311. The flow of blood in the veins and arteries is a transient process in which the elastic conduits
expand and contract.
As a simplified example, consider the artery shown in Figure 311.
At some
instant in time, the inner radius has a radial velocity of 0.012 cm/s.
The length of the artery is 13
cm and the volumetric flow rate at the
entrance
of the artery is 0.3 cm
3
/s.
If the inner radius of
the artery is 0.15 cm, at the particular instant of time, what is the volumetric flow rate at the exit of
the artery?
Figure 3.11
. Expanding artery
311. In this problem we consider the expanding artery having an inner radius of 0.15 cm,
a length of 13 cm, and a uniform radial velocity of 0.012 cm/s.
We begin our analysis
with the control volume illustrated in Figure 3.11a along with the appropriate
macroscopic mass balance given by
()
0
tt
d
dV
dA
dt
ρ+
ρ
−
⋅
=
∫
∫
vwn
9$
(1)
At the wall of the tube we have the condition
(
)
0 ,
at the tube wall
−⋅
=
(2)
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 Winter '10
 B.G.Higgins
 Fluid Dynamics, Trigraph

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