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

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Multiple Choice

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

Explanation:
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.

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