A fluid between two very long parallel plates is heated in a way that its viscosity decreases linearly from 0.90 Pa⋅s at the lower plate to 0.50 Pa⋅s at the upper plate. The spacing between the two plates is 0.4 mm. The upper plate moves steadily at a velocity of 10 m/s, in a direction parallel to both plates. The pressure is constant everywhere, the fluid is Newtonian, and it is assumed to be incompressible. Neglect gravitational effects.

(a) Obtain the fluid velocity u as a function of y, u(y), where y is the vertical axis perpendicular to the plates. Plot the velocity profile across the gap between the plates. 

(b) Calculate the value of the shear stress. Show the direction of the shear stress on the moving plate and on the top surface of the fluid element adjacent to the moving plate.

Transcribed Image Text:

y h = 0.4 mm 0 FIGURE P10-54 U = 10 m/s X