A flat plate 0.1 m² area is pulled at 30 cm/s relative to another plate located at a distance of 0.01 cm from it, the fluid separating them being water with viscosity of 0.001 Ns/m². The power required to maintain velocity will be

Concept:

The tangential shear stress between two adjoining is proportional to velocity gradient in direction of perpendicular to the layer. This is known as law of viscosity.

\(\tau = \;\mu \frac{{du}}{{dy}}\)

Shear force acting on the moving plate is given by F = τ × A

Power required to maintain velocity U is given by P = F × U

Calculation:

Given μ = 0.001 Ns/m², U = 0.3 m/s, Y = 0.01 cm = 0.01 × 10^-2 m, A = 0.1 m²;

Velocity gradient or rate of shear strain is given by

\(\left( {\;\frac{{du}}{{dy}}\;} \right) = \;\frac{U}{Y} = 3000\;{s^{ - 1}}\)

τ = 0.001 × 3000 = 3 N/m²

F = 3 × 0.1 = 0.3 N,

P = 0.3 × 0.3 = 0.09 W