Question

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

Answer 1

F = 0.0022N

Step-by-step 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