If the radius of a pipe carrying water is doubled, what happens to the volume flow rate of the water?

When examining how the volume flow rate of water in a pipe changes with the radius, it is crucial to analyze the relationship dictated by the principles of fluid dynamics, particularly the equation of continuity and the flow rate calculation.

The volume flow rate, often denoted as Q, is given by the relationship Q = A × v, where A is the cross-sectional area of the pipe and v is the fluid's velocity. The cross-sectional area for a circular pipe is calculated using the formula A = πr².

If the radius of the pipe is doubled, the new area becomes A' = π(2r)² = π × 4r² = 4A. Hence, the cross-sectional area increases by a factor of four when the radius is doubled.

According to the principle of continuity, which states that the flow rate must remain constant in a closed system if incompressible fluid is assumed, if the area increases and no other factors change (like the flow speed), the volume flow rate would also increase.

However, if other conditions such as the pressure driving the fluid or its velocity are not adjusted to maintain flow through the larger diameter pipe, the velocity will change accordingly to compensate for the increase in area to maintain the same