Which velocity profile best describes laminar flow in a circular vessel?

• A. Flat velocity
• B. Parabolic velocity
• C. Turbulent
• D. Wavy

Answer: (B)

In laminar flow through a circular tube, the velocity distribution is parabolic. This shape comes from the balance of viscous forces and the pressure gradient, along with the no-slip condition at the wall. For a Newtonian fluid steady in a circular cross-section, the velocity as a function of radius r is u(r) = Umax [1 − (r/R)²], where R is the tube radius and Umax is the centerline velocity. This means the speed is highest at the center and drops smoothly to zero at the wall, forming a parabola when plotted across the radius.

A flat profile would require slip at the wall or a plug-flow situation, which isn’t typical for Newtonian laminar flow in a circular vessel. Turbulent flow features chaotic fluctuations and a different, more flattened profile, while a wavy description doesn’t represent a steady laminar pattern.