Question

A river water is flowing at $5m{s}^{-1}$. The depth of river water is $10m.$ The shearing stress between horizontal layers of the river water is

(Viscosity of water is $1$ decapoise)

• A. $0.1\times {10}^{-3}N{m}^{-1}$
• B. $0.5\times {10}^{-3}N{m}^{-1}$
• C. ${10}^{-3}N{m}^{-1}$
• D. $2\times {10}^{-3}N{m}^{-1}$

Answer 1

Answer: (B)

$0.5\times {10}^{-3}N{m}^{-1}$

$F=\eta A\frac{dv}{dx}\to$ viscous force

shearing stress $=\frac{F}{A}=\eta \frac{dv}{dx}$

$\frac{dv}{dx}=\frac{5m{s}^{-1}}{10m}=0.5$

$\eta =1$ millideca poise $={10}^{-3}$decapoise

$\therefore$ shearing stress$=0.5\times {10}^{-3}N{m}^{-2}$