In laminar flow, the average flow velocity is equal to what fraction of the maximum velocity at the center?

• A. 1/2
• B. 1
• C. 2
• D. 1/4

Answer: (A)

In laminar flow through a circular pipe, the velocity profile is parabolic: the fluid is fastest at the center and slows toward the wall. The velocity distribution can be written as u(r) = umax [1 − (r/R)²]. To get the average velocity across the cross-section, average this over the area: Vavg = (1/πR²) ∫0^R u(r) 2πr dr = umax/2. Thus, the average flow velocity is one-half of the maximum (center) velocity. This explains why the correct fraction is 1/2. If you think about the other options: 1 would mean the average equals the center value everywhere, which isn’t the case; 1/4 would be too small; 2 would exceed the maximum, which isn’t possible.