EGM 6812 Fluid Mechanics 1  Fall 2010
10/4/10, 6
th
Homework
1/2
1.
Consider the flow in an annulus generated by a solid cylinder of radius
b
rotating at a speed
in a larger cylindrical tube of inner radius
a
.
The space between the cylinders is filled
with a viscous incompressible fluid.
Find the resulting velocity distribution in the fluid.
Plot
the velocity profile for different ratios
ba
and discuss the analytical limit of small gaps
(Hint: perform a series expansion, truncate appropriately and examine the limits).
2.
For the same geometry as problem 1, find the velocity profile if the rod is pulled in the axial
direction at a constant speed
0
z
vV
, neglecting gravity and assuming constant pressure.
Plot
the velocity profile for different ratios
and discuss the analytical limit of small gaps.
3.
For the same geometry as problem 1, find the velocity profile if a constant pressure gradient
p
z
is applied in the axial direction and discuss the analytical limit of small gaps.
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 Fall '09
 RENWEIMEI
 Fluid Dynamics, Fluid Mechanics, Navier Stokes, fully developed region, analytical limit, velocity profile vz

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