Question

The velocity of water in a river is 18 km h^-1 near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = 10^-2 poise.

• A. 0.2 N
• B. 0.02 N
• C. 0.002 N
• D. 2N

Answer 1

The correct option is B

0.02 N

The velocity gradient in vertical direction is
$\frac{dv}{dz}=\frac{18km{h}^1}{5m}=1.0s^1$
The magnitude of the force of viscosity is
$F=\eta A\frac{dv}{dz}$
The shearing stress is
$\frac{F}{A}=\eta A\frac{dv}{dz}=\left({10}^{-2}poise\right)\left(1.0s^{-1}\right)={10}^{-3}\frac{N}{m^{-2}}$