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

Properties of fluids:-

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)

Properties of fluids:-

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)

Properties of fluids:-

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

Properties of fluids:-

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

Properties of fluids:-

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

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