Question

The velocity of water in a river is 18 km near the surface. If the river is 5m deep find the shearing stress between the horizontal layer of water in

Answer 1

the minus sign is indication of frictional force which is opposite to the direction of motion

Answer 2

The shearing stress between the horizontal layer of waters is 10⁻³ Nm⁻² .

Velocity of water = 18km/hr.

To express in m/s, we multiply with (1000/3600) to the value in km/hr.

[1 km = 1000m and 1 hr = 3600s].

So, velocity = 18×10/36 = 5m/s

The coefficient of viscosity of water is 10⁻² Poise

= 10⁻²/10 = 10⁻³ Nsm⁻².                                             [1 Poise = 0.1 Nsm⁻².]

Shear stress is given as :

Shear stress = (Coeffecient of viscosity)×(Velocity/Depth)

Coeffecient of viscosity = 10⁻³ Nsm⁻²

Velocity = 5m/s

Depth = 5m.

Putting these values, we get

Shear stress = 10⁻³ × (5/5) Nm⁻²

= 10⁻³ Nm⁻²