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

To understand why the correct answer is four, it's important to consider the principles of fluid dynamics and the relationship between flow rate and pressure in a pump system. According to the hydraulic principles governing pump performance, the flow rate produced by a pump is proportional to the pressure applied to the fluid. Specifically, the flow rate increases with the square root of the pressure increase.

When you want to double the flow rate, you need to apply a pressure that is four times greater than the original pressure. This is derived from the equation governing flow rates, which indicates that flow rate (Q) is proportional to the square root of pressure (P):

Q ∝ √P.

If you set the new flow rate to be double the original, mathematically this can be expressed as:

2Q ∝ √(P_new).

Setting up the equation based on the relationships:

2Q = k√(P_new),

where k is the constant relating flow rate to pressure.

Assuming the original flow rate corresponds to original pressure (P):

Q = k√P.

To achieve double the flow (2Q), you find:

2Q = k√(P_new)

→ 2 (k√P) = k√(P_new)