Brochure

4. Pump theory

The purpose of this chapter is to describe the theoretical foundation of en-

ergy conversion in a centrifugal pump. Despite advanced calculation meth-

ods which have seen the light of day in the last couple of years, there is still

much to be learned by evaluating the pump’s performance based on funda-

mental and simple models.

When the pump operates, energy is added to the shaft in the form of me-

chanical energy. In the impeller it is converted to internal (static pressure)

and kinetic energy (velocity). The process is described through Euler’s pump

equation which is covered in this chapter. By means of velocity triangles for

the ﬂow in the impeller in- and outlet, the pump equation can be interpreted

and a theoretical loss-free head and power consumption can be calculated.

Velocity triangles can also be used for prediction of the pump’s performance

in connection with changes of e.g. speed, impeller diameter and width.

4.1 Velocity triangles

For ﬂuid ﬂowing through an impeller it is possible to determine the absolute

velocity (C) as the sum of the relative velocity (W) with respect to the im-

peller, i.e. the tangential velocity of the impeller (U). These velocity vectors

are added through vector addition, forming velocity triangles at the in- and

outlet of the impeller. The relative and absolute velocity are the same in the

stationary part of the pump.

The ﬂow in the impeller can be described by means of velocity triangles,

which state the direction and magnitude of the ﬂow. The ﬂow is three-di-

mensional and in order to describe it completely, it is necessary to make two

plane illustrations. The ﬁrst one is the meridional plane which is an axial

cut through the pump’s centre axis, where the blade edge is mapped into

the plane, as shown in ﬁgure 4.1. Here index 1 represents the inlet and index

2 represents the outlet. As the tangential velocity is perpendicular to this

plane, only absolute velocities are present in the ﬁgure. The plane shown in

ﬁgure 4.1 contains the meridional velocity, C

, which runs along the channel

and is the vector sum of the axial velocity, C

, and the radial velocity, C

Figure 4.1: Meridional cut.