Problem 8 An infinite plate is moved over a second plate on

Problem 8: An infinite plate is moved over a second plate on a layer of liquid as shown. For small gap width, d, we assume a linear velocity distribution in the liquid. The liquid viscosity is 1.2x104 N s m2 and its specific gravity is 0.88. Find the following: U= 0.3 m/s d= 0.3 mm a) The velocity of the fluid in m/s at y = 0.25 mm, where y=0 is located at the bottom plate. b) The fluid shear stress on the upper plate, in Pa c) The fluid shear stress at d=0.15 mm, in Pa.

Solution

In the laminar flow , For a parallel plate

a) velocity of the fluid=(3÷2)ו25=•45

b)shear stress on the upper plate=1•2×(10)^(-4)ו45÷(•3)=180Pa

c)shear strss= 1•2×(10)^(-4)×(•45)÷(•15)=360Pa