Question

A plate is moving with velocity $5\text{m/s}$ parallel to a plate that is held stationary at a distance of $10\text{mm}$ below the upper plate. If the space between the plates is filled with water having coefficient of viscosity $9\times {10}^{-4}$ Pa $s$, then the shear stress acting on the surface of the moving plate assuming linear velocity profile between plates will be

• A. $0.45{\text{Nm}}^{-2}$
• B. $4.5\times {10}^{-3}{\text{Nm}}^{-2}$
• C. $2\times {10}^{-4}{\text{Nm}}^{-2}$
• D. ${10}^{-3}{\text{Nm}}^{-2}$

Answer 1

The correct option is A $0.45{\text{Nm}}^{-2}$

According to Newtons law of viscosity,
Shear stress, $\tau =\mu \frac{du}{dy}$
where $\mu =$ Dynamic viscosity of fluid
$\frac{du}{dy}=$ velocity gradient perpendicular to the direction of flow
Shear stress acting on plate, $\tau =9\times {10}^{-4}\frac{(5-0)}{10\times {10}^{-3}}=0.45N/m^2$