2. Learning outcomes
1) Understand the basic concepts of Fluid Mechanics, its importance
and applications.
2) Recognize the importance of dimensional homogeneity in
engineering calculations.
3) Define some important fluid properties, like density, viscosity,
etc.
4) Classify various types of fluids and flows commonly encountered
in practice for solving problems in fluid mechanics.
5. Introduction
● Dimples on a golf ball create a thin
turbulent boundary layer of air that
clings to the ball's surface.
● This allows the smoothly flowing air
to follow the ball's surface a little
farther around the back side of the
ball
Why a golf ball has
dimples?
6. Fluid Mechanics is based on the following
three conservation principles:
Mass
Momentum
01
02
03
Energy
http://www.northcoastjournal.com/humboldt/watts-in-coffee-pot-and-brakes/Content?oid=2126652
7.
8.
9. 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.
1. Introduction
11. A fluid is defined as a substance that deforms (flows)
when acted on by a shearing stress of any magnitude.
LIQUIDS GASES
01 02
Also we can say
“any substance in the
liquid or gas phase is
referred to as a fluid”.
12. The difference between a solid and a fluid?
A solid can resist an applied shear stress
by deforming, whereas a fluid deforms
continuously under the influence of
shear stress, no matter how small.
Solid
Liquid
Gas
13. 1. A liquid takes the shape of the container it is in
and forms a free surface in the presence of
gravity.
2. A gas expands until it encounters the walls of
the container and fills the entire available space.
Gases cannot form a free surface.
3. Gas and vapor are often used as synonymous
words
Whatisafluid?
14. Do all liquids behave same?
If the applied shearing stress is small, they behave as a solid.
But, if the stress exceeds some critical value, they will flow.
Toothpaste Sauce
Tar Slurry
16. Knowledge and understanding of basic
principle of fluid mechanics are essential to
analyse any system in which a fluid is the
working medium.
All means of transportation
20. 4. Dimensions, Dimensional homogeneity,
and Units
Any physical quantity
can be characterised
by dimensions.
The arbitrary
magnitudes assigned
to the dimensions are
called units.
21. 4. Dimensions, Dimensional homogeneity, and Units
The primary quantities; Length, L, Mass, M, and Time, T
can be used to provide qualitative description of any other
secondary quantity. The system of these primary
dimensions is called MLT system.
Example 1:
Area - L2 Velocity - L / T or LT-1
Volume - L3
Acceleration - L / T2 or LT-2
22. In engineering, all equations must be dimensionally homogeneous. That is
every term in an equation must have the same dimensions.
It means that if an equation is dimensionally homogenous, the dimensions of
the left side of the equation must be the same as those on the right side.
Checking dimensions can serve as a valuable tool to spot errors. With some
attention and skill, dimensions can be used to our advantages. How?
■ They can be used to check formulas
■ They can be even used to derive formulas.
4. Dimensions, Dimensional homogeneity, and Units
Dimensional Homogeneity
23. 4. Dimensions, Dimensional homogeneity, and Units
Dimensional Homogeneity
Example 1:
It is required to determine the mass of a fluid in a tank. The oil density
and the tank volume are given with units kg/m3 and m3 respectively.
Suppose we forgot the formula that relates mass to density and
volume.
How we can use the principle of dimensional homogeneity to find
the required formula to determine the mass of the fluid?
25. 4. Dimensions, Dimensional homogeneity, and Units
•Prefixes: Multiples and Fractions.
•Prefixes are standard for all units.
Encouraged to
memorize them
because of their
widespread use.
29. 5. Some Important Fluid Properties
⮚ Before we proceed, it is necessary to define and discuss certain
fluid properties that are intimately related to fluid behavior.
⮚ Different fluids can have grossly different characteristics.
⮚ Gases are light and compressible, whereas liquids are heavy (by
comparison) and relatively incompressible.
⮚ A syrup flows slowly from a container, but water flows rapidly
when poured from the same container.
⮚ To quantify these and other differences certain fluid properties are
used.
33. 5.4. Pressure
❑ From definition, pressure has the unit of newton per square meter
(N/m2), which is called pascal (Pa). That is:
1 Pa = 1 N/m2
❑ Pascal is too small for pressures encounters in practice
1 kPa = 103 Pa, 1 MPa = 106 Pa
Pressure: is defined as normal force exerted by a fluid per unit area on
any real or imaginary surface.
❑ We use the term "Pressure" when we deal with a gas or a liquid.
But for solid we use the term "normal stress".
34. 5.4. Pressure
❑ Three other pressure units commonly used in practice:
bar, standard atmosphere, and kilogram-force per
square centimeter :
1 bar = 105 Pa = 0.1 MPa = 100 kPa
1 atm = 101 325 Pa
1 kgf/cm2 == 9.807 × 104 Pa
1 torr = 133.3 Pa, 1 atm = 760 mmHg
35. 5.4. Pressure
Graphical representation of gage and absolute pressure.
Pa = Pg + Patm
❑Absolute pressure (Pa),
❑Gage pressure (Pg),
❑Atmospheric pressure
(Patm).
❑Vacuum pressure.
36. 5.4. Pressure
❑Absolute pressure (Pa): is the actual pressure at a given position and it is
measured relative to absolute zero pressure (i.e., absolute vacuum.)
❑ Gage pressure (Pg): It is measured relative to the local atmospheric
pressure (Patm). Most pressure-measuring devices are calibrated to read
zero in the atmosphere, and so they indicate the difference between the
absolute pressure and the local atmospheric pressure. Gage pressure may be
positive or negative (vacuum). Pressure is particularly important fluid
characteristic and it will be discussed more fully in the next classes.
❑Vacuum pressures are pressures below that of the atmosphere.
Absolute, gage, and atmospheric pressures are all related to each other by:
Pa = Pg + Patm
37. 5.5. Density, ρ
⮚ Density for water is 1000 kg/m3
⮚ However, for most gases the density is proportional to P and
inversely proportional to T.
⮚ For ideal gases, this relation is given by the equation of state.
p = ρ R T R is a gas constant, J/kg.K
p absolute pressure, Pa
T absolute temperature, K
For air:
R = 287 J/kg.K
38. 5.6. Specific Volume, v, Specific weight, γ, and
Specific gravity, SG
❑ In fluid mechanics, we use three specific properties
that are related to density. These are:
❑ Specific Volume, v
❑ Specific Weight, γ
❑ Specific Gravity, SG.
(Not Commonly use in Fluid Mechanics)
39. 5.6.1. Specific volume, v
⮚ Specific volume, v, is the volume per unit mass and is
therefore the reciprocal of the density.
⮚ This property is not commonly used
in fluid mechanics but is used in
thermodynamics.
40. 5.6.2. Specific weight, γ
❑ Specific Weight, γ, of a fluid is defined as its weight per unit
volume. Thus, specific weight is related to density through the
equation:
where g is the local acceleration of gravity.
❑ Just as density is used to characterise the mass of a fluid system,
the specific weight is used to characterise the weight of the
system.
(N/m3)
41. 5.6.3. Specific Gravity, SG
❑ Since it is the ratio of densities, the value of SG does not depend on the
system of units used.
❑ It is clear that density, specific weight, and specific gravity are all
interrelated, and from knowledge of any one of the three the others can
be calculated.
❑ Specific Gravity, SG: The ratio of the density of the
fluid (or any other substance) to the density of water
at some specified temperature (usually at 4oC, where
the density of water is 1000 kg/m3).
43. 5.7. Viscosity
⮚ Intuitively we all know what viscosity is:
it's the "thickness" of a liquid.
▪ Honey is more viscous than water,
▪ Engine oil is somewhere in between and so forth.
⮚ We also understand that the viscosity of a liquid depends on
temperature.
▪ Maple syrup will run out of the bottle faster if it is heated,
▪ Engine oil is more viscous on a cold winter day, etc.
44. 5.7. Viscosity
We move with relative ease in air, but not so in water.
• There is a property that represents the internal resistance of a fluid to
motion or the “fluidity,” and that property is the viscosity.
• The force a flowing fluid exerts on a body in the flow direction is called
the drag force, and the magnitude of this force depends, in part, on
viscosity.
45. 5.7. Viscosity
❑ By definition, the viscosity of a fluid is the proportionality
constant that relates shear stress and the velocity profile
(velocity gradient) of a fluid under that stress.
❑ Viscosity is usually designated by the Greek symbol µ (mu).
❑ There is also something called the kinematic viscosity, ν. This
is simply the absolute viscosity divided by the fluid density.
(m2/s)
46. 5.7. Viscosity
⮚ Two very wide parallel plates with a fluid in between them. The bottom
plate is rigidly fixed, but the upper plate, it’s area A, is free to move.
⮚ If you try to move the top plate at a constant velocity (Vtop) then you'll need
to apply a force (F) to overcome the resistance (drag) of the fluid. Measure the
force and divide by the plate area to get the shear stress τ. (τ = F / A).
τ = F/A = µ dv/dy
Newton’s law of viscosity
47. 5.7. Viscosity
Newtonian Fluids: obey Newton’s law of
viscosity. The viscosity is independent of
rate of shear μ = μ (T, P) only
•e.g., gases, water, and most petroleum
products
Non-Newtonian Fluids:
•Viscosity varies with rate of shear (or
with time) μ = μ (T, P, du/dy)
•e.g., Long-chain polymers, blood,
printing ink, ketchup (shear thinning),
corn starch + water (shear thickening)
48. 5.7. Viscosity
Example:
A thin plate of dimensions 0.4 m by 0.6 m is supported
horizontally by a thin oil film of thickness 5.5 mm. If the
oil has a viscosity of 0.29 kg/m.s what force is required to
pull that plate at a constant velocity of 0.34 m/s assuming
a linear variation of velocity within the oil?
49. Applying Newton’s law of viscosity:
where u is the plate velocity and y = t is the film thickness.
With assumption a linear variation of velocity with the oil:
= 17.93 N/m2
The force required to pull the plate is:
= 4.3 N
5.7. Viscosity
Solution:
50. 5.8. Compressibility
• How easily can the volume (and thus the density) of a given mass
of the fluid be changed when there is a change in pressure?
How compressible is the fluid?
• A property that is commonly used to characterise compressibility
is called bulk modulus, K
• Large values for the bulk
modulus (also referred to as
the bulk modulus of elasticity)
indicate that the fluid is
relatively incompressible- that
is, it takes a large pressure
change to create a small
change in volume.
51. Example:
A liquid compressed in a cylinder has a volume of 1
L (1000 cm3) at 1 MN/m2 and a volume of 995 cm3
at 2 MN/m2. What is its bulk modulus of elasticity of
this liquid?
5.8. Compressibility
52. Solution:
5.8. Compressibility
• This means it would required a pressure of 200 MPa
to compress a unit volume of water only 0.5% !!!.
• We conclude that liquids can be considered as
incompressible for most practical engineering applications.
53. 5.9. Surface Tension
- At the interface between a liquid and a gas, or between two
immiscible liquids, forces develop in the liquid surface which
cause the surface to behave as if it were a “skin” or “membrane”
stretched over the fluid mass.
54. 5.9. Surface Tension
Fresh morning dew on a Water Horsetail Flowing water adhering to a
hand. Surface tension creates
the sheet of water between
the flow and the hand.
- is defined as force per unit length.
- Basic SI units of surface tension
[N/m]
56. 6.1. Viscous and Inviscid flows
Viscous flows: Flows in which the frictional effects are significant.
Inviscid flow regions: 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.
57. 6.2. Internal versus External Flow
External flow: The flow of an unbounded fluid over a surface such
as a plate, a wire, or a pipe.
Internal flow: The flow in a pipe or duct if the fluid is completely
bounded by solid surfaces.
Internal vs. External
58. 6.3. Incompressible and Compressible Flows
Incompressible flow: If the density of flowing fluid remains nearly
constant throughout (e.g., liquid flow).
Compressible flow: If the density of fluid changes during flow
(e.g., high-speed gas flow)
When analysing rockets, spacecraft, and other systems that
involve high-speed gas flows, the flow speed is often expressed
by Mach number
59. 6.3. Incompressible and Compressible Flows
Schlieren image of a small model of
the space shuttle orbiter being tested at
Mach 3 in the supersonic wind tunnel
of the Penn State Gas Dynamics Lab.
Several oblique shocks are seen in the
air surrounding the spacecraft.
Ma = 1 Sonic flow
Ma < 1 Subsonic flow
Ma > 1 Supersonic flow
Ma >> 1 Hypersonic flow
QUICK QUESTION: What Is the Fastest Speed Jet in the World?
60. 6.4. Steady vs. 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.
61. 6.5. Natural vs. Forced
• Depending on how the fluid motion is initiated.
• In 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.
• In natural flows, any fluid motion is due to natural means such as the
buoyancy effect.
