Question

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

• A. Minimum
• B. Maximum
• C. Zero
• D. Could be any value

Answer 1

The correct option is C Zero

Correct option is (c)


At central line
$r=0,\text{hence}\tau =0$

• Shear stress variation is linear with maximum value at the boundary of pipe.
• $\text{From newton's law of viscosity}\tau =\mu \frac{du}{dr}$
• $\text{Expression of velocity}u=\frac{1}{4\mu }\left(\frac{-dp}{dx}\right)(R^2-r^2)$
• From the above expression, it is clear that velocity distribution across the pipe is parabolic with maximum value at centre and zero at the boundary.