A Newtonian fluid is filled in the clearance between a shaft and a concentric sleeve. The sleeve attains a speed of 80 cm/s, when a force of 40 N is applied to the sleeve parallel to the shaft. Determine the speed if a force of 300N is applied.

Concept:

Newtonian fluids always follow Newton's law of Viscosity. Mathematically Newton's law of viscosity is represented as

\(τ = μ\frac{du}{dy}\)

Force equation from the above equation can be obtained as

\(F = Aμ\frac{du}{dy}\)                                                                        

where, μ = Coefficient of Viscosity, τ = Shear Stress

From the given question we can observe that Area(A), Viscosity(\(μ\)) and clearance(dy) is constant, hence Force is directly proportional to velocity.

\(\frac{F_{1}}{F_{2}} = \frac{V_{1}}{V_{2}}\)                              

Calculation:

Given:

F₁ = 40 N, F₂ = 300 N, V₁ = 80 cm/s

\(\frac{40}{300} = \frac{80}{V_{2}}\)

V₂ = 600 cm/s