2. FLUID MECHANICS
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.
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.
7. 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.
8. 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.
9. 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]
10. 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
obtainKinematic 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]
ed by dividing the absolute viscosity of a fluid with the fluid mass density.
11. 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
12. 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).
13. 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
14. 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.
15. 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.
16. 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
17. FLUID STATICS (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.
18. 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.
19. 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).
20. 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
21. TYPES OF FLUID FLOW
Laminar Flow:- in which the
fluid particles move along well
defined paths or stream line.
22. 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.
23. 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.
24. 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
25. 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.
