The velocity of water in a river is 18, km/h | vedclass

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(C) Given:Velocity $v = 18\, km/h = 18 	imes \frac{5}{18} = 5\, m/s$.Depth $l = 5\, m$.Coefficient of viscosity $\eta = 10^{-2}\, 	ext{poise} = 10^{

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

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(C) Given:Velocity $v = 18\, km/h = 18 	imes \frac{5}{18} = 5\, m/s$.Depth $l = 5\, m$.Coefficient of viscosity $\eta = 10^{-2}\, 	ext{poise} = 10^{-2} 	imes 0.1\, N\cdot s/m^2 = 10^{-3}\, N\cdot s/m^2$.The velocity gradient (strain rate) is given by $\frac{dv}{dx} = \frac{v}{l} = \frac{5\, m/s}{5\, m} = 1\, s^{-1}$.According to Newton's law of viscosity,the shearing stress $	au$ is given by:$	au = \eta 	imes \frac{dv}{dx}$.Substituting the values:$	au = 10^{-3}\, N\cdot s/m^2 	imes 1\, s^{-1} = 10^{-3}\, N/m^2$.Therefore,the correct option is $C$.

The velocity of water in a river is $18\, km/h$ near the surface. If the river is $5\, m$ deep,find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water is $\eta = 10^{-2}\, \text{poise}$.

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