Faculty of Mechanical and Production

Engineering

Fluid Mechanics
(MEng2113)
Chapter l

Introduction to Fluid Mechanics

Prepared by: Melkamu G.

February, 2021 1
 Introduction
 Mechanics is a branch of physical science concerned with the behavior of
the object (in the state of rest or in motion) subjected to the action of
forces.
Mechanics

Solid Mechanics Fluid Mechanics

Deformable Body Rigid Body Fluid Statics

Mechanics Mechanics

Fluid Kinematics
Dynamics Statics

Fluid Dynamics
Kinematics Kinetics
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Fluid Mechanics is the study of the behavior of fluids (liquids or gases)
either in motion (fluid dynamics) or at rest (fluid statics).

 The study of fluids at rest is called fluid statics.

 The study of fluids in motion, where pressure force are not considered, is
called fluid kinematics and if the pressure forces are considered for the
fluids in motion, then it is called fluid dynamics.

 The study of the motion of fluids that are practically incompressible (such
as liquids, especially water, and gases at low speeds) is usually referred to
as hydrodynamics.

 Other categories includes hydraulics, Gas dynamics, aerodynamics and

etc.
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What is a Fluid?
Fluid: A substance in the liquid or
gas phase.
 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. Deformation of a rubber block
 When a constant shear force is placed between two parallel
applied, a solid eventually stops plates under the influence of a
deforming at some fixed strain
shear force. The shear stress
angle, whereas a fluid never
stops deforming and approaches shown is that on the rubber—
a constant rate of strain. an equal but opposite shear
stress acts on the upper plate.
Figure 4
What is a Fluid?
 In a liquid, molecules can move relative to each other, but the
volume remains relatively constant because of the strong cohesive
forces between the molecules.
 As a result, a liquid takes the shape of the container it is in, and it
forms a free surface in a larger container in a gravitational field.
 A gas, on the other hand, expands until it encounters the walls of the
container and fills the entire available space.
 This is because the gas molecules are widely spaced, and the
cohesive forces between them are very small.

Unlike a liquid, a gas does not form a

free surface
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What is a Fluid?
Differences between liquids and gases
Liquid Gases
Difficult to compress and Easily to compress -changes
often regarded as of volume is large, cannot
incompressible normally be neglected and
are related to temperature
Occupies a fixed volume No fixed volume, it
and will take the shape of changes volume to
the container expand to fill the
containing vessels
A free surface is formed if Completely fill the vessel so
the volume of container is that no free surface is
greater than the liquid. formed.
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Types of Fluids
1. Ideal Fluid: A fluid, which is incompressible and is having no
viscosity, is known as an ideal fluid. It is only an imaginary fluid.
2. Real fluid: A fluid, which possesses viscosity, is known as real
fluid. All the fluids: in actual practice, are real fluids.
3. Newtonian Fluid: A real fluid, in which the shear stress is directly,
proportional to the rate of shear strain (or velocity gradient), is
known as a Newtonian fluid.
4. Non-Newtonian fluid: A real fluid, in which shear stress is not
proportional to the rate of shear strain (or velocity gradient),
known as a Non-Newtonian fluid.
5. Ideal Plastic Fluid: A fluid, in which shear stress is more than the
yield value and shear stress is proportional to the rate of shear
strain (or velocity gradient), is known as ideal plastic fluid

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Cont…

Types of fluids

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Dimensions and Units

 A dimension is the measure by which a physical variable is expressed

quantitatively and a unit is a particular way of attaching a number to the
quantitative dimension.

 In fluid mechanics there are only four primary dimensions from which all other
dimensions can be derived: mass, length, time, and temperature.

Primary dimension SI unit BG unit Conversion factor

Mass {M} Kilogram (kg) Slug 1slug = 14.5939 kg

Length {L} Meter (m) Foot (ft) 1ft = 0.3048 m

Time {T} Second (s) Second (s) 1s = 1s

Temperature {ϴ} Kelvin (K) Rankine (°R) 1K = 1.8 °R

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Cont…
Secondary Dimensions, in fluid mechanics, are dimensions which are
derived from primary dimensions as shown below the table.

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Fluid Properties
Density or Mass Density
 Density or mass density of a fluid is defined as the ratio of the mass of a
fluid to its volume. It is denoted the symbol ρ (rho). The unit of mass
density in SI unit is kg per cubic meter.

i.e. 𝑘𝑔/𝑚3 .

 The density of liquids may be considered as constant while that of gases

changes with the variation of pressure and temperature.

𝐦𝐚𝐬𝐬 𝐨𝐟 𝐟𝐥𝐮𝐢𝐝
 Mathematically mass density is written as: 𝛒 =
𝐯𝐨𝐥𝐮𝐦𝐞 𝐨𝐟 𝐟𝐥𝐮𝐢𝐝

 The value of density of water is 1𝑔𝑟𝑎𝑚/𝑐𝑚3 or 1000 𝑘𝑔/𝑚3

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Specific weight or Weight Density
 Specific weight or weight density of a fluid is the ratio between the
weight of a fluid to its volume. It is denoted by the symbol w.
 Mathematically,

 The unit of specific weight or weight density is kg/𝐦𝟐 𝐬 𝟐 or 𝐍/𝐦𝟑

 The value of specific weight or weight density for water is
9.81 × 1000 𝑁/𝑚3
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Cont…
Specific Volume

 Specific volume (ν) of a fluid is defined as the volume of a fluid

occupied by a unit mass or volume per unit mass of a fluid.

 Mathematically, it is expressed as

 Thus specific volume (ν) is the reciprocal of mass density. It is

expressed as 𝑚3 /𝑘𝑔.

 It is commonly applied to gases.

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Cont…
Specific Gravity
 Specific gravity is defined as the ratio of the weight density (or density) of
a fluid to the weight density (or density) of a standard fluid.
 For liquids, the standard fluid is taken water and for gases, the standard
fluid is taken air. Specific gravity is also called relative density. It is
dimensionless quantity and is denoted by the symbol S.

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Viscosity
 Viscosity is defined as the property of a fluid which offers resistance to the
movement of one layer of fluid over another adjacent layer of the fluid.
 When two layers of a fluid, a distance 'dy' apart move one over the other at
different velocities say u and u+ du as shown in Fig below , the viscosity
together with relative velocity causes a shear stress acting between the
fluid layers.

Velocity variation near a solid boundary

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Cont…
 The top layer causes a shear stress on the adjacent lower layer while the
lower layer causes a shear stress on the adjacent top layer.

 This shear stress is proportional to the rate of change of velocity with

respect to y. It is denoted by symbol τ called Tau.
 Mathematically,
or
 Where µ (called mu) is the constant of proportionality and is known as the
coefficient of dynamic viscosity or only viscosity.

 𝑑𝑢 𝑑𝑦 represents the rate of shear strain or rate of shear deformation or

velocity gradient.

 Thus viscosity is also defined as the shear stress required to produce unit
rate of shear strain. 19
Cont…
Unit of Viscosity
 The unit of viscosity is obtained by putting the dimension of the
quantities in the above equation.

i.e.

Newton second Ns
 SI unit of viscosity = =
meter2 m2

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Cont…
Kinematic Viscosity
 It is defined as the ratio between the dynamic viscosity and density
of fluid. It is denoted by the Greek symbol (ν) called 'nu' . Thus,
mathematically,

 The SI unit of kinematic viscosity is 𝑚2 /𝑠.

Newton's Law of Viscosity
 It states that the shear stress (τ) on a fluid element layer is directly
proportional to the rate of shear strain. The constant of
proportionality is called the co-efficient viscosity. Mathematically, it
is expressed as the same as shear stress.
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Cont…
 Fluids which obey the above relation are known as Newtonian fluids and the
fluids which do not obey the above relation are called Non-Newtonian fluids.

Variation of Viscosity with Temperature

 Temperature affects the viscosity.

 The viscosity of liquids decreases with the increase of temperature while the
viscosity of gases increases with increase of temperature. This is due to reason that
the viscous forces in a fluid are due to cohesive forces and molecular momentum
transfer.

 In liquids the cohesive forces predominates the molecular momentum transfer due
to closely packed molecules and with the increase in temperature, the cohesive
forces decreases with the result of decreasing viscosity.

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Cont…
 But in the case of gases the cohesive force are small and molecular
momentum transfer predominates. With the increase in temperature,
molecular momentum transfer increases and hence viscosity
increases. The relation between viscosity and temperature for liquids
and gases are:
Cont…
Example 3

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 Example 4

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Example 5

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Thermodynamic Properties of a Fluid
 The most common such properties are: Pressure (p), Density (ρ) and
Temperature (T).

 These three are constant companions of the velocity vector in flow

analyses. Four other intensive thermodynamic properties are: Internal
energy (û), Enthalpy (h), Entropy (s) and Specific heats 𝒄𝒑 and 𝒄𝒗 .

 In addition, friction and heat conduction effects are governed by the two
so-called transport properties: Coefficient of viscosity (μ) and Thermal
conductivity (k).

 All nine of these quantities are true thermodynamic properties that are
determined by the thermodynamic condition or state of the fluid.
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Cont…
 With the change of pressure and temperature, the gases undergo
large variation in density.

 The relationship between pressure (absolute), specific volume and

temperature (absolute) of a gas is given by the equation of state as:

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Cont…
 Pressure is the (compression) stress at a point in a static fluid. Next to
velocity, the pressure p is the most dynamic variable in fluid mechanics.
Differences or gradients in pressure often drive a fluid flow, especially in
ducts. we set many such problem assignments at the level of:

 Temperature is related to the internal energy level of a fluid. It may vary

considerably during high-speed flow of a gas. Although engineers often use
Celsius, Fahrenheit or Kelvin (Rankine) temperature scales:

 Density (ρ) is highly variable in gases and increases nearly proportionally

to the pressure level. Density in liquids is nearly constant; the density of
water (about 1000𝑘𝑔 𝑚3 ) increases only 1 percent if the pressure is
increased by a factor of 220. The heaviest common liquid is mercury, and
the lightest gas is hydrogen. Compare their densities at 20 °C and 1 atm:

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Compressibility and Bulk Modulus
 Compressibility is the reciprocal of the bulk modulus of elasticity, K
which is defined as the ratio of compressive stress to volumetric strain.
 Consider a cylinder fitted with a piston as shown in the Fig below.

Let, V = Volume and P = Pressure of gas

Let the pressure is increased to p+ dp
the volume of gas decreases from V to V-dV
Then increase in pressure = dp, Decrease in volume = dV
Volumetric strain = - dV/V
Note: - ve sign means the volume decreases with increase of pressure.

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Cont…
Surface Tension and Capillarity
 Surface tension is defined as the tensile force acting on the surface
of a liquid in contact with a gas or on the surface between two
immiscible liquids such that the contact surface behaves like a
membrane under tension.
 The intensity of the molecular attraction per unit length along any
line in the surface is called the surface tension.
 Surface tension is created due to the unbalanced cohesive forces
acting on the liquid molecules at the fluid surface.
 It is denoted by Greek letter σ (called sigma).
 The SI unit is N/m.
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Cont…

drops of water beading up a water strider sitting on top of the

on a leaf surface of water

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Cont…
Surface Tension on liquid Droplet and
Bubble
 Consider a small spherical droplet of
a liquid of radius 'R'. On the entire
surface of the droplet, the tensile
force due to surface tension will be
acting.
 Let σ = surface tension of the liquid
 P = Pressure intensity inside the
droplet (in excess of the outside
pressure intensity)
 R = Radius of droplet.
 Let the droplet is cut into two halves.
The forces acting on one half (say left
half) will be
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Cont…
1. tensile force due to surface tension acting around the circumference
of the cut portion as shown and this is equal to
= σ × Circumference
= σ×2πR
2. pressure force on the area (π/4)𝑑2 = ∆𝑃 × 𝜋𝑅 2
 These two forces will be equal and opposite under equilibrium
conditions, i.e.

 A hollow bubble like a soap bubble in air has two surfaces in contact
with air, one inside and other outside. Its pressure force given as:

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Capillarity
 Capillarity is defined as a phenomenon of rise or fall of a liquid
surface in a small tube relative to the adjacent general level of liquid
when the tube is held vertically in the liquid.

 The rise of liquid surface is known as capillary rise while the fall of
the liquid surface is known as capillary depression.

 It is expressed in terms of cm or mm of liquid. Its value depends

upon the specific weight of the liquid, diameter of the tube and
surface tension of the liquid.

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Expression for Capillary Rise
 The height of water rise is given by:

How it becomes? proof

Expression for Capillary Fall

Capillary Rise

 The height of depression of water is given by:

How it becomes? proof

Capillary Fall 41
Cont…

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Basic Flow Analysis Techniques:- There are three basic ways to attack a fluid
flow problem.

 Control-volume, or integral analysis

 Infinitesimal system, or differential analysis

 Experimental study, or dimensional analysis

In all cases, the flow must satisfy the three basic laws of mechanics plus a
thermodynamic state relation and associated boundary conditions:

 Conservation of mass (continuity).

 Linear momentum (Newton’s second law).

 First law of thermodynamics (conservation of energy).

 A state relation like ρ = ρ ( p , T ).

 Appropriate boundary conditions at solid surfaces, interfaces, inlets, and exits. 45

Cont…
Flow Patterns: Streamlines, Streaklines, and Pathlines
Fluid mechanics is a highly visual subject. Four basic types of line patterns
are used to visualize flows:

 A streamline is a line every where tangent to the velocity vector at a given

instant.

 A pathline is the actual path traversed by a given fluid particle.

 A streakline is the locus of particles that have earlier passed through a

prescribed point.

 A timeline is a set of fluid particles that form a line at a given instant.

Note: If the flow is steady, streamlines, pathlines, and streaklines are

identical.
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Cont…

Streamlines
Streaklines

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Applications of Fluid Mechanics

 Design of pumps, turbines, air-conditioning equipment, pollution-

control equipment, etc.

 Design and analysis of aircraft, boats, submarines, rockets, jet

engines, wind turbines, biomedical devices, the cooling of electronic
components, and the transportation of water, crude oil, and natural
gas.

 To analysis Transport of river sediments, Pollution of air and water,

design of piping systems, Flood control systems, Design of chemical
processing equipment and etc.
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 Summary
Introduction
Fluid properties
Mass density
Weight density
Specific gravity
Specific volume
viscosity
Thermodynamics properties
Compressibility and bulk modulus
Surface tension and capillarity
Fluid analysis techniques
Flow patterns
Application of fluid mechanics 51
 END OF CHAPTER 1

THANK YOU !!!

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