What is the relationship between the pump’s pressure and flow rate, and the motor’s power?

Your question is quite broad, but generally speaking: ? 1. Positive displacement pumps see an increase in power as the outlet pressure rises (with little change in flow rate). 2. In ordinary centrifugal pumps, as the flow rate increases, the head decreases while the power increases. 3. For axial flow pumps and vortex pumps, as the flow rate increases, the head decreases and so does the power consumption. (Starting with the valve closed is not allowed) 4. For some centrifugal pumps that are close to the mixed-flow regime, as the flow rate increases, the head decreases, while the power first increases and then decreases.

The main performance parameters of a centrifugal pump are flow rate Q, head H, efficiency, and shaft power P. At a certain speed, the relationships between H and Q, P and Q, as well as Q itself are represented by curves; these curves are known as the performance curves of the centrifugal pump. The performance curves serve as an important basis for determining the appropriate operating conditions for the pump and for selecting the right type of centrifugal pump. It is easy to understand by looking at the pump’s performance curve graph.

Referring to the characteristic curves of centrifugal pumps as described in \"Principles of Chemical Engineering,\" these curves represent the relationship among the pump’s power, head, and flow rate. For pumps of the same model transferring the same medium, and assuming constant pump efficiency, the relationships between power, head, and flow rate as a function of pump speed are as follows: P2/P1 = (n2/n1)³, H2/H1 = (n2/n1)², and Qv2/Qv1 = (n2/n1). When the pump speed changes by less than 20%, the efficiency remains essentially unchanged. For a given pump, at a constant speed, there are three types of characteristic curves: (1) Head-flow curve: the head decreases as the flow rate increases； (2) Power-flow curve: Power increases as flow rate increases ； Therefore, when qv=0, P is minimum. Therefore, when starting the centrifugal pump, the outlet valve should be closed to minimize the motor’s starting current and protect the motor. (3) Efficiency-flow curve: Initially, efficiency increases as flow rate increases; after reaching a maximum value, it decreases again as the flow rate rises. The maximum efficiency point is the design operating point of the pump; in engineering terms, it is designated as the rated point, and the flow rate corresponding to this point is known as the rated flow rate.