The document discusses key concepts in biofluid mechanics including: 1) Fluid mechanics and its two branches - fluid statics and fluid dynamics 2) Biofluid mechanics focuses on how biological systems interact with liquids/gases like transporting oxygen in blood 3) Properties of fluids like density, viscosity, pressure, and temperature 4) Fluid statics examines fluids at rest using concepts like pressure variation, buoyancy, and Archimedes' principle 5) Types of fluid flow include steady/unsteady, laminar/turbulent, compressible/incompressible flows

1. Biofluid Mechanics

2. Fluid mechanics
• Mechanics is " ... the application of the laws of force and motion.
• fluid mechanics is the application of the laws of force and motion to
fluids
• There are two branches of fluid mechanics:
1. Fluid Statics or hydrostatics is the study of fluids at rest. The main
equation required for this is Newton's second law for
nonaccelerating bodies,
2. Fluid Dynamics is the study of fluids in motion. The main equation
required for this is Newton's second law for accelerating bodies

3. Biofluid mechanics
• Biofluid mechanics is focused on how biological systems interact with
and/or use liquids/gases. For humans, this includes obtaining and
transporting oxygen blood, maintaining body temperature, and
regulating homeostasis.

4. Fluid
• A fluid is a substance which deforms continuously under the
application of a shear stress.
• Some define a fluid as any material that takes the shape of the
container in which it is held.
• A fluid is either a liquid or a gas. For example, blood ,water air and oil.

5. Shear Stress
• A stress is defined as a force per unit area, acting on surface element.
• Stresses have both magnitude (force per unit area) and direction, and
the direction is relative to the surface on which the stress acts.
• There are normal stresses and tangential stresses.
• Pressure is an example of a normal stress, and acts inward, toward
the surface, and perpendicular to the surface.
• A shear stress is an example of a tangential stress, i.e. it acts along
the surface, parallel to the surface.

6. Shear stress

8. Fluid as a continuum
• By assuming a fluid is a continuum, we can suppose that there are no
inhomogeneities within the smallest division of fluid that are made.
Properties such as viscosity, density, and temperature, among others,
must be constant throughout the entire fluid.
• In most engineering applications the average or macroscopic effects
of a large number of molecules is considered. We thus do not concern
about the behavior of individual molecules. The fluid is treated as an
infinitely divisible substance, a continuum at which the properties of
the fluid are considered as a continuous (smooth) function of the
space variables and time

9. Properties of fluid
• 1. Density:
• Density is the mass per unit volume of a fluid. In other words, it is the
ratio between mass (m) and volume (V) of a fluid.
• Density is denoted by the symbol ‘ρ’. Its unit is kg/m3.

10. Properties of fluid
2.Viscosity
Viscosity is the quantity that describes a fluid's resistance to flow.
Fluids resist the relative motion of immersed objects through them as
well as to the motion of layers with differing velocities within them.

11. Properties of fluid
• There are actually two quantities that are called viscosity.
• The quantity defined above is sometimes
called dynamic viscosity, absolute viscosity, or simple viscosity to
distinguish it from the other quantity, but is usually just called
viscosity. The other quantity called kinematic viscosity.
• The SI unit of viscosity is the pascal second [Pa s]

12. Properties of fluid
• Kinematic viscosity is the measure of the inherent resistance of a fluid to
flow when no external force is exerted, except gravity. It is the ratio of the
dynamic viscosity to its density, a force independent quantity. Kinematic
viscosity can be obtained by dividing the absolute viscosity of a fluid with
the fluid mass density.
• Kinematic viscosity = Dynamic viscosity / Fluid mass density
• ν = η / ρ
• We have:
• ν: Kinematic viscosity
• ρ: fluid density
• η: Dynamic viscosity
• The SI unit of kinematic viscosity is the square meter per second [m2/s]

13. Properties of fluid
• 1) In a liter of mercury that weights 2 Kg, what is its kinematic
viscosity?
• Answer: The dynamic viscosity of mercury is η= 1.526 Pa*s. First
calculate the density mass of mercury using the formula ρ =
mass/volume.
• ρ = 2 Kg/ 1 L = 2 Kg/ 0.001 m3 = 2000 Kg/m3
• Then calculate the kinematic viscosity using its formula,
• ν = η / ρ
• ν = 1.526 Pa*s / 2000 Kg/m3 = (1.526 N*s/m2) / (2000 Kg/m3)
• ν = 0.000763 m2/s

14. Properties of fluid
• 3. Pressure:
• Pressure of a fluid is the force per unit area of
the fluid. In other words, it is the ratio of force
on a fluid to the area of the fluid held
perpendicular to the direction of the force.
• Pressure is denoted by the letter ‘P’. Its unit
are N/m^2 or atm or pascal(pa)

15. Properties of fluid
• Absolute Pressure. When pressure
is measured relative to a perfect
vacuum.
• Gauge Pressure. When pressure is
measured relative to atmospheric
pressure.
• pgauge = pabsolute – pabsolute; atm

16. Properties of fluid
• 4.Temperature: It is the property that determines the degree of
hotness or coldness or the level of heat intensity of a fluid.
• 5. Specific Volume is the volume of a fluid (V) occupied per unit mass
(m). It is the reciprocal of density.
• Specific volume is denoted by the symbol ‘v’. Its unit is m3/kg.

17. Properties of fluid
• 6. Specific Weight: is the weight possessed by unit volume of a fluid.
It is denoted by ‘w’. Its unit is N/m3.
•
• 7. Specific Gravity: is the ratio of specific weight of the given fluid to
the specific weight of standard fluid. It is denoted by the letter ‘S’. It
has no unit.

18. Fluid statics
• Fluid statics or hydrostatics is the branch of fluid mechanics that
studies "fluids at rest and the pressure in a fluid or exerted by
a fluid on an immersed body.
• Newton’s second law of motion, simplified to the sum of the forces
acting on the fluid is equal to zero is the primary governing equation
that is used to solve fluid static problems.
• The primary quantity of interest within fluid statics problems is the
pressure field throughout the fluid.
• No acceleration and the density is constant

19. Pressure Variation in a Static Fluid
• This equation indicates that the
pressure difference between two
points in a static incompressible
fluid can be determined by
measuring the elevation
difference between the two
points. Devices used for this
purpose are called manometers.

20. Pressure Variation in a Static Fluid

21. Pressure Variation in a Static Fluid

22. Fluid statics (Buoyancy)
• Buoyancy
• Buoyancy is defined as the net vertical
force acting on an object that is either
floating on a fluid’s surface or immersed
within the fluid(Archimedes' Principle).
• To determine the net force acting on an
immersed of floating object, the same
relationship for pressure variation within
a static fluid can be applied.

23. Fluid statics (Buoyancy)
• buoyant force =(density of liquid)(gravitational acceleration)(volume of
liquid)
• = (density)(gravitational acceleration)(height of liquid)(surface area of
object)
• Fb = ρgV = ρghA
• Fb = buoyant force of a liquid acting on an object (N)
• ρ = density of the liquid(kg/m3)
• g = gravitational acceleration(9.80 m/s2)
• V = volume of liquid displaced (m3 or liters, where 1 m3 = 1000 L)
• h = height of water displaced by a floating object(m)
• A = surface area of a floating object(m2)

24. Fluid statics (Buoyancy)
• 1) A golden crown has been placed in a tub of water. The volume of water
displaced is measured to be 1.50 liters. The density of water is 1000 kg/m3,
or 1.000 kg/L. What is the buoyant force acting on the crown?
• Answer: The buoyant force can be found using the formula. First, we
ensure that the units used for volume are the same. If 1 m3 = 1000 L, then
1.50 L = 0.00150 m3. The buoyant force is:
• Fb = ρgV
• Fb = (1000 kg/m3)(9.80 m/s2)(0.00150 m3)
• Fb = 14.7 kg∙m/s2
• Fb = 14.7 N
• The buoyant force acting on the golden crown is 14.7 N.

25. Types of fluid
• 1. Ideal Fluid: A fluid which can not be compressed and have no
viscosity falls in the category of ideal fluid. Ideal fluid is not found in
actual practice but it is an imaginary fluid because all the fluid that
exist in the environment have some viscosity. there in no ideal fluid in
reality
• 2. Real Fluid: A fluid which has atleast some viscosity is called real
fluid. Actually all the fluids existing or present in the environment are
called real fluids. for example water.

26. Types of fluid
• 3. Newtonian Fluid: If a real fluid obeys the Newton’s law of viscosity
(the shear stress is directly proportional to the shear strain) then it is
known as the Newtonian fluid( water, oil, gasoline, alcohol).
• 4. Non-Newtonian Fluid: If real fluid does not obeys the Newton’s law
of viscosity then it is called Non-Newtonian fluid.(Blood yogurt ,
ketchup, gels)
• 5. Ideal Plastic Fluid: A fluid having the value of shear stress more
than the yield value and shear stress is proportional to the shear
strain (velocity gradient) is known as ideal plastic fluid(tooth paste).

27. Types of fluid

28. Fluid kinematics
• Kinematics is the generalized study of motion. Using kinematic
relationships you can describe the motion of any particle in space and
time.

29. Types Of Fluid Flow
• Steady Flows:- In which the fluid Characteristics Like velocity,
pressure, density , etc. At a Point do not change with time.
• Unsteady Flow:- In which the fluid velocity , pressure or density at a
point changes with respect to time.
• Uniform Flow:- In which the velocity at given time does not change
with respect to space ( length of direction of the flow ).
• Non-Uniform Flow:- In which the velocity at any time changes with
respect to space. Changing in space

30. Types Of Fluid Flow
• Laminar Flow:- in which the fluid
particles move along well
defined paths or stream line.

31. Types Of Fluid Flow
• Turbulent flow: In turbulent flow
occurs when the liquid is moving
fast with mixing between layers.
The speed of the fluid at a point
is continuously undergoing
changes in both magnitude and
direction.

32. Types Of Fluid Flow
• Compressible Flows:- In which
the density of the fluid changes
from point to point. The density
is not constant for the fluid.
• Incompressible Flows:- In which
the density of fluid changes from
point to point. the density is
constant for the fluid.

33. CONSERVATION LAWS
• CONSERVATION OF MASS
The mass can neither be created nor destroyed
within the volume/system of interest.
• In special, we can use the conservation of mass
to solve various fluid mechanics problems. For
example, The volume flow rate

34. CONSERVATION OF MASS
• the volume (or volumetric) flow
rate, Q. For an incompressible flow
through a nondeformable volume,
the volume flow rate into the
volume must be balanced by the
flow out of the volume.
• However, since the volume is
nondeformable, the volume flow
rate can be calculated at any one
location at any time within the
system of interest. Its definition
would be

35. Conservation of Energy
• In physics, the law of conservation of energy states that the
total energy of an isolated system remains constant, it is said to be
conserved over time. This law means that energy can neither be
created nor destroyed; rather, it can only be transformed or
transferred from one form to another.