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BLOOD CIRCULATIONINTRODUCTION
Blood is considered as a fluid. In simplest cases it
supposed to be single-component, non-viscous, non-
compressible while the most complicated models include
chemical reactions between the components dissolved in
blood. In any case, it should be mentioned that blood has
very complicated rheological properties. It may beconsidered in terms of continuum media due to the certain
conditions taken place in most parts of the circulatory
system of the organism under the normal conditions
BERNOULLIS EFFECT
In the engineering sense, blood is not an idealfluid. This
is basically because blood is non-Newtonian fluid which
represents pseudoplastic behaviour. Hence, Bernoulli
cannot be used completely in human body since it usually
refer to Newtonian fluid only. However, in a way Bernoullis
insight is helpful. For instance, blood pressure is the
summation of three components lateral pressure, kinetic
energy (also known as the impact pressure or the
pressure required to cause flow to stop), and gravitational
forces. Kinetic energy is greatest in the ascending aorta
where velocity is highest but even there it contributes less
than 5 mm Hg of equivalent pressure.
Total energy (TE) = potential energy + kinetic energy
TE = (perpendicular pressure + gravitational pressure) +
kinetic energy
TE = (PPer+ Pgrav) + 1/2 V2
where Vis velocity and is blood density (approximately1060 kg/m3)
TE = PPer+ ( h g) + 1/2 V2
where gis gravitational constant and his height of fluid.
POWER LAW FOR NON-NEWTONIAN FLUID
Blood which give pseudoplastic behaviour can be
considered as a non-Newtonian power law model of
the form:
= K (du/dr)n= shear stressK = flow consistancy index
n = non Newtonian behaviour index (dimensionless)
du/dr: = shear rate or velocity gradient
PROPERTIES OF BLOOD
The flow of blood in blood vessels, like the flow in
liquids in narrow rigid tubes, is normally laminar
(streamline). Within the blood vessel, an infinitely
thin layer of blood in contact with the wall of the
vessels does not move. The next layer within the
vessel has a small velocity, the next a higher
velocity, and so forth, velocity greatest in the center
of the stream. Laminar flow occurs at velocities up
to a certain critical velocity. At or above this velocity
flow is turbulent. Streamline flow is silent, but
turbulent flow creates sound, frequently presenting
in clinical practice as a bruit.
DARCY LAWS & HAGEN-POISEUILLES LAW
For blood flow in the cardiovascular system,
mathematically, is described by Darcy's law and
approximatelyby Hagen-Poiseuille's law. Blood is an
inhomogeneous medium consisting mainly of plasma
and a suspension of red blood cells. Red cells tend
to coagulate when the flow shear rates are low, while
increasing shear rates break these formations apart,
thus reducing blood viscosity. This result in two non-
Newtonian blood properties, shear thinning and yield
stress. In healthy large arteries blood can be
successfully approximated as a homogeneous,
Newtonian fluid since the vessel size is much greater
than the size of particles and shear rates are
sufficiently high that particle interactions may have a
negligible effect on the flow. In smaller vessels,however, non-Newtonian blood behavior should be
taken into account. The flow in healthy vessels is
generally laminar; however in diseased arteries the
flow may be transitional or turbulent. Equations for:
Darcys Law Hagen-Poiseuilles Law
F = P
R
F = blood flow L = length oftube P = pressure
R = resistance = fluid viscosity r = radius of tube
It is important to note that resistance to flow changes
dramatically with respect to the radius of the tube. In
angioplasty, as it enables to increase of blood flow
with balloon catheter to the deprived organ
significantly with only a small increase in radius of a
vessel.
R = L 8
r4 ( () )
ECH 3103
Prepared by:
Nur Shazlinda Binti Zaini (141273)Siti Atiqah Hanim Binti Ramli (141776)
Siti Fatimah Binti Ibrahim (142444)
References:
http://en.wikipedia.org/wiki/Blood_flow#column-one
Basic of Hemodynamic; James E. Faber; Chapter 1
Hemodynamic Physical Principle; Jim Baun; Chapter12
r. Siti Aslina Hussain