First slide

Viscous flow/Laminar flow

Question

A plate of area 2 m² is made to move horizontally with a speed of 2 ms^-1 by applying a horizontal tangential force over the free surface of a liquid. The depth of the liquid is 1 m and the liquid in contact with the bed is stationary. Coefficient of viscosity of liquid = 0.01 poise. The tangential force needed to move the plate is $α$ x 10^-3 N. The valve of $α$ is________.

Moderate

Solution

$Velocity gradient = \frac{Δ v}{Δ y} = \frac{2 - 0}{1 - 0} = 2 {ms}^{- 1} m^{- 1}$
$Viscous force, | F | = η A \frac{Δ v}{Δ y} = (0.01 \times 10^{- 1}) (2) (2) = 0.004 N$
So, to keep the plate moving with constant velocity, a force of 4 x 10^-3N has to be applied. Thus, $α$ = 4.

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