Question

Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as $v=k\left(\frac{2 y^{2}}{a^{2}}-\frac{y^{3}}{a^{3}}\right)$ If coefficient of viscosity for water is $h$, what will be shear stress between layers of water at $y =a$.

• A. $\frac{\eta k}{a}$
• B. $\frac{\eta }{ka}$
• C. $\frac{\eta a}{k}$
• D. None of these

Answer 1

Answer: (A)

Newton's law of viscosity, $F=\eta A \frac{d v}{d y}$
Stress $=\frac{F}{A}=\eta\left(\frac{d v}{d y}\right)$
$=\eta k\left(\frac{4 y}{a^{2}}-\frac{3 y^{2}}{a^{3}}\right)$
At $y=a$, stress $=\eta k\left(\frac{4}{a}-\frac{3}{a}\right)$
$=\frac{\eta k}{a}$