Question

A large wooden plate of area ${10}^2$ floating on the surface of a river is made to move horizontally with a speed of $2m/s$ by applying a tangential force. If the river is 1 m deep and the water in contact with the bed is stationary, find the tangential force needed to keep the plate moving. Coefficient of viscosity of water at the temperature of the river; ${10}^{-2}$ poise.

Answer 1

Velocity gradient $=\frac{dv}{dx}=\frac{2}{1}=2s^{-1}$

Now, we know that

$F=\eta A\frac{dv}{dx}$

$\Rightarrow F={10}^{-3}\times 10\times 2=0.02N$ $\because$ $1$ poise $=0.1N-s/m^2$