Question

A boat of area $10{\text{m}}^2$ floating on the surface of a river is made to move horizontally with a speed of $2\text{m/s}$ by applying a tangential force. If the river is $1\text{m}$ deep and the water in contact with the bed is stationary, find the tangential force needed to keep the boat moving with same velocity. (Assume the viscosity of water as $0.01\text{poise}$).

• A. $0.02\text{N}$
• B. $0.03\text{N}$
• C. $0.04\text{N}$
• D. $0.05\text{N}$

Answer 1

The correct option is A $0.02\text{N}$

Assuming linear velocity profile, velocity changes from $2\text{m/s}$ at the surface to zero at the bed which is at a depth of $1\text{m}$
$\therefore$ Velocity gradient $=\frac{dv}{dy}=\frac{2-0}{1}=2{\text{s}}^{-1}$
Now from Newton's law of viscous force,
$|F|=\eta A\frac{dv}{dy}=({10}^{-2}\times {10}^{-1})\times 10\times 2=0.02\text{N}$