Question

The velocity of water in the river is $9km/hr$ of the upper surface. The river is $10$m deep. If the coefficient of viscosity of water is ${10}^{-2}$ poise then the shearing stress between horizontal layers of water is.

• A. $0.25\times {10}^{-2}N/m^2$
• B. $0.25\times {10}^{-3}N/m^2$
• C. $0.5\times {10}^{-3}N/m^2$
• D. $0.75\times {10}^{-3}N/m^2$

Answer 1

Answer: (B)

$0.25\times {10}^{-3}N/m^2$

Coefficient of viscosity $\eta ={10}^{-2}$ poise $={10}^{-3}$ poiseuille

Rate of change of velocity w.r.t depth $\frac{\Delta u}{\Delta z}=\frac{9\times \frac{5}{18}}{10}=0.25$ $m{s}^{-1}/m$

Shear stress $\frac{F}{A}=\eta \frac{\Delta u}{\Delta z}$

$\therefore$ $\frac{F}{A}={10}^{-3}\times 0.25$

$⟹$ $\frac{F}{A}=0.25\times {10}^{-3}N/m^2$