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

In fluid mechanics, shear stress in a pipe flow is related to the velocity gradient (rate of change of velocity with respect to radial distance from the pipe wall).

In laminar flow through a circular pipe, the velocity is maximum at the center and decreases toward the pipe wall.

At the center line of the pipe, the velocity gradient is zero because the slope of the velocity profile flattens out at the peak.

Since shear stress is directly proportional to the velocity gradient, a zero velocity gradient results in zero shear stress.

Hence, the shear stress is minimum (actually zero) at the center line of the pipe.

Therefore, the correct answer is: minimum (Option A).