At the center line of a pipe flowing under pressure where the velocity gradient is zero, the shear stress will be

In a pipe flowing under pressure, the velocity gradient represents the change in velocity across the cross-section of the pipe. When the velocity gradient is zero, it means that the velocity is constant at that point, and there is no change in velocity with respect to distance.

This condition occurs at the centerline of the pipe, where the velocity is at its maximum and is constant. Shear stress is the force parallel to the surface that one layer of fluid exerts on an adjacent layer as they slide past each other. When the velocity gradient is zero, it implies that there is no change in velocity, and, consequently, there is no relative motion between fluid layers.

As a result, the shear stress at the centerline of the pipe, where the velocity gradient is zero, will be Option C: Zero. There is no relative motion between fluid layers, so the shear stress is minimum or effectively non-existent at this location.