Physics - Fluid Question with Solution | TestHub

The viscous force formula is given by,

$F=-\eta A\frac{dv}{dy}$

Therefore, shear stress $\frac{F}{A}=-\eta \frac{dv}{dy}$. Here negative sign tells us that the direction of force is opposite to the velocity gradient.

$\Rightarrow \left|\frac{F}{A}\right|=\eta \frac{dv}{dy}$

Now $v=36\times \frac{5}{18}=10 \mathrm{m} {\mathrm{s}}^{-1}$ and if the depth is $d$

$\frac{dv}{dy}=\frac{10}{d}$

$$\begin{gathered} \Rightarrow {10}^{-3}={10}^{-2}\times \frac{10}{d} \\ \Rightarrow d=100 \mathrm{m} \end{gathered}$$