Question

In a 4 cm diameter pipeline carrying laminar flow of a liquid with $\mu =1.6$ centipoise, the velocity at the axis is 2 m/s. What is the shear stress midway between the wall and the axis?

• A. $0.1{\text{N/m}}^2$
• B. $0.125{\text{N/m}}^2$
• C. $0.16{\text{N/m}}^2$
• D. $0.01{\text{N/m}}^2$

Answer 1

The correct option is C $0.16{\text{N/m}}^2$

The wall shear stress is given as

${\tau }_0=\frac{8\mu V}{D}[V=\frac{U_{\text{max}}}{2}=\frac{2}{2}=1\text{m/s}]$

$\Rightarrow {\tau }_0=\frac{8\times 1.6\times {10}^{-3}\times 1}{4\times {10}^{-2}}$

$\Rightarrow \tau =0.32{\text{N/m}}^2$

$\text{The shear stress varies linearly from zero at the axis to}{\tau }_0\text{at the periphery.}$

$\therefore \frac{\tau }{r}=\frac{{\tau }_0}{R}$

$\Rightarrow \tau ={\tau }_0\times \frac{r}{R}[\because r=\frac{R}{2}]$

$\Rightarrow \tau =\frac{0.32\times R}{2R}$

$\Rightarrow \tau =0.16{\text{N/m}}^2$