The power require to keep the plate in steady motion is

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Direction: The laminar row takes place between closely spaced parallel plates as shown in figure below. The velocity profile is given by
u = V = v/h. The gap height, h is 5 mm and the space is filled with oil (specific gravity = 0.86, viscosity m = 2 × 10^–1 N-s/m²). The bottom plate is stationary and the top plate moves with a steady velocity of V = 5 cm/s. The area of the plate is 0.25 m².

The power require to keep the plate in steady motion is

1. 5 × 10^–4 watts
2. 10^–5 watts
3. 2.5 × 10^–5 watts
4. 5 × 10^–5 watts

Correct Option: C

Velocity profile, U = V		y
		h

V = 5 cm/s = 0.05 m/s
Newton’s law of viscosity,

τ = μ	du
	dy

= μ	d		v.	y		= μ.	V
	dy			h			h

Shear force = shear stress × surface area
F = τ × A

= μ.	v	.A
	h

Power required = F.

= μ.	V	.A × V
	h

= μ	V²	A
	h

=	(2 × 10⁻⁴) × (0.05)² × 0.25
	0.005

= 2.5 × 10^–5 W