The velocity of water in a river is `18kmh^-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.`

Explanation

The velocity gradient in vertical direction is `(dv)/(dx)=(18kmh^-1)/(5m)=1.0s^-1`
the magnitude of the force of viscosity is
`F=etaA(dv)/(dx)`
The shearing stress is
`F/A=eta(dv)/(dx)=(10^-2poise)(1.0s^-1)=10^-3Nm^-2`