The Shell Momentum Balance:
StepbyStep Method
CBE 320, DJK, Fall 2010
Step 1:
Draw a (crude) picture and list assumptions
•
What velocity components are nonzero?
•
What spatial variables does the velocity depend on?
•
Choose coordinate system.
•
Start a list of assumptions.
Step 2:
Select system
•
Draw a second picture, showing the “shell” in detail.
•
“Shell”:
•
a ‘box’ with sides
bardbl
or
⊥
to the velocity
v
.
•
box faces should lie on coordinate surfaces (you choose your
coordinate system to guarantee this).
•
Make shell thin in the direction the velocity is varying.
•
You will develop intuition about how to do this as you work prob
lems.
Step 3:
Apply conservation of momentum (compo
nent of interest)
Rate at which
momentum is
transported
into
the system
{
{
Rate at which
momentum is
transported
out of
the system
{
{
Force of gravity
acting on
the system
{
{
+
= 0

f
d
t
r
ij
ij
ij
i
j
=
+
+
p
vv
add other body
forces here (e.g.,
electrical, magnetic,
etc.)
if unsteady, then
the RHS is the time
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 Spring '10
 idk
 Derivative, Force, Momentum, RHS

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