Download Problem 2.33 Given: Thin film of crude oil SG = 0.85, µ = 2.15 x 10

ME3834 ‐ Fluid Mechanics Problem 2.33 Given: Thin film of crude oil
SG = 0.85, µ = 2.15 x 10-3 lbf s/ft2
Film thickness:
h = 0.125 in,
Flows down an incline with slope: θ=300
The velocity profile:
h
µ
sinθ
Find: a) The magnitude and direction of the shear stress, ,acting on the surface
b) Plot the velocity profile
Solution: The shear stress is given by
So,
µ
h
At the inclined surface y=0, so,
0.85
1.94
sinθ
µ
hsinθ
SG
32.2
0.125
0.277
Therefore,
µ
sinθ h
h sinθ
12
.
sin 30
.
-------------------------------------(a)
0, the shear force on the solid
The surface is a positive y surface. Since the
surface corresponding to the stress must act in the positive x direction as shown on the
sketch below.
To plot the velocity profile, note that
Therefore,
=
max
2
is at y = h, so
µ
sinθ
sinθ
-------------------------------------(b)
1