3.1.5 Pump curve theory
Pump curve theory
Pump curve theory describe the performance for any given pump with regards to the relationship between flow and head, the energy (power in watt) needed to perform that work and the efficiency (rate of mechanical energy, or torque, added to the pump shaft compared with the hydraulic energy developed in the fluid) of the pump.
In accordance with Euler’s equation, delivery head is dependent upon the size and direction of the velocity vectors and the size of the hydraulic losses. Both these factors are affected, among others, by the volume rate of flow Q, which passes through the pump.
In many cases the tangential component of the absolute velocity entering the impeller is small, c1u ≅ 0. In such cases Eulers equation is simplified to:
If the flow through the pump were free of losses (η = 1) the theoretical delivery head would be given by the following equation
With reference to figure 3.13a
and
or
The angle β2 in the velocity vector diagram is somewhat smaller than the blade angle in the impeller outlet. This angular difference is called the deviation angle and is due to the blade’s inability to completely control the relative flow. The size of the deviation angle is primarily dependent upon the number of blades. For a given pump, operating at a certain constant speed, the theoretical delivery head Htheoretical decreases according to equation 3.14, linearly with increasing volume flow Q.
The actual delivery head H differs from Htheoretical due to the hydraulic losses hf. These, as in all other cases of flow, are dependent upon the inlet flow direction towards the body around which the liquid flows. In the case of pumps the inlet flow direction, towards for example the blades, varies with the volume flow. A certain inlet flow angle gives the most favourable flow and thus the smallest losses. Both higher and lower values of Q result in an increase of hf. By subtracting hf from Htheoretical, the actual Q-H curve of the pump
at constant speed is obtained, see figure 3.15a. The shape of the Q-H curve varies from one pump type to another dependent upon the different value of the parameters which are included in Htheoretical and hf, i.e. different designs of pumps.
In addition to the pump’s Q-H curve the required shaft power P and the pump’s total efficiency as shown in figure 3.10 are also usually given as a function of the volume rate of flow in a pump diagram. The pump can, in principle, operate at any point whatsoever along the Q-H curve. The position of the operating point in an actual case is determined by the characteristics of the system to which the pump is connected.
Figure 3.15b Pump diagram.