Question

A block of weight W slides down an inclined plane with a constant velocity V while lubricated by a thin film of a fluid. The film contact area is A and its thickness is h. Assuming a linear velocity distribution in the film, derive an expression for the viscosity ? of the fluid. Calculate the viscosity ? of the fluid if the block mass is 6 kg, A = 35 cm, , ? = 30°, V = 20 m/s and h = 1 mm. Liquid film of thickness h Block contact area A

Answer 1

Draw the free body diagram of the block Block contact Liquid Film of thickness area Wcos Calculate the shear force lu dy Apply the equations of equilibrium and calculate the horizontal forces mg sin VA Calculate the viscosity of the fluid 1000609.81)sin30° (20) 35x10-4 0.42043 Ns/m. 1-0.42043 Ns/m2