Calculating Power in a Moving Fluid

Here we must consider energy forms as well as how they relate to fluid flow. Since the input and output hoses have the same diameters and are at the same height, the pump does not change the speed of the water nor its height, and so the water’s kinetic energy and gravitational potential energy are unchanged. That means the pump only supplies power to increase water pressure by $0\text{.}\text{92}\times {\text{10}}^6{\text{N/m}}^2$ (from $0.700\times {\text{10}}^6{\text{N/m}}^2$ to $1.62\times {\text{10}}^6{\text{N/m}}^2$).

As discussed above, the power associated with pressure is

Such a substantial amount of power requires a large pump, such as is found on some fire trucks. (This kilowatt value converts to about 50 hp.) The pump in this example increases only the water’s pressure. If a pump—such as the heart—directly increases velocity and height as well as pressure, we would have to calculate all three terms to find the power it supplies.