## Fundamentals of Turbomachinery

Turbomachinery devices inject life into fluids. Principles of turbomachinery form the preliminary design tools in design of them.

Following article gives details of the video lecture.## Turbomachinery Principles

Consider following turbo machines. An axial turbine, a centrifugal machine or a pelton wheel, you can predict performance of all of these from same turbo machinery fundamentals.

Fig.1 Impeller of axial turbine, centrifugal machine and Pelton wheel |

## Euler Turbomachine Equation

To develop turbo machinery fundamentals consider fluid flow through channel shown below. The inlet velocity, V_{1} gets changed to outlet velocity V_{2}. Velocity of fluid can be split into tangential and radial components. This is shown in following figure.

Fig.2 Velocities at inlet and outlet can be split into tangential and radial components |

*Euler turbomachine*equation. This is the most important equation in turbo machinery.

## Pump or Turbine?

If the channel is rotating at an angular velocity omega, power required to maintain the fluid flow will be torque multiplied by angular velocity.

*ω*times radius becomes channel velocity or blade velocity. So power required for this fluid motion can be taken as difference in product of blade velocity times tangential fluid velocity.

*V*is positive, if it is in same direction of blade velocity. Otherwise it is negative.

_{θ}Fig.3 Blade and tangential velocity of flow are shown at inlet and outlet |

*V _{θ}* more precisely means, component of fluid velocity which is parallel to blade velocity.

Fig.4 V is the component which is parallel to blade velocity_{θ} |

## Concept of Relative Velocity & Velocity Triangle

The key idea in turbo machinery is concept of relative velocity. Suppose you are standing on this rotating turbo machine. The velocity of fluid you experience while moving with it is called as relative velocity. If fluid is having an absolute velocity V, and the blade is moving with a velocity U, then relative velocity experienced by you will be as follows.

For a stationary device in order to have smooth operation, flow should be tangential to the blade. Similarly in a moving device relative velocity should be tangential to blade profile. With knowledge of direction of relative velocity and the vectorial representation of relative velocity, these 3 velocities could be drawn as shown below. This is known as a velocity triangle.

Fig.5 Velocity triangle in a turbmachine |

## Performance of Centrifugal Pump

We will see, how to predict performance of a centrifugal pump using the concepts we developed. Here we have shown impeller of a centrifugal pump. If you know the blade geometry, you can find out blade angle at inlet and outlet. Blade angle is defined as angle opposite of blade velocity. So we can easily fix direction of relative velocity. This is shown in Fig. 6(b).

Radial component of flow velocity determines how much the volume flow rate is leaving the impeller. So you can determine *V _{r}* at outlet from this equation. Here

*b*means width of the impeller.

_{2}*V*in Fig. 6(c).

_{θ2}Fig.6 Development of inlet at outlet velocity triangles in a centrifugal pump |

*V*from this equation, into head equation. After substituting value of

_{θ2}*V*also in that, we get most important performance equation of centrifugal pump. How energy head is varied with flow rate. Importance of this equation in predicting performance of a centrifugal pump is elaborated in a different article. We can predict performance of an axial flow device and pelton wheel using the same concepts we developed before.

_{r2}