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

Explanation:

Shear stress equation for a laminar flow through the pipe is given by:

\({\rm{\tau }} = - \frac{{\rm{r}}}{2} \times \frac{{\partial {\rm{P}}}}{{\partial {\rm{x}}}}\)

Where,

τ = Shear stress at any distance “r” from the center of the pipe

∂P/∂x = Pressure gradient

r = distance from the center of the pipe,

At r = 0, τ = 0,

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

The velocity is zero at the wall of the pipe increasing to a maximum at the center, then symmetrically to the other wall, and the velocity distribution is parabolic.

Shear stress maximum at the wall of the pipe decreases to a minimum (zero) at the center, then symmetrically to the other wall, shear stress increase and shear distribution is linear