Biomedical Engineering Reference
In-Depth Information
If were lying down, with head and feet and equal level, then the pressure between
the two points are now the same and there is zero potential energy difference. As
we stand up from a lying position our body has to adjust, and if this adjustment is
not quick enough, then we experience dizziness as a result a sudden pressure drop
that reduces blood flow to the brain. Furthermore there is an increase in fluid build-
up in the legs because of the larger pressure difference needed for fluids to travel
upwards.
4.6.5
Pressure Drop Estimates
Flow through a pipe experiences a pressure difference between an upstream and
downstream location due to viscous effects. This pressure loss for all types of fully
developed internal flows is given as
2
ave
2
L
ρ
U
(4.20)
∆=
Pf
D
where
L
is the pipe length,
D
is the diameter, and
f
is the friction factor. For laminar
flow, the friction factor is a function of the Reynolds number only and is indepen-
dent of the roughness of the pipe surface
64
Re
f
=
(4.21)
For turbulent flows we saw that the velocity profile is blunt in the centre of the
pipe with a sharper velocity gradient at the wall. This effect has two important
consequences: (i) shear stress increases and therefore the resistance to flow greatly
increases, (ii) and wall roughness must be accounted for in determining the friction
factor since the thickness of this roughness becomes comparable with the sharp ve-
locity gradient. The friction factor can be determined from the well-known Moody
chart or by the Colebrook equation (Colebrook 1939)
1
ε
/
D
2.51
=−
2.0 log
+
(4.22)
3.7
f
Re
f
where
/
ε
is the relative roughness. The Colebrook equation is a representation of
the Moody chart which is plots the friction factor for pipe flow as a function of Re
number and the relative roughness
/
ε
.
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