Biomedical Engineering Reference
In-Depth Information
Fig. 4.13
Blood flow examples showing the significance of occluded arteries on flow rate and
pressure
Fig. 4.14 a
A moving fluid exhibits kinetic energy
g
ρ
, and press
(P).
b
Bernoulli's equation in a
horizontal line
shows the interchanging energy from kinetic to
pressure as the fluid passes through a stenosis
ρ
, potential energy
(
2
)
(1 / 2
)
4.6.4
Bernoulli's Equation
The Bernoulli equation is derived from the energy conservation law, relating blood
pressure with flow velocity (Fig.
4.14
). This is given as
1
1
2
2
P
+ + =+ +
ρ ρ ρρ
u
gy
P
u
gy
1
1
1
2
2
2
2
2
(4.18)
pressure energy
potential energy
kinetic energy
where
P
is pressure,
u
is velocity,
g
is gravity, and
y
is height.
In Poiseulle's Law, we saw that pressure is a driving force for blood flow. How-
ever this is one contribution to the total energy that drives flow between two points.
Bernoulli's equation states that the total energy of the flow is given by the pressure
force exerted on the flow plus its kinetic energy produced from its mass and veloc-
ity, plus the potential energy produced by gravitational effects. Bernoulli's equation
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