or

Figure 9.1: Control volume for a general turbo-machine.

The input power is = ? ? A, or

 (9.1)

This equation is often referred to as the Euler pump equation. Application of the first law of thermodynamics to the flow through the control volume gives

Combining this expression with Eq. (9.1) gives

 (9.2)

Likewise, for a steady-flow turbine, the output torque ? O is equal to the change in angular momentum of the fluid, or

The output power is

or

 (9.3)

This equation is often referred to as the Euler turbine equation. Application of the first law of thermodynamics to the flow through the control volume gives

Combining this expression with Eq. (9.3) gives

 (9.4)

##### Products & Services
Fluid Transfer Pump Systems
Fluid transfer pump systems are used in processing, water purification and desalination, or liquid handling applications.
Gas Compressors and Gas Compressor Systems
Gas compressors and gas compressor systems are used to circulate gas through a process, enhance conditions for chemical reactions, provide inert gas for safety or control systems, recover and recompress process gas, and maintain correct pressure levels by either adding and removing gas or vapors from a process system.
Computational Fluid Dynamics Software (CFD)
Computational fluid dynamics software (CFD) is used for the calculation of flow parameters in fluids, and for the design and simulation of the behavior of fluidic systems. CFD is also used to simulate fluid mechanics.
Rheometers
Rheometers characterize a liquid according to its viscous properties and elastic responses.
Servo Valves
Servo valves provide closed loop flow or pressure response to an electrical or electronic control signal. They are used in air, gas, and liquid applications.

##### Topics of Interest

9.3 Axial-Flow Compressor Analysis The axial-flow compressor is one of the most common compressor types in use today. It finds its major application in large gas turbine engines like those that...

5.2 Compressor Geometry and the Flow Pattern To determine the temperature rise of an existing compressor stage, one must relate the flow Mach numbers and angles contained in equation 5.10 to the...

5.1 Energy Exchange, Rotor to Fluid The feature that distinguishes compressors and turbines from the fixed aerodynamic components of the engine and the aircraft is the energy exchange between rotor...

3.1. Introduction Definition: A Newtonian fluid is a substance that may resist a shearing (tangential) stress no matter how small only by continuous motion. The application of fundamental fluid...

7.1 Thermal Boundary Layers If temperature gradients exist in a flow, the momentum boundary layer for large Reynolds numbers discussed in Chapter 6 can be accompanied by a thermal boundary layer.

Product Announcements
KNF Neuberger, Inc.
Thermal Fluid Systems, Inc.