If the pipe diameter decreases while maintaining the same flow rate, what happens to the fluid velocity and the frictional losses?

If the pipe diameter decreases while maintaining the same flow rate, what happens to the fluid velocity and the frictional losses?

• A. Velocity decreases; friction decreases.
• B. Velocity increases; friction increases.
• C. Velocity stays the same; friction increases.
• D. Velocity increases; friction decreases.

Answer: (B)

At a fixed flow rate, the relationship Q = A v (where A is the cross-sectional area) forces the velocity to rise when the diameter and hence the area shrink. Since a smaller diameter means less area, the same amount of fluid must move faster to keep the flow rate the same, so velocity increases. Frictional losses in pipe flow scale with velocity and with the pipe’s length-to-diameter ratio, roughly as h_f ∝ (L/D) (v^2). With a smaller diameter, D decreases (increasing L/D), and v increases, so the energy lost to friction goes up. In other words, pushing the same volume of fluid through a thinner pipe both speeds it up and raises the friction losses.

At a fixed flow rate, the relationship Q = A v (where A is the cross-sectional area) forces the velocity to rise when the diameter and hence the area shrink. Since a smaller diameter means less area, the same amount of fluid must move faster to keep the flow rate the same, so velocity increases.

Frictional losses in pipe flow scale with velocity and with the pipe’s length-to-diameter ratio, roughly as h_f ∝ (L/D) (v^2). With a smaller diameter, D decreases (increasing L/D), and v increases, so the energy lost to friction goes up. In other words, pushing the same volume of fluid through a thinner pipe both speeds it up and raises the friction losses.