FLUID MECHANICS UNIT 1 BASIC

1. SYLLABUS FOR
FLUID MECHANICS &
HYDRAULIC MACHINES

2. FLUID MECHANICS AND HYDRAULIC MACHINES
FLUID STATICS : Dimensions and units: physical properties of fluids – specific gravity, porosity surface tension –
vapor pressure and their influence on fluid motion – atmospheric gauge and vacuum pressure – measurement of
pressure – Piezometer, U-tube differential manometers.
FLUID KINEMATICS : stream line, path line and streak lines and steam tube, classification of flows-steady &
unsteady, uniform, non-uniform, laminar, turbulent, rotational and irrotational flows-equation of continuity for one
dimensional flow. Fluid dynamics: surface and body forces – Euler‟s and Bernoulli‟s equations for flowing stream
line, momentum equation and its application on force on pipe bend.
CONDUIT FLOW: Reynold‟s experiment – Darcy Weisbach equation – Minor losses in pipes – pipes in series and
pipes in parallel – total energy line-hydraulic gradient line. Measurement of flow: pitot tube, venturi meter and
orifice meter, Flow nozzle and Turbine current meter.
TURBO MACHINERY : hydrodynamic force of jets on stationary and moving flat, inclined, and curved vanes, jet
striking centrally and at tip, velocity diagrams, work done efficiency, flow over radial vanes. HYDROELECTRIC POWER
STATIONS: Elements of hydro electric power station types-concept of pumped storage plants-storage requirements.
HYDRAULIC TURBINES: Classification of turbines, impulse and reaction turbines, Pelton wheel, Francis turbine and
Kaplan turbine-working proportions, work done, efficiencies, hydraulic design-draft tube- theory- functions and
efficiency. PERFORMANCE OF HYDRAULIC TURBINES : Unit and specific quantities, characteristics, governing of
turbines, selection of type of turbine, cavitation and surge tank.
CENTRIFUGAL PUMPS : Classification- working-work done – manometric head – loss efficiencies – specific speed
– pumps in series and parallel – performance characteristic curves and NPSH.

3. Introduction To FLUID MECHANICS :
A FLUID is may be defined as a substance which is incapable
of flowing.
FLUID MECHANICS is a branch of science which deals about
the behaviour of the fluids at the sate of rest as well as motion.
The study of fluids at rest position is called FLUID STATICS.
The study of fluids in motion, where pressure force are not
consider is called FLUID KINEMATICS.
The study of fluids in motion, where pressure force are also
consider is called FLUID DYNAMICS.

4. FLUID MECHANICS :
PROPERTIES OF FLUIDS :
1. Density or mass density,
2. Specific weight (or) weight density,
3. Specific gravity,
4. Specific volume,
5. Viscosity,
6. Temperature,
7. Pressure.

5. 1. DENSITY OR MASS DENSITY:
It is the ratio of the mass of a fluid to volume of fluids. (or)
Mass per unit volume of a fluid is called density of a fluid.
It is denoted by Greek symbol ρ (rho) .
The units of mass density in SI units is kg/m³.
The density of a liquids may be consider as constant while that of
gases changes with the variation of pressure and temperature.
The Density of water is 1 gm/cm³ or 1000 kg/m³
Mathematically, mass density is written as
ρ=dm/dv

6. 2. SPECIFIC WEIGHT (OR) WEIGHT DENSITY:
It is the ratio of the weight of a fluid to volume of fluids.
It is denoted by symbol W.
The units of mass density in SI units is N/m³.
The Specific weight of water is 9.81*1000 N/m³
Mathematically, mass density is written as
W=m/v or W= ρg/v

7. 3. SPECIFIC GRAVITY:
It is the ratio of the weight density of fluid to weight
density of water/gas.
For liquids the standard fluid is water, For gases the
standard fluid is air.
It is denoted by symbol S.
The units of mass density in SI units is KN/m³.
Mathematically, mass density is written as
S=Wli/g/Ww/a

8. 4. SPECIFIC VOLUME :
It is defined as the volume of fluid occupied by a
unit mass (or)
volume per unit mass of fluid of fluid to mass of
fluids.
It is denoted by symbol V.
The units of mass density in SI units is m³/kg.
Mathematically, mass density is written as
V=1/ρ

9. 5.Viscosity
Viscosity is the fluid property that determines the amount of
resistance of the fluid to shear stress.
It is the property of the fluid due to
which the fluid offers resistance to flow of
one layer of the fluid over another adjacent
layer.
In a liquid, viscosity decreases with increase in temperature. In
a gas, viscosity increases with increase in temperature
The units of mass density in SI units is m³/kg.
Mathematically, mass density is written as
Ƭαdu/dy Ƭ=Ʋ(du/dy)

10. 6. Temperature:
It is the property that determines the degree of
hotness or coldness or the level of heat intensity of
a fluid.
It is denoted by symbol T.
Units for temperature is K( Kelvin ), C(Celsius or
centigrade), F(Fahrenheit).

11. 7. Pressure:
Pressure of a fluid is the force per unit area of the
fluid.
In other words, it is the ratio of force on a fluid to
the area of the fluid held perpendicular to the direction
of the force.
Pressure is denoted by the letter ‘P’.
Its unit is N/m2

12. SURFACE TENSION:
It is defined as the tensile force acting on the surface of the
liquid in contact with a gas
It is denoted by Greek letter ‘σ’ (sigma)
In SI units of surface tension is N/m
The phenomenon of surface tension is
explained by experiment as showing in fig
A,B,C are the fluid molecule of a liquid in amass of liquid
The molecule A is attracted in all direction. Thus the resultant
force on molecule A is zero.
Molecule B which is situated at near the free surface is acted upon
by up & downward forces which are unbalanced

13. The molecule C, situated on the half on free surface of the
liquid so the resultant force is in downward direction.
Surface tension & Pressure force on a liquid droplets.
Surface tension on hollow bubble &liquid jet.

14. CAPILLARITY
It is the phenomenon of rise or fall of a liquid surface in a
small tube relative to the adjacent general level of liquid when
tubes are in vertically in the liquid.
The rise of liquid surface is known as
capillary rise while the fall of liquid surface
is known as capillary depression
The units for capillarity is cm or mm.
The value is depend on the specific
weight of the liquid.
Mathematically it can defined as

15. VAPOUR PRESSURE:
A change from the liquid state to gaseous state is known
as vaporization.
It occurs because of continuous escaping of the molecules
through free surface.
ABSOLUTE PRESSURE:
It is defines as the pressure which is measured with the
reference to absolute vacuum pressure.
GAUGE PRESSURE:
It is depend as the pressure which is measured with the
help of a pressure measuring instrument, in which the
atmospheric pressure is taken as datum.

16. SIMPLE MANOMETERS:
A simple manometer consist of a glass tube having one of
its ends connected to a point where pressure is to be measured
and other end remains open to atmosphere.
TYPE OF MANOMETERS
1. Piezometer,
2. U-tube manometer &
3. Single column manometer.

17. PIEZOMETER:
It is the simplest form of manometer used for measuring
gauge pressures.
One end of the manometer is connected to the point where
pressure is to be measured and other
end is open to atmosphere as show in fig.
The rise of liquid gives the pressure head
at the point.
If at point A, the height of liquid (water)
is h in piezometer at A
Mathematically it defined as

18. U-TUBE MANOMETER
It consist of a glass tube bent in U-shape, One end of which
is connected to a point at which pressure is to be measured and
other end remains open to the atmosphere as shown in fig.
The general consist of mercury or any other high density
liquids.
U-TUBE MANOMETER FOR GAUGE PRESSURE:
Let ‘A-A’ be the datum line & ‘B’ is the point at which
pressure is to be measured, whose value is ‘p’

19. U-TUBE MANOMETER FOR VACUUM PRESSURE:
For measuring vacuum pressure, the level of the heavy
liquid in the manometer will be as shown fig

20. DIFFERENTIAL MANOMETERS:
This are the devices used for measuring the difference of
pressures between two points in a same pipe or different
pipes.
It consist of a U-tube, containing a heavy liquid (mercury)
whose ends are connected to the two points.
TYPES OF DIFFERENTIAL MANOMETER:
1. U-tube differential manometer
2. Inverted U-tube differential manometer.

21. U-TUBE DIFFERENTIAL MANOMETERS:
The two points A and B are at
same/different level and also
contains liquids of different
Specific gravity.
These points are connected
to the U-tube differential
manometer. Mathematically expressed as

22. INVERTED U-TUBE DIFFERENTIAL MANOMETERS:
It consist of an inverted U-tube, containing a light liquid.
The two points A and B are at same/different
level and also contains liquids of same/different
Specific gravity.
These two points are connected to the
inverted U-tube differential manometer.
mathematically expressed as
Then pressure in the left limb below X-X
Then pressure in the right limb below X-X

23. FLUID KINEMATICS:
It is a branch of fluid dynamics which deals about
behaviour of a fluid at motion with out considering of
external forces.
FLUID MOTION:
There are two methods to describe the parameters of the
flowing fluid
1. Lagrange method,
2. Eulerian method.

24. LAGRANGE METHOD:
In this method the flow parameters like velocity,
pressure, density, time, specific
Gravity etc..
For a single fluid particles is
describe during it’s motion.
EULERIAN METHOD:
In this the flow parameters like velocity, pressure, density
etc.. are described at a path in flowing fluid.
This method is commonly used in fluid mechanics.

25. CLASSIFICATION OF FLUID FLOWS:
1. STEADY FLOW: Steady flow is defined as that type of flow
in which in which the fluid properties like velocity, pressure,
density, temperature etc., do not change with respect to
time.
mathematically it can represent as
2. UNSTEADY FLOW: In this the fluid properties may change
with respect to time.
mathematically it can represent as

26. 3. UNIFORM FLOWS :
It is defined as that type of flow in which the velocity at any
given time does not change with respect to space ( length,
direction of flow).
Mathematically it can represent as
4. NON-UNIFORM FLOWS:
In this the velocity at any given time changes with respect
to space.
Mathematically it can represent as

27. 5. LAMINAR FLOWS:
It is defined as that type of flow in which the fluid particles
move along well defined paths or stream line.
6. TURBULENT FLOWS:
It is defined as that type of flow in which the fluid particles
move in zig-zag way.
Due to the moment of fluid particles in
zig-zag way, the eddies formation takes
place which are responsible for high energy loss.
If Reynolds number < 2000 then it is laminar.
If Reynolds number > 4000 then it is turbulent.

28. 7. COMPRESSIBLE FLOWS:
It is defined as that type of flow in which the density of the
fluid changes from a point to point.
Mathematically it can represent as
ρ ǂ constant
8. INCOMPARABLE FLOWS:
The density of the fluid is constant for the fluid flow.
Mathematically it can represent as
ρ = constant
Liquid are generally incomparable .
Gases are compressible.

29. 9.ROTATIONAL FLOWS:
The fluid particles while flowing along stream line, also
rotate about their own axis.
10. IRROTATIONAL FLOWS:
Fluid particles flows along stream line, do not rotate about
their own axis.
11. ONE DIMENSIONAL FLOWS:
Flow parameters may vary in only one direction /
coordinate
Mathematically it can represent as u=f(x), v=0, w=0

30. 12. TWO DIMENSIONAL FLOWS:
The flow parameters may vary in two
direction/coordinates.
13. THREE DIMENSIONAL FLOWS:
The flow parameters may vary in all three directions/
coordinates.

31. TYPES OF FLUID FLOWS:
1. STREAM LINE: It is an imaginary curve
drawn through a flowing fluid in such as a
way that the tangent to it at any point gives
the direction of velocity of fluid at a point.
A streamline is a line that is tangential to the
instantaneous velocity direction
From the fig “some of the streamline for a
flow pattern in the xy plane in which a stream line passing through a
point p(x,y) is tangential to the velocity vector V along x & y
direction”, then
v/u = tanθ = dy/dx
For 3 dimensional flow dx/u = dy/v = dz/w
=> since a streamline is everywhere tangent to velocity vector.

32. 2.STREAM TUBE:
A stream tube is an imaginary curved tube which can formed by
set of stream lines are flowing in a closed path either it may be
circular or non-circular.
There can be no flow across the
boundary surface of a stream-tube.
A fluid may enter or leave a stream tube
only at its ends.
A stream tube with cross sectional area small enough for the
variation f velocity over it to be negligible is sometimes termed as a
stream filament.
The concept of stream tube is quite useful in analysing several
fluid flows problems, since the entry flow field may be divided into a
large number of stream-tubes.

33. 3. PATH LINE:
A path line is an line traced by a single particle in flowing
liquid as it moves at distance in the period of time.
This path lines shows the direction
of flow and velocity of the same fluid
particle at successive instant of time.
A fluid particle move in the
tangent to the stream line.
In unsteady flow path lines and
streamlines are different.

34. 4. Streak line:
It is line or well defined path traced by the fluid particles
through a fixed point.
example for the streak line as shown in the figs.

35. CONTINTI EQIATION:
It works on the conservation of mass principle
i.e. mass flow rate, rate of flow, discharge, inlet, outlet all are
same.
The inflow and outflow are one-dimensional, so that the
velocity V and density ρ are constant over the area A.
The above equation is called continuity equation.

36. FLUID DYNAMICS:
The study of fluids in motion, where pressure force are
also consider is called FLUID DYNAMICS.
According to the newton’s second law of motion, the force
acting on the fluid element in the direction of x is equal to the
mass m of the fluid element multiplied by the acceleration a in
the same direction.
Fx = m.ag
If any fluid is flowing then these forces are present.
Gravitation force (Fg), Force due to viscosity (Fv), Force
due to turbulence (Ft), pressure force (Fp),
Force due to compressibility (Fc).

37. The total net forces
Fx = Fg + Fp + Fv + Ft + Fc
If the forces due to compressibility, Fc is negligible, the
resultant net force is.
Fx = Fg + Fp + Fv + Ft (Reynold’s equation of motion)
If the forces due to turbulent, Ft is negligible, the resultant
net force is.
Fx = Fg + Fp + Fv (Navier-stokes equation)
If the forces assumed as ideal, Fv is negligible, the resultant
net force is.
Fx = Fg + Fp (Euler’s equation of motion)

38. EULER’S EQUATION OF MOTION:
This is an equation of motion in which the forces due to
gravity and pressure are taken into consideration.
This is derived by considering the motion of the fluid
element along a stream-line
From the fig flow is takes place in s- direction,
dA is the cross sectional area,
ds is the length.
Let pressure force in the direction of flow is pdA.
Pressure force in the opposite direction is p+dp.dA.
Weight of the element ρ.g.dA.ds.
Let θ is the angle between the direction of flow and the line of
the weight of element.

39. Weight of the fluid element in the flow direction
ρg*dA*ds*cosθ
According to the newton law of motion
F = m*a
We know that a=dv/dt =>a = (dv/ds)*(ds/dt) =>a = v(dv/dt)
=>> Net forces (F) = (p*dA)-(p-dp)dA-(ρg*dA*ds*cosθ)
=>> m*a = ρdAds*v(dv/ds)
By the equating both above equations
(p*dA)-(p+dp)dA-(ρg*dA*ds*cosθ)= ρdAds*v(dv/ds)
pdA-pdA+dAdp-ρgdAdscosθ)= ρdAds*v(dv/ds)
dA(dp-ρgdscosθ)= ρdA*vdv
dp-ρgdscosθ= ρ*vdv
(dp/ ρ)-vdv-gdz=0
The above equation is called Euler's equation of motion

40. BERNOLLI’S EQUATION:
This is obtained by integrating the Euler's equation of motion.
Statement: For study ideal incompressible, irrotational, type of
fluids the sum of total energy (pressure, kinetic, potential energy) is
constant.
proof: let us consider a stream tube having the cross sectional
area 1& 2 as shown in fig.
If the liquid is flowing from 1 & 2then
a1, v1, p1 and a2, v2, p2 are the cross section area velocity,
pressure, at section 1&2 respectively.

41. work done(W)=force*velocity =p*a*v
Net work done= w1 -w2
p1a1v1-p2a2v2=(½mv2²-½mv1²)+(mgz2-mgz1) (a1=a2)
p1v1-½mv1²-mgz1= p2v2-½mv2²-mgz2 (v1=v2)
p1-½(m/v1)v1²-(m/v1)gz1= p2-½(m/v1)v2²- (m/v2)gz2