To double the flow rate from a pump, by how many times must you increase the pressure?

To understand why increasing the pressure by a factor of four is necessary to double the flow rate from a pump, it's important to refer to the fundamental relationship described by the pump affinity laws. According to these laws, the flow rate (Q) of a pump is proportional to the square root of the pressure increase (P) across the pump.

Mathematically, this is represented as:

[ Q_1 / Q_2 = \sqrt{P_1 / P_2} ]

Where Q is flow rate and P is pressure. If we are aiming to double the flow rate (i.e., Q_2 = 2 * Q_1), we can rearrange the equation to find the pressure ratio required for this change in flow.

By substituting in the desired flow rate, we find:

[ 2 = \sqrt{P_1 / P_2} ]

To eliminate the square root, we square both sides:

[ 4 = P_1 / P_2 ]

This indicates that in order to achieve a doubling of the flow rate, the pressure must increase by a factor of four. Thus, to double the flow rate, pressure should indeed be increased fourfold. This relationship is crucial in