Fluid flow

FLOW OF FLUID
Ms. Deepika Bairagee
Assistant Professor (Quality Assurance)
OCPR, Oriental University, Indore

CONTENT
Definition
Fluid properties
Reynolds experiment
Manometer
Orificemeter
Venturimeter
Pitot tube
Rotameter

 A fluid is a substance that continually deforms (flows) under an
applied shear stress.
 Fluids are a subset of the phases of matter and include liquids,
gases.
 Fluid flow may be defined as the flow of substances that do not
permanently resist distortion
 The subject of fluid flow can be divided into fluid static's and fluid
dynamics
FLUID FLOW

THE PROPERTIES OF FLUIDS
VISCOSITY
SURFACE TENSION

Viscosity is a measure of a fluid's resistance to flow
 It describes the internal friction of a moving fluid.
 A fluid with large viscosity resists motion because
its molecular makeup gives it a lot of internal
friction.
 A fluid with low viscosity flows easily because its
molecular makeup results in very little friction
when it is in motion.

SURFACE TENSION
"Surface tension is a contractive tendency of
the surface of a fluid that allows it to resist an
external force."

Fluid tends to attend the minimum surface as possible
Why?
1. The reason behind this is that while a molecule
inside the fluid bulk is pulled in each and every
direction by the adjacent molecules
2. But at the surface of the fluid , the case is different.
The adhesive forces causes downward pull on the
molecule due to cohesent.
3. So the molecule on the surface tends to move down.

FLUID STATICS
 Fluid static's deals with the fluids at rest in equilibrium
 Behavior of liquid at rest
 Nature of pressure it exerts and the variation of pressure at
different layers
Pressure differences between layers of liquids
h1
h2
Point 1
Point 2
Ps

• Consider a column of liquid with two openings Which are
provided at the wall of the vessel at different height
• The rate of flow through these openings are different due
to the pressure exerted at the different heights are
different
• Consider a stationary column the pressure P is acting on the
surface of the fluid, column is maintained at constant
pressure by applying pressure
• The force acting below and above the point 1 are
evaluated
• Substituting the force with pressure x area of cross section in
the above equation

At point 1
Force acting on the liquid = +
Force on thesurface Force excreted by the liquid
Above point1
P1S = PsS + volume x density x g
Pressure at point 1 x Area= (Pressure on the surface x surface area)+ (mass x g)
Substituting the force with pressure X area of cross section in the above equation
= PsS + height x area x density x g
Since surface area is same
Similarly, the pressure acting on the liquid at point 2
By subtracting equation

FLUID DYNAMICS
Fluid dynamics deals with the study of fluids in motion
• This knowledge is important for liquids, gels, ointments
which will change their flow behavior when exposed to
different stress conditions
Mixing
Flow Through
Pipes
Filled in
Container

Importance
Identification of type of flow is important in Manufacture of
dosage forms & Handling of drugs for administration
• The flow of fluid through a pipe can be viscous or
turbulent and it can be determined by Reynolds
number
• Reynolds number have no unit

Reynolds Experiment
• Glass tube is connected to reservoir of water, rate of flow
of water is adjusted by a valve,
• A reservoir of colored solution is connected to one
end of the glass tube with help of nozzle.
• Colored solution is introduced into the nozzle as
fine stream through jet tube.

water
valve
Colored liquid
LAMINAR OR VISCOUS FLOW
TURBULENT FLOW

TYPES OF FLOW
• Laminar flow is one in which
the fluid particles move in
layers or laminar with one
layer sliding with other
• There is no exchange of
fluid particles from one
layer to other
• Avg velocity = 0.5 Vmax
Re < 2000
• When velocity of the water is
increased the thread of the
colored water disappears and
mass of the water gets
uniformly colored
• There is complete mixing of
the solution and the flow of the
fluid is called as turbulent flow
• Avg velocity = 0.8 Vmax è
Re >4000
The velocity at which the fluid changes from laminar flow to turbulent flow that velocity is called as
critical velocity

REYNOLDS NUMBER
In Reynolds experiment the flow conditions are affected by
Diameter of pipe
Averagevelocity
Density ofliquid
Viscosity of thefluid
This four factors are combined in one way as Reynolds number
Re=
• Inertial forces are due to mass and the velocity of the fluid particles
trying to diffuse the fluid particles
• viscous force if the frictional force due to the viscosity of the fluid which
make the motion of the fluid in parallel.
D u ρ
η
INERTIAL FORCES
= ------------------------------
VISCOUS FORCES

 At low velocities the inertial forces are less when compared
to the frictional forces
 Resulting flow will be viscous innature
 Other hand when inertial forces are predominant the fluid
layers break up due to the increase in velocity hence turbulent
flow takes place.
 If Re < 2000 the flow is said to belaminar
 If Re > 4000 the flow is said to beturbulent
 If Re lies between 2000 to 4000 theflow change between
laminar to turbulent

APPLICATIONS
• Reynolds number is used to predict the nature of the flow
• Stocks law equation is modified to include Reynolds number
to study the rate of sedimentation in suspension
When velocity is plotted against the distance from the wall
following conclusions can be drawn
• The flow of fluid in the middle of the pipe is faster then the
fluid near to the wall
• At the actual surface of the pipe – wall the velocity of the
fluid is zero

BERNOULLI'S THEOREM
When the principles of the law of energy is applied to the flow of the
fluids the resulting equation is a Bernoulli's theorem
• Consider a pump working under isothermal conditions between points A
and B
• Bernoulli's theorem statement, "In a steady state the total energy per
unit mass consists of pressure, kinetic and potential energies are
constant"
Kinetic energy = u2 / 2g
Pump
Pressure energy = Pa / ρAg
Friction energy = F
A
B

Ø At point a one kilogram of liquid is assumed to be entering at point a,
Pressure energy = PA /g ρ A
Where PA = Pressure at point a
g = Acceleration due to gravity ρ A = Density of
theliquid
Potential energy of a body is defined as the energy possessed by the body by the virtue of
its position
Potential energy = XA
Kinetic energy of a body is defined as the energy possessed by the body by virtue of its
motion,
kinetic energy = U2
A/ 2g
Total energy at point A = Pressure energy + Potential energy +K. E Total energy at point
A = PA /g ρ A +XA+U 2
A/ 2g

According to the Bernoulli's theorem the total energy at point A is constant
Total energy at point A = PA / ρ A g +XA+ (UA2/ 2g) = Constant
After the system reaches the steady state, whenever one kilogram of liquid enters at
point A, another one kilogram of liquid leaves at point B
Total energy at point B = PB /ρB g +XB+ (UB2/ 2g) = Constant
INPUT = OUTPUT
Total Energy at point A = Total Energy at Point B
PA / ρ A g +XA+ (UA2/ 2g) = PB /ρ B g +XB+ (UB2/ 2g)
Theoretically all kinds of the energies involved in fluid flow should be accounted,
pump has added certain amount of energy.

During the transport some energy is converted to heat due to frictional
Forces
Energy loss due to friction in the line = F Energy
added by pump = W
PA /ρ A +XA + UA
2 / 2g – F + W = PB /ρ B +XB +UB2/ 2g
This equation is called as Bernoulli's equation

ENERGY LOSS
According to the law of conversation of energy, energy
balance have to be properly calculated fluids experiences
energy losses in several ways
while flowing through pipes, they are
•Frictional losses
•Losses in the fitting
•Enlargement losses
•Contractionlosses

Application of
BERNOULLI'S THEOREM
• Used in the measurement of rateof fluid flow
using flowmeters
• It applied in the working of the centrifugal
pump, in this kinetic energy is converted in to
pressure.

MANOMETERS
Manometers are the devices used for measuring
the pressure difference
Different type of manometers are there they are
1)Simple manometer
2)Differential manometer
3)Inclined manometer

 This manometer is the most commonly used
one
 It consists of a glass U shaped tube filled with a
liquid A- of density ρA kg /meter cube and above A
the arms are filled with liquid B of density ρB
 The liquid A and B are immiscible and the
interference can be seen clearly
 If two different pressures are applied on the two
arms the meniscus of the one liquid will be
higher than the other
SIMPLE MANOMETER

Let pressure at point 1 will be P1 Pascal's and
point 5 will be P2 Pascal's
The pressure at point 2 can be written as
=P1+ (m + R )ρB g
since ∆P = ∆ h ρ g
(m + R ) = distance from 3 to 5

Since the points 2 and 3 are at same height the pressure
Pressure at 3 =P1+ (m + R ) ρ B g
Pressure at 4 is less than pressure at point 3 by R
=P2+ m ρ B g
In another manner, the pressure at point 4
= P1+ (m + R ) ρ Bg - Rρ Ag
This can be summarise as
P1 + (m + R ) ρB g - R ρA g =P2 + gmρB
P1-P2 = gmρB- (m + R ) ρBg + R ρA g
∆P = gmρB – mρBg - RρBg + R ρA g
∆P=R (ρ A- ρ B )g

Application
• Pressure difference can be determined
by measuring R
• Manometers are use in measuring flow of
fluid.

DIFFERENTIAL MANOMETERS
• These manometers are suitable for measurement of small
pressure differences
• It is also known as two – Fluid U- tube manometer
• It contains two immiscible liquids A and B having nearly
same densities
• The U tube contains of enlarged chambers on both limbs,
• Using the principle of simple manometer the pressure
differences can be written as , ∆P =P1 –P2 =R (ρc – ρA)g

Diffrential Manometer
∆P =P1 –P2 =R (ρc – ρA) g
Hence smaller the difference between
ρcand ρAlarger will be R

INCLINED TUBE MANOMETERS
Many applications require accurate measurement of low pressure such
as drafts and very low differentials, primarily in air and gas installations.
In these applications the manometer is arranged with the indicating tube
inclined,
This enables the measurement of small pressure changes with
increased accuracy.
P1 –P2 = g R (ρ A - ρ B) sin α

MEASUREMENT OF RATE OF FLOW OF
FLUIDS
Methods of measurement are
Direct weighing ormeasuring
Hydrodynamicmethods
•Orifice meter
•Venturi meter
•Pitot meter
•Rotameter
Direct displacement meter

DIRECT WEIGHING OR
MEASURING
The liquid flowing through a pipe is collected for
specific period at any point and weighed or
measured, and the rate of flow can be determined.
Gases can not be determined by this method

ORIFICE METER
Variable head meter
Principle
o Orifice meter is a thin plate containing a narrow and sharp aperture.
o When a fluid stream is allowed to pass through a narrow constriction
the velocity of the fluid increase compared to up stream
o This results in decrease in pressure head and the difference in the
pressure may be read from a manometer

CONSTRUCTION
• It is consider to be a thin plate containing a sharp aperture through which
fluid flows
• Normally it is placed between long straight pipes
• For present discussion plate is introduced into pipe and manometer is
connected at points A and B
WORKING
• When fluid is allowed to pass through the orifice the velocity of the fluid at
point B increase, as a result at point A pressure will be increased.
• Difference in the pressure is measured by manometer
• Bernoulli's equation is applied to point A and point B for experimental
conditions

Bernaulis eqn...
PA /ρ A +XA + UA / 2g – F + W = PB /ρ B +XB + UB / 2g2 2
UB
2 - UA
2 = 2gc.PA /ρ-2gc.PB/ρ
No work is done on the liquid or by the liquid, w = 0
UB
2 - UA
2 = 2gc/ρ (PA –PB)
√UB
2- UA
2 = √2gc∆H
As (PA - PB)/ρ=∆H

Assumptions
• Pipeline is horizantal A and B are at same position
Therefore XA=XB
• Suppose friction losses are neglisible F=0
• As liquid is incompressible so density remain same,
Therefore ρ A=ρ B=ρ
• No work is done on liquid therefore w=0

Applications
• §Velocity at either of the point A and B can
be measured
• § Volume of liquid flowing perhour can be
determined by knowing area of cross section

VENTURI METER
Variable head meter
Principle
• When fluid is allowed to pass through narrow venturi throat
then velocity of fluid increases and pressure decreases
• Difference in upstream and downstream pressure head
can be measured by using Manometer
• U v = C v √ 2g . ∆H

Why Venturi meter if Orifice meter is available?
• Main disadvantage of orifice meter is power loss due to
sudden contraction with consequent eddies on other
side of orifice plate
• We can minimize power loss by gradual
contraction of pipe
• Ventury meter consist of two tapperd (conical section)
inserted in pipeline
• Friction losses and eddies can be minimized by this
arrangement.

DISADVANTAGES
Ø Expensive
Ø Need technical export
Ø Not flexible it is permanent
ADVANTAGES
Ø For permanent installations
Ø Power loss is less
Ø Head loss is negligible

Pitot tube
(Insertion meter)
Principle of Pitot tube
According to Bernoulli's therom
Total energy at any point =
Pressure energy + Potential energy +K. E
U0 = C 0 √ 2g∆H ........∆H= Difference in pressure head
∆H = U2 /2g ........U= Velocity at point of incertion

CONSTRUCTION
• It is also known as insertion meter
• The size of the sensing element is small compared
to the flow channel
• One tube is perpendicular to the flow direction and
the other is parallel to the flow
• Two tubes are connected to the manometer
2g∆Hp = U2

WORKING
• Pitot tube is used to measure the velocity head of flow.
• Parallel tube (to Upstream) measure velocity head +
pressure head
• Perpendicular tube (downstream) measure only
pressure head
• Difference of head between two tubes gives velocity
head ∆H.
• Working of pitot tube video

Difference between venturi-
orifice and Pitot tube
• Orifice and venturi
meter measure
average velocity of
whole stream of fluid
• More pressure drop
• Pitot tube measure
relative fluid velocity
at single point only
• Less pressure drop

PRINCIPLE
 In this device a stream of water enters Transparent
tapered tube and strikes the moving plummet
 During fluid flow plummet rise orfall
 As a result, annular space(area) between plummet and
tapperd tube may increase or decrease, depending on
variation of flow rate.
 Head across annulus is equal to weight of plummet.

CONSTRUCTION
• It consists of vertically tapered and transparent tube
generally made of glass in which a plummet is centrally
placed with guiding wire.
• Linear scale is etched on glass
• During the flow the plummetrise due to variation in flow
• The upper edge of the plummet is used as an index to note
the reading

WORKING
• As the flow is upward through the tapered tube the
plummet rises and falls depend on the flow rate
• Greater the flow rate higher the rise of plummet.
• Working of rotameter
USE
• To measure flow rate of gas as well as liquid
• Easy to use and allow direct visual inspection

Fluid flow

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