THE VELOCITY OF WATER IN A RIVER IS 18km/hr NEAR THE SURFACE.IF THE RIVER IS 5M DEEP,FIND THE SHEARING STRESS BETWEEN THE HORIZONTAL LAYERS OF WATER.THE COEFFICIENT OF VISCOSITY OF WATER IS 10POWER-2 POISE.

Since we are given the velocity at surface at 18 km/hr and hence velocity gradient dv/dx = 18 km/hr / 5m = 1.0 per second

But viscous force F = h A dv/dx

h = 10^–3 Pa s (Since 1 poise = 0.1 Pa s and 10^–2 poise = 10^–3 Pa s)

F/A = h dv/dx

Shearing stress or viscous force per unit area = 10^–3 x 1.0 = 10^–3 Nm^–2

Thanks & Regards,

Vasantha Sivaraj,

askIITians faculty