1. 1
INTRODUCTION
.
Mechanics
The oldest physical science that deals with both stationary and
moving bodies under the influence of forces.
Statics
The branch of mechanics that deals with bodies at rest.
Dynamics
The branch that deals with bodies in motion.
Fluid mechanics
The science that deals with the behavior of fluids at rest (fluid
statics) or in motion (fluid dynamics), and the interaction of
fluids with solids or other fluids at the boundaries.
Fluid dynamics
Fluid mechanics is also referred to as fluid dynamics by
considering fluids at rest as a special case of motion with zero
velocity.
2. 2
Hydrodynamics
The study of the motion of fluids that can be approximated as
incompressible (such as liquids, especially water, and gases at low
speeds).
Hydraulics
A subcategory of hydrodynamics, which deals with liquid flows in
pipes and open channels.
Gas dynamics
Deals with the flow of fluids that undergo significant density
changes, such as the flow of gases through nozzles at high speeds.
Aerodynamics
Deals with the flow of gases (especially air) over bodies such as
aircraft, rockets, and automobiles at high or low speeds.
Meteorology, oceanography and hydrology
Deal with naturally occurring flows.
3. 3
Fluid: A substance in the liquid
or gas phase. In physics, a fluid is
a substance that
continually deforms (flows)
under an applied shear stress.
A solid can resist an applied
shear stress by deforming.
A fluid deforms continuously
under the influence of a shear
stress, no matter how small.
In solids, stress is proportional to
strain, but in fluids, stress is
proportional to strain rate.
When a constant shear force is
applied, a solid eventually stops
deforming at some fixed strain
angle, whereas a fluid never
stops deforming and approaches
a constant rate of strain.
Deformation of a rubber block
placed between two parallel plates
under the influence of a shear force.
The shear stress shown is that on the
rubber—an equal but opposite shear
stress acts on the upper plate.
4. 1. Viscous versus Inviscid Regions of Flow
2. Internal versus External Flow
3. Compressible versus Incompressible Flow
4. Laminar versus Turbulent Flow
5. Natural (or Unforced) versus Forced Flow
6. Steady versus Unsteady Flow
7. One-, Two-, and Three-Dimensional Flows
8. Irrational Flow
5. 5
CLASSIFICATION OF FLUID FLOW
Viscous versus Inviscid Regions of Flow
Flows in which the frictional effects are significant is called viscous flow.
In many flows of practical interest, there are regions (typically regions not close
to solid surfaces) where viscous forces are negligibly small compared to inertial
or pressure forces is called inviscid flow.
The flow of an originally
uniform fluid stream
over a flat plate, and
the regions of viscous
flow (next to the plate on
both sides) and inviscid
flow (away from the
plate).
6. 6
Internal versus External Flow
External flow over a tennis ball, and the
turbulent wake region behind.
The flow of an unbounded fluid over a surface such as a plate, a wire,
or a pipe, whereas the flow in a pipe or duct if the fluid is completely
bounded by solid surfaces.
• Water flow in a pipe is
internal flow, and
airflow over a ball is
external flow .
• The flow of liquids in a
duct is called open-
channel flow if the
duct is only partially
filled with the liquid
and there is a free
surface.
7. 7
Compressible versus Incompressible Flow
If the density of flowing fluid
remains nearly constant throughout
the flow is referred to as
incompressible flow (e.g., liquid
flow). But the case of density of fluid
changes during flow (e.g., high-
speed gas flow) is compressible flow.
When analyzing rockets, spacecraft,
and other systems that involve high-
speed gas flows, the flow speed is often
expressed by Mach number
Schlieren image of the spherical shock
wave produced by a bursting ballon
at the Penn State Gas Dynamics Lab.
Several secondary shocks are seen in
the air surrounding the ballon.
Ma = 1 Sonic flow
Ma < 1 Subsonic flow
Ma > 1 Supersonic flow
Ma >> 1 Hypersonic flow
8. 8
Laminar versus Turbulent Flow
The highly ordered fluid
motion characterized by
smooth layers of fluid. The
flow of high-viscosity fluids
such as oils at low velocities is
typically laminar.
The highly disordered fluid
motion that typically occurs
at high velocities and is
characterized by velocity
fluctuations. The flow of low-
viscosity fluids such as air at
high velocities is typically
turbulent.
A flow that alternates
between being laminar and
turbulent is called
transitional flow.
Laminar, transitional, and turbulent flows
over a flat plate.
9. 9
Natural (or Unforced)
versus Forced Flow
A fluid is forced to flow over a
surface or in a pipe by external
means such as a pump or a fan
is called Forced flow.
Fluid motion is due to natural
means such as the buoyancy
effect, which manifests itself as
the rise of warmer (and thus
lighter) fluid and the fall of
cooler (and thus denser) fluid
is called Natural flow.
In this schlieren image of a girl in a swimming
suit, the rise of lighter, warmer air adjacent to
her body indicates that humans and warm-
blooded animals are surrounded by thermal
plumes of rising warm air.
10. 10
Steady versus Unsteady Flow
• The term steady implies no change at a
point with time.
• The opposite of steady is unsteady.
• The term uniform implies no change
with location over a specified region.
• The term periodic refers to the kind of
unsteady flow in which the flow
oscillates about a steady mean.
• Many devices such as turbines,
compressors, boilers, condensers, and
heat exchangers operate for long
periods of time under the same
conditions, and they are classified as
steady-flow devices.
Oscillating wake of a blunt-based airfoil
at Mach number 0.6. Photo (a) is an
instantaneous image, while photo (b) is a
long-exposure (time-averaged) image.
11. 11
One-, Two-, and Three-Dimensional Flows
• A flow field is best characterized by its
velocity distribution.
• A flow is said to be one-, two-, or three-
dimensional if the flow velocity varies in
one, two, or three dimensions, respectively.
• However, the variation of velocity in certain
directions can be small relative to the
variation in other directions and can be
ignored.
The development of the velocity profile in a circular pipe. V = V(r, z) and thus the
flow is two-dimensional in the entrance region, and becomes one-dimensional
downstream when the velocity profile fully develops and remains unchanged in the
flow direction, V = V(r).
Flow over a car antenna is
approximately two-dimensional
except near the top and bottom of
the antenna.
12. The mass of a moving fluid doesn’t change as it
flows. This leads to an important relationship
called the continuity equation
13. Derivation
Let’s Consider a portion of a flow tube between two
stationary cross sections ,
here,
The areas are = A1 , A2
Speeds are = V1, V2
Time interval = dt
Acquired distance’s ds1=V1.dt , ds2=V2.dt
volume dV1 = A1V1 dt , dV2=A2V2
Mass of fluid at point a & b, dm1 = ρA1V1 dt , dm2=
ρA2V2.dt
14. Now,
In steady flow the mass across all cross-sections is same,
dm1 = dm1 and
ρA1v1 dt = ρA2v2 dt
A1v1 = A2v2 ……….[01]
This is the continuity equation for the flow of ideal fluid .It
tells us that the flow of speed increases when the cross-
sectional area through which the fluid flows decreases.
16. Here,
Equation [01] can be written as,
Rv= AV=constant
Rv is the volume flow rate.
Again, If the density [ρ] of the fluid is constant the product of
density to volume flow rate gives the mass flow rate Rm,
Rm=Rv.ρ
17. The equation which relates the pressure, flow speed, and
height for flow of an ideal, incompressible fluid is known
as Bernoulli’s equation.
18. Deriving Bernoulli’s Equation
To derive Bernoulli’s Equation, let us apply work-energy
theorem to a fluid in a section of flow tube. The figure
represents a tube through which a fluid is flowing. According
to the limitations of Bernoulli’s equation the fluid must be,
• An Ideal fluid
• Flow must be Incompressible
• A steady flow
• There should be no viscous effects involved
20. Here,
For the fluid between cross sections a & b let,
• flow speed = v1
• In time interval dt achieved distance ds1= v1dt
• The cross-sectional area between point a & b = A1
For the fluid between cross-sections c & d let,
• flow speed = v2
• In time interval dt achieved distance ds2 = v2dt
• The cross-sectional area between point c & d =A2
Since the fluid is incompressible volume dv passing
through any cross-sectional area
dv = A1ds1 = A2ds2
21. Calculation,
By applying the principle of conservation of energy to
the fluid , we shall show that these quantities are
related by,
P1 + ½ ρv1
2 +ρgY1 = P2 + ½ ρv2
2 + ρgY2
This equation can also be simplified as,
P + ½ρv2 + ρgY=constant
Those equation are equivalent forms of Bernoulli’s
equation.
22. It is observed that Bernoulli’s equation is strictly
valid only to the extent that the fluid is ideal .If
viscous forces are present , thermal energy will be
involved neglected here.
23. Steady viscous fluid flow driven by an
effective pressure gradient established
between two ends of a long straight pipe of
uniform circular cross-section s generally
known as poiseuille’s flow.
24. DERIVATION
Let’s consider a discharge of streamlined volume flow
through a smooth-walled circular pipe. Where,
•V = discharge volume flow
• ΔP= pressure difference between the ends of the pipe
•r = internal radius of pipe
• l = length of pipe
• η = viscosity of fluid
25. Here,
The driving force on the cylinder due to the pressure difference,
FPRESSURE = Δp[πr2]
The viscous drag force depends on the surface area of
pipe,
In an state of constant speed, where the net forces goes to zero,
28. At the center,
• r=0
• dv/dr =0
• v is at its maximum.
At the edge
• r=R
• v=0
Now, we get an expression for the velocity,
v[r] = [Δp/4ηl] [R2- r2]
29. Now,
Now the equation of continuity giving the volume flux
for a variable speed is:
Substituting the velocity profile equation and the
surface area of the moving cylinder we can arrive at the
Poiseuille's equation.
31. Viscosity
Viscosity is internal
friction in a fluid .
Viscous forces oppose
the motion of one
portion of a fluid relative
to another . Viscosity is
the reason takes effort to
paddle a canoe through
calm water.
32. Measurments
Dynamic (or Absolute)
Viscosity:
The dynamic
viscosity(η) of a fluid is
a measure of the
resistance it offers to
relative shearing
motion.
η= F/ [A×(u/h)]
η= τ /(u/h) N-s/m²
Kinematic Viscosity :
It is defined as the
ratio of absolute
viscosity to the density
of fluid.
ν= η/ρ m²/s
ρ= density of fluid
33. Effects of temperature
The viscosity of liquids decreases with increase the
temperature.
The viscosity of gases increases with the increase the
temperature.
34. Effects of temperature
The lubricant oil viscosity at a specific temperature can
be either calculated from the viscosity - temperature
equation or obtained from the viscosity-temperature
ASTM chart.
Viscosity-Temperature Equations
35. Effects of pressure
Lubricants viscosity increases with pressure.
For most lubricants this effect is considerably
largest than the other effects when the pressure is
significantly above atmospheric.
The Barus equation :
