– Do not change the equations.The Bernoulli equation, shown in Equation 1, relates pressure, velocity, and gravitational potential energy for incompressible fluid systems at steady-state.(1)where is the average fluid velocity, is the acceleration due to gravity, is the height, is the fluid pressure, and is the fluid density. Using the assumptions that the fluid frictional losses and change in potential energy are negligible, a mechanical energy balance equation for a fluid circuit with a centrifugal pump can be derived from the above Bernoulli equation. Equation 2 relates the mechanical energy state at the fluid circuit outlet to that of the inlet, and the shaft work done by the pump per unit mass, -:(2)The average fluid velocities can be represented in terms of volumetric flow rate, , using the following relationships:and (3)where is the inlet diameter (2 inches) and is the outlet diameter (1.5 inches). The pressure drop across the pump, , can be represented by the sum of the discharge pressure and the suction pressure, . To express Equation 2 in units of power to obtain the work done on the fluid per unit time, -, it must be multiplied by the constant mass flow rate, :(4)The electrical power supplied to the motor of the pump, , depends on the current and voltage:(5)The rotational power delivered from the motor to the impeller, , is calculated as follows:(6)where the motor torque is defined as and the angular frequency of the motor as . The motor frequency, in rotations per minute, is related to the angular motor frequency by Equation 7.(7)The efficiency of the pump motor can be determined using the previous power calculations, shown below:(8)The efficiency of the impeller can be calculated as follows:(9)Finally, the overall efficiency of the pump can be calculated by multiplying Equation 8 by Equation 9:
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