Fluid mechanics(2130602)

ENGINEERING COLLEGE, TUWA
 Subject:- Fluid Mechanics.
(2130602)
Prepared by,
Sujith Velloor Sudarsanakumar.
Designation:- Lecturer.
Branch:- Civil Engineering
Engineering college, Tuwa.
Topics:- Fluid , Properties & Types
Fluid Dynamics &
Kinematics.

Fluid :-
When a body or matter flows from one place to another
point on application of shear force is called fluid.
Fluid
Liquid (e.g. Water, Oil, Petrol) Gas
Compressible Fluid Incompressible Fluid
(Due to change in pressure
volume of fluid changes
e.g gas)
(Due to change in pressure
volume of fluid does not
change. e.g. All liquid)

Properties of fluids:-
1. Density or Mass
density.
2. Specific weight.
3. Specific Volume.
4. Specific Gravity.
5. Surface Tension
6. Vapor Pressure
7. Elasticity
8. Compressibility
9. Capillarity

Mass Density:- Mass Density is defined as ratio of mass of fluid to
its Volume.
Mass Density(Density)= Mass of fluid (m)
Volume of fluid(V)
Specific Weight :- Specific Weight is defined as ratio of weight of
fluid to its Volume
Specific Weight (Weight Density)= weight of fluid (W) (W=mg)
volume of fluid(V)

Specific Gravity:- Specific gravity is defined as ratio of weight density of
fluid to weight density of standard fluid.
Specific Gravity= Weight Density of Liquid
Weight Density of Water
Specific Volume:- Volume per unit mass of fluid is called Specific
Volume
Specific Volume= Volume of fluid (V)
Mass of fluid (M)

Surface tension:- Tensile force acting on free surface of
liquid per unit length is called Surface Tension.
S.I unit is N/m OR N/mm.
Vapor Pressure:- Vapor Pressure is defined as pressure
exerted by vapor of liquid formed at free surface of
liquid at a particular temperature in a close container

Elasticity:- Elasticity is ratio of change in pressure to the
corresponding volumetric strain.
Elasticity or Bulk Modules(k) = -dp
dv/v
Compressibility:- The reciprocal of bulk Modules of
elasticity is called Compressibility.
Compressibility= 1/K

Capillarity:- Capillarity is defined as phenomenon of rise
or fall of liquid in small tube , when the tube is held
vertically in liquid.
The rise of liquid surface is known as Capillary Rise while
fall of liquid surface is known as Capillary fall (Capillary
depression)
It is expressed in terms of mm or cm

Types of fluids:-
1. Ideal fluid
2. Real fluid
3. Newtonian fluid
4. Non – Newtonian fluid
5. Ideal Plastic fluid.
6. Thixo Tropic Fluid.

Types of fluids:-
Ideal fluid :- A fluid which is incompressible and is
having no viscosity no surface tension is known as an
ideal fluid.
Ideal fluid is an imaginary fluid.
Real fluid :- A fluid which is compressible has viscosity
and surface tension is known as Real fluid
All fluid in practice are real fluid e.g. water, petrol,
kerosene etc.

Types of fluids:-
Newtonian fluid:- A real fluid in which shear stress is
directly proportional to ratio of shear strain (velocity
gradient) is known as Newtonian fluid.
Non-Newtonian fluid:- A real fluid in which shear stress is
not proportional to shear strain (velocity gradient) is
known as Non-Newtonian fluid.

Types of fluids:-
Ideal Plastic Fluid:- A fluid in which shear stress is more
than yield value and shear stress is proportional to rate
of shear strain
Thixo Tropic Fluid:- A thixo tropic fluid is a non-Newtonian
fluid which has a non-linear relationship between shear
stress and rate of shear strain, beyond an initial yield
stress.

Energy Equation  The first law of thermodynamics for a system: that the heat QH added to a
system minus the work W done by the system depends only upon the initial
and final states of the system - the internal energy E
or by the above Eq.:
 The work done by the system on its surroundings:
 the work Wpr done by pressure forces on the moving boundaries
 the work Ws done by shear forces such as the torque exerted on a
rotating shaft.
 The work done by pressure forces in time δt is
Fluid Dynamics:-

 By use of the definitions of the work terms
 In the absence of nuclear, electrical, magnetic, and surface-tension
effects, the internal energy e of a pure substance is the sum of potential,
kinetic, and "intrinsic" energies. The intrinsic energy u per unit mass
is due to molecular spacing and forces (dependent upon p, ρ, or T):
Fluid dynamics

Euler's Equation of Motion Along a Streamline
 In addition to the continuity equation: other general controlling equations - Euler's
equation.
 In this section Euler's equation is derived in differential form
 The first law of thermodynamics is then developed for steady flow, and some of the
interrelations of the equations are explored, including an introduction to the second
law of thermodynamics. Here it is restricted to flow along a streamline.
 Two derivations of Euler's equation of motion are presented
 The first one is developed by use of the control volume for a small cylindrical
element of fluid with axis align a streamline. This approach to a differential
equation usually requires both the linear-momentum and the continuity
equations to be utilized.
 The second approach uses Eq. (5), which is Newton's second law of motion in the
form force equals mass times acceleration.
Fluid dynamics

Figure 3.8 Application of continuity and momentum to flow through a control volume in the
S direction
Fluid dynamics

 Fig. 3.8: a prismatic control volume of very small size, with cross-sectional area δA and length
δs
 Fluid velocity is along the streamline s. By assuming that the viscosity is zero (the flow is
frictionless), the only forces acting on the control volume in the x direction are the end forces
and the gravity force. The momentum equation [Eq․(8)] is applied to the control volume for
the s component. (1)
 The forces acting are as follows, since as s increases, the vertical coordinate increases in such a
manner that cosθ=∂z/∂s. (2)
 The net efflux of s momentum must consider flow through the cylindrical surface , as well as
flow through the end faces (Fig. 3.8c).
(3)
Fluid dynamics

 To determine the value of m·t , the continuity equation (1) is applied to the control volume (Flg.).
 Substituting Eqs. (3.5.2) and Eq. (3.5.5) into equation (3.5.1)
(4)
(5)
 Two assumptions : (1) that the flow is along a streamline and (2) that the flow is
frictionless. If the flow is also steady, Eq․(3.5.6)
(6)
 Now s is the only independent variable, and total differentials may replace the partials,
(7)
(8)
Fluid dynamics

The Bernoulli Equation
 Integration of equation (3.5.8) for constant density yields the Bernoulli equation (1)
 The constant of integration (the Bernoulli constant) varies from one
streamline to another but remains constant along a streamline in steady,
frictionless, incompressible flow
 Each term has the dimensions of the units metre-newtons per kilogram:
 Therefore, Eq. (3.6.1) is energy per unit mass. When it is divided by g,
(3.6.2)
 Multiplying equation (3.6.1) by ρ gives
(3.6.3)
Fluid dynamics

 Each of the terms of Bernoulli's equation may be interpreted as a form
of energy.
 Eq. (3.6.1): the first term is potential energy per unit mass. Fig. 3.9: the
work needed to lift W newtons a distance z metres is WZ. The mass of
W newtons is W/g kg  the potential energy, in metre-newtons per
kilogram, is
 The next term, v2/2: kinetic energy of a particle of mass is δm v2/2; to
place this on a unit mass basis, divide by δm  v2/2 is metre-newtons
per kilogram kinetic energy
Fluid dynamics

 The last term, p/ρ: the flow work or flow energy per unit mass
 Flow work is net work done by the fluid element on its surroundings while it is flowing
 Fig. 3.10: imagine a turbine consisting of a vanes unit that rotates as fluid passes through
it, exerting a torque on its shaft. For a small rotation the pressure drop across a vane
times the exposed area of vane is a force on the rotor. When multiplied by the distance
from center of force to axis of the rotor, a torque is obtained. Elemental work done is p
δA ds by ρ δA ds units of mass of flowing fluid  the work per unit mass is p/ρ
 The three energy terms in Eq (3.6.1) are referred to as available energy
 By applying Eq. (3.6.2) to two points on a streamline,
(3.6.4)
Fluid dynamics

Figure.
Potential energy
Figure. Work done by
sustained pressure
Fluid dynamics

Kinetic-Energy Correction Factor
 In dealing with flow situations in open- or closed-channel flow, the so-
called one-dimensional form of analysis is frequently used
 The whole flow is considered to be one large stream tube with
average velocity V at each cross section.
 The kinetic energy per unit mass given by V2/2, however, is not the
average of v2/2 taken over the cross section
 It is necessary to compute a correction factor α for V2/2, so that αV2/2
is the he average kinetic energy per unit mass passing the section
Fluid dynamics

Figure:- Velocity distribution and average velocity
Fluid dynamics

Fig. 3.18: the kinetic energy passing the cross section per unit time is
in which ρv δA is the mass per unit time passing δA and v2/2ρ is the kinetic energy per unit mass.
Equating this to the kinetic energy per unit time passing the section, in terms of αV2/2
By solving for α, the kinetic-energy correction factor,
 The energy equation (3.10.1) becomes
 For laminar flow in a pipe, α=2
 For turbulent flow in a pipe, α varies from about 1.01 to 1.10 and is usually neglected except for precise
work.
Fluid dynamics

 All the terms in the energy equation (3.10.1) except the term losses are available energy
 for real fluids flowing through a system, the available energy decreases in the downstream
direction
 it is available to do work, as in passing through a water turbine
 A plot showing the available energy along a stream tube portrays the energy grade line
 A plot of the two terms z+p/γ along a stream tube portrays the piezometric head, or hydraulic grade
line
 The energy grade line always slopes downward in real-fluid flow, except at a pump or other source
of energy
 Reductions in energy grade line are also referred to as head losses
Fluid dynamics

-:I appreciate for taking your valuable time:-

Fluid mechanics(2130602)

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