What is the relationship between the flow rate, power, and head of a pump

Pump Flow - Often referred to as discharge quantity, pump flow quantifies the volume of water that the pump can transfer in a unit of time. It's a crucial metric displayed on flow meters, symbolized by (Q), measured in liters per second (L/s), cubic meters per second (m³/s), or cubic meters per hour (m³/h). Pump Head - The term 'head' in pumps specifically refers to the vertical distance a fluid is lifted against gravity. Symbolized by (H), typically in meters (m), it consists of two components: the suction head ((H_s)) - the maximum height a pump can lift water from the source, and the discharge head ((H_d)) - the maximum height the pump can push the water to. Thus, pump head is expressed as (H = H_s + H_d). It's worth noting that the manufacturer's specified head does not account for friction losses within the piping system; hence, this must be factored in for accurate application. Pump Power - Defined as the rate at which work is done, power is a measure of energy conversion over time. The standard symbol is (N) and is commonly quantified in units such as kilograms-meters per second (kg·m/s), kilowatts (kW), or horsepower (hp). In the context of motors, power output is often expressed in kW, whereas engines might be rated in hp. Relationships among Parameters For a centrifugal pump (considering two identical impellers with outer diameters (D_1) and (D_2)), the flow rate ((Q)) varies linearly with the diameter, indicated by: [Q_1/Q_2 = D_1/D_2] The relationship between head and outer diameter exhibits a square relationship: [H_1/H_2 = (D_1/D_2)^2] Similarly, the power consumption shows a cubic relationship: [W_1/W_2 = (D_1/D_2)^3] Understanding these relationships ensures informed decision-making in pump selection, optimizing performance and efficiency in various applications.