In pipes, the velocity profile of laminar flow is parabolic.

• A. True
• B. False
• C. Depends on Reynolds number
• D. Only in non-circular pipes

Answer: (A)

In fully developed laminar flow through a circular pipe, the velocity depends only on the radial position and forms a parabola. The Navier–Stokes equations balance the pressure-driven push with viscous diffusion, and with the no-slip condition at the wall (zero velocity) and symmetry at the center, the solution is a quadratic function in radius: u(r) = Umax[1 − (r/R)²]. This means the center has the highest speed, and the speed smoothly drops to zero at the wall, creating the classic parabolic shape.

This parabolic profile is characteristic of Hagen–Poiseuille flow and holds as long as the flow is fully developed and laminar in a circular pipe, regardless of the Reynolds number within that regime. If flow is developing (near the inlet) or becomes turbulent, or if the cross-section isn’t circular, the profile won’t be a perfect parabola.