For a fluid moving through a cylindrical tube in a streamlined motion, a fluid layer in immediate contact with the wall of the tube remains effectively at rest. The layers away from the wall has gradually increasing velocities attaining the maximum at the axis of the cylinder.
The molecules of the fluid layer $L_1$ in immediate contact with the wall are at rest because fluid molecules of this layer collide with those of the wall and make them jiggle. In this process, they transfer energy and momentum to the wall. But instead of coming to rest, the fluid molecules of $L_1$ must gain a backward momentum due to recoil. But that is being cancelled by the collisions with the molecules of the forward moving layer $L_2$ just below it (which might be causing it to be at rest). But why doesn't the layer $L_2$ also come to rest?