Q: A boat of area 10 m^{2} floating on the surface of a river is made to move horizontally with a speed of 2 m/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 boat moving with constant speed.

(coefficient of viscosity of water = 10^{-2} poise)

Sol: Velocity gradient $\large = \frac{dv}{dx} = \frac{2-0}{1-0}$

= 2 s^{-1}

From, Newton’s law of viscous force,

$\large F_v = \eta A \frac{dv}{dx} $

$\large = 10^{-2}\times 10^{-1} \times 10 \times 2 $

= 0.02 N