How does fluid pressure change with flow rate?

Fluid pressure increases with flow rate due to the Bernoulli principle and conservation of mass.

As fluid flows through a pipe, its velocity increases in areas of constriction and decreases in areas of expansion. According to the Bernoulli principle, this change in velocity results in a change in pressure. As the velocity increases, the pressure decreases, and vice versa. This is why a fluid flowing through a constriction, such as a nozzle, can produce a high-pressure jet. To understand this in more detail, review the principles on the Bernoulli's Principle page.

Additionally, the conservation of mass dictates that the mass flow rate of a fluid must remain constant throughout a pipe. This means that as the velocity increases in a constriction, the cross-sectional area of the pipe must decrease to maintain a constant mass flow rate. This decrease in area further increases the fluid pressure. For further reading on mass conservation and its implications, see Understanding the Mole.

Therefore, as flow rate increases, the velocity of the fluid increases, resulting in a decrease in pressure according to the Bernoulli principle. However, the decrease in pressure is offset by the decrease in cross-sectional area, resulting in an overall increase in fluid pressure. This relationship between flow rate and pressure is important in many applications, such as in the design of fluid systems and the operation of hydraulic machinery.