Question

A Newtonian liquid of density 2400 kg m^-3 flows down under gravity in steady, laminar conditions over an inclined flat plate at an angle of 30° to the horizontal plane. The thickness of the film can be taken as constant. The velocity distribution across the liquid film is given by:

ux= (ρgδ/μ)y(1-y2/δ)sinθ

where u_x= velocity in the x-direction along the plate, r = density of liquid, g = gravitational acceleration, d = liquid film thickness, m = viscosity of liquid, y = perpendicular distance measured from the plate surface, q = angle between the plate and the horizontal plane.

(i)        If the liquid is flowing at an average velocity of 0.75 m s^-1 and the film is
20 mm thick determine the viscosity of the liquid.                             

(ii)        Calculate the maximum shear stress in the liquid film.

Answer 1