Question Bank • QB_SWCE_FM_001 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Ideal and real fluids, properties of fluids

Question Statement:

A flat plate of area $0.80\text{ m}^2$ is pulled horizontally at a constant velocity of $2.0\text{ m/s}$ over a stationary plate. The gap between the plates is $0.50\text{ mm}$ and is filled with lubricating oil having dynamic viscosity $\mu = 0.25\text{ Pa}\cdot\text{s}$. Assuming a linear velocity profile in the oil film, the viscous shear force required to pull the plate in newtons (N) is ________ (answer in integer).

Answer Key:

800

Step-by-Step Solution & Explanation

From Newton's law of viscosity: $\tau = \mu \frac{du}{dy}$ Given: • $\mu = 0.25\text{ Pa}\cdot\text{s}$ • $du = 2.0\text{ m/s}$ • $dy = 0.50\text{ mm} = 0.0005\text{ m}$ • Plate area $A = 0.80\text{ m}^2$ $\tau = 0.25 \times \frac{2.0}{0.0005} = 0.25 \times 4000 = 1000\text{ N/m}^2$ Total viscous shear force: $F = \tau \times A = 1000 \times 0.80 = 800\text{ N}$
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