Question

The velocity of water in a river is $18kmph$ near the surface. If the river is $4m$ deep, the shearing stress between horizontal layers of water in Nm${}^{-2}$ is $({\eta }_{water}=1\times {10}^{-3}pa.s)$:

• A. $2.5\times {10}^{-3}$
• B. $12.5\times {10}^{-3}$
• C. $0.75\times {10}^{-3}$
• D. zero

Answer 1

The correct option is B $12.5\times {10}^{-3}$

Force = $\eta A\frac{dv}{dy}$
Shearing stress $=\eta \frac{dv}{dy}$
Now,
$\frac{dv}{dy}=\frac{18\times 1000\times 1000}{4m\times 3600}{S}^{-1}$$=1.25S^{-1}$

So, shearing stress = ${10}^{-3}\times 1.25$$=1.25\times {10}^{-3}Pa$