Question

The speed of the water in a river is 'V near the surface. If the coefficient of viscosity of water is '$\eta$' and the depth of the river is 'H, then the shearing stress between the horizontal layers of water is

• A. $\eta$H/V
• B. $\eta$V/H
• C. $\frac{V}{\eta H}$
• D. $\eta$V/H

Answer 1

Answer: (B), (D)

B, D

Answer 2

Newton's law of viscosity states that the shearing stress ($\tau$) is proportional to the velocity gradient ($\frac{dv}{dy}$): $\tau = \eta \frac{dv}{dy}$ Assuming a linear velocity profile, where the velocity is 0 at the riverbed and V at the surface over a depth H, the velocity gradient is $\frac{V}{H}$. Substituting this into the formula gives: $\tau = \eta \frac{V}{H}$