ECM 005 Quiz 3 Solutions
D.M. Lavenson
February 10, 2011
1
Problem 1
1.1
Part A
We are examining Brinkman’s equation in this problem, given as
μ
d
2
v
dx
2

μ
κ
v

Δ
P
L
= 0
,
(1)
where
v
is the velocity,
x
is the position, or distance, along which the fluid velocity is
directed (direction of fluid motion),
μ
is the fluid viscosity,
κ
is the porous membrane
permeability through which the fluid flows,
L
is the length across which the pressure
drop is measured, and
Δ
P
is the pressure difference across the length
L
. Below in
table 1 are the dimensions (and units) of the variables requested. Recall that dimensions
are NOT units, Force and Pressure are not dimensions, and that
x
does indeed have
dimensions (of length). The legend for the primary dimensions in the table is as follows:
M
= mass,
L
= length,
t
= time,
Θ
= temperature.
1.2
Part B
Now we must determine the SI units of the permeability,
κ
. We can do this by realizing
that in the Brinkman’s equation, all separate terms must have the same units/dimensions
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 Spring '08
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