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Calculate average velocity (vav), volumetric flow rate (Q),
total z-direction force on the wall (Fz), and the
maximum
velocity (vmax) for the flow of a falling film of constant
viscosity
(problem we did in class).
SOLUTION
-
In class we solved for the velocity field in a liquid film falling down
an inclined plane. In that example we used Newton’s law of viscosity
which has a constant viscosity, m.
Calculate
the velocity field for the same geometry but for a fluid whose
viscosity
is a function of position according to the equation below. Such a
variation
might come about if the inclined wall were heated.
where m is the viscosity, d=H is the film thickness, x
is the coordinate direction perpendicular
to the wall, and mo
and
a
are constants. SOLUTION
- Calculate average velocity (vav), volumetric flow rate
(Q),
total z-direction force on the wall (Fz), and the
maximum
velocity (vmax) for the flow of a falling film of variable
viscosity
(see problem 3 above). SOLUTION
-
Calculate average velocity (vav), volumetric flow rate (Q),
total z-direction force on the wall (Fz), and the
maximum
velocity (vmax) for the Poiseuille flow (pressure-driven
flow
of a Newtonian fluid) in a tube (solution for velocity profile will be
performed in class). Note: these calculations are performed in
cylindrical
coordinates. SOLUTION
-
Using shell balances, calculate the velocity profile (vx(y))
for steady, pressure-driven flow of a Newtonian (constant viscosity)
fluid
between large parallel plates (see below). You may assume that the flow
is well developed, that is that the disturbances from the entry and
exit
of the flow are negligible. The pressure at x=0 is Po,
and at x=L the pressure is PL. Both walls are
stationary,
the gap between the plates is 2H, and the width of the flow region of
interest
is W. SOLUTION
