7/30/2019 Blood Circulation-Chemical Engineering

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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