The velocity profile for a thin film of a Newtonian fluid that is confined between the plate and a fixed surface is defined by u = (5y-0.5y2) mm/s where y is in mm. Determine the force P that must be applied to the plate to cause this motion. The plate has a surface area of 4000mm2 in contact with the fluid. Take µ = 0.55 N. s/m2

Question

Tiana Good

Engineering

13 December, 15:13

The velocity profile for a thin film of a Newtonian fluid that is confined between the plate and a fixed surface is defined by u = (5y-0.5y2) mm/s where y is in mm. Determine the force P that must be applied to the plate to cause this motion. The plate has a surface area of 4000mm2 in contact with the fluid. Take µ = 0.55 N. s/m2

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India Morse · Answer 1

F = 0.0022N

Explanation:

Given:

Surface area (A) = 4,000mm² = 0.004m²

Viscosity = µ = 0.55 N. s/m²

u = (5y-0.5y²) mm/s

Assume y = 4

Computation:

F/A = µ (du/dy)

F = µA (du/dy)

F = µA[ (d/dy) (5y-0.5y²) ]

F = (0.55) (0.004) [ (5-1 (4)) ]

F = 0.0022N