The velocity of upper layer of water in a river is 36 km h - 1 . Shearing stress between horizontal layers of water is 10 - 3 N m - 2 . Depth of the river is _____ m . (Co-efficient of viscosity of water is 10 - 2 Pa s )

Step-by-step solution

The viscous force formula is given by, F = - η A d v d y Therefore, shear stress F A = - η d v d y . Here negative sign tells us that the direction of force is opposite to the velocity gradient. ⇒ F A = η d v d y Now v = 36 × 5 18 = 10   m   s - 1 and if the depth is d d v d y = 10 d ⇒ 10 - 3 = 10 - 2 × 10 d ⇒ d = 100   m