In laminar flow, where is the maximum velocity typically located within the vessel?

In laminar flow, where is the maximum velocity typically located within the vessel?

• A. At the center of the vessel
• B. Right at the wall
• C. Uniform across the diameter
• D. At the entrance

Answer: (A)

In laminar flow through a straight vessel, the velocity profile is parabolic: fluid moves fastest at the center and slows toward the walls because of friction with the boundary. The wall enforces zero velocity (no-slip), while symmetry about the center makes the center the point of maximum speed. In a circular pipe, the velocity varies with radius r as v(r) = vmax[1 − (r/R)²], so vmax occurs at the center (r = 0). At the entrance, the flow is not fully developed yet, but in fully developed laminar flow, the maximum velocity is at the center.

In laminar flow through a straight vessel, the velocity profile is parabolic: fluid moves fastest at the center and slows toward the walls because of friction with the boundary. The wall enforces zero velocity (no-slip), while symmetry about the center makes the center the point of maximum speed. In a circular pipe, the velocity varies with radius r as v(r) = vmax[1 − (r/R)²], so vmax occurs at the center (r = 0). At the entrance, the flow is not fully developed yet, but in fully developed laminar flow, the maximum velocity is at the center.