Water in a river $20 \mathrm{~m}$ deep is flowing at a speed of $10 \mathrm{~ms}^{-1}$. The shearing stress…

Water in a river $20 \mathrm{~m}$ deep is flowing at a speed of $10 \mathrm{~ms}^{-1}$. The shearing stress between the horizontal layers of water in the river in $\mathrm{Nm}^{-2}$ is (Coefficient of viscosity of water $=10^{-3} \mathrm{ \ SI}$ units)
  1. $1 \times 10^{-2}$
  2. $0.5 \times 10^{-2}$
  3. $1 \times 10^{-3}$
  4. $0.5 \times 10^{-3}$

Solution

$\begin{aligned} \text { Shearing stress } & =\eta\left(\frac{d v}{d x}\right) \\ & =10^{-3}\left(\frac{10}{20}\right) \\ & =0.5 \times 10^{-3} \mathrm{Nm}^{-2}\end{aligned}$

Asked in: AP EAMCET 2004

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