Flow of fluids

TPCTs College of Engineering, Osmanabad
Dept of Pharmacy
B. Pharm IInd yr, 3rd Sem
Subject- Pharmaceutical Engineering
Prepared by:- Kokare Pratima S.
Unit-I
1. Flow of Fluids

Contents:
• Types of manometers, Reynolds number and its
significance,
• Bernoulli’s theorem and its applications,
• Energy losses,
• Orifice meter, Venturimeter, Pitot tube and
Rotometer.
Flow of Fluids- Kokare Pratima S. 2

Introduction
• Flow of substances that do not permanently resist
distortion.
• Fluid- Liquid & Gases
• Fluid – Mass of substances formed by series of layer
• It mentions fluid properties such as viscocity,
compresability & surface tension
• Transporation- behaviour of liquids changes- effect on
heat transfer process, energy changes during pumping.
• Areas of applications-
✓Transportion of sterile air & water in manufacturing of
parenterals.
✓mixing of solids & liquids in suspension
✓packing of semisolids in containers
• Fluid flow-
A. Fluid Static- at rest (equillibrium)
B. Fluid Dynamic- in motion
3
Flow of Fluids- Kokare Pratima S.

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
4

P1s = P2s + volume x density x acceleration
P1s = P2s + height x area x density x acceleration
P1s = P2s + h1 s ρ g
Since surface area is same
P1 = Ps + h1 ρ g
Pressure acting on point 2 may be written as
P2 = Ps + h2 ρ g
Difference in the pressure is obtained by
P2 - P1 = g (Ps + h2 ρ ) – ( Ps + h1 ρ) g
∆P = (Ps + h2 ρ – Ps - h1 ρ ) g
∆P = ∆ h ρ g
Force acting on the liquid
At point 1
+Force on the surface Force excreted by the liquid
Above point 1
=
Pressure at point 1 x Area = Pressure on the surface x area + mass x acceleration
5

Applications of Fluid Static
• Working of manometers
• Quantification of fluid flow
in Bernoulli's theorem
6

Manometers
➢Manometers are the devices used for measuring the
pressure difference
➢Principle- hydrostatic equilibrium and is used for
measuring the pressure (static pressure) exerted by a still
liquid or gas.
➢Hydrostatic equilibrium states that the pressure at any
point in a fluid at rest is equal, and its value is just the
weight of the overlying fluid.
➢Advantages of manometers:
(i) Simple and time proven.
(ii) They have high accuracy and sensitivity.
(iii) Availability of a wide range of filling fluids of varying
specific gravities.
(iv) It has reasonable cost.
(v) They are suitable for low pressure and low differential
pressure applications.
7

Different type of Manometers
Manometers
Simple
manometer
Differential
manometer
Inclined
manometer
8Flow of Fluids- Kokare Pratima S.

Simple Manometer
• This manometer is the most commonly used
• 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

➢ Let pressure at point 1 will be P1 Pascal's and
at point 5 will be P2 Pascal’s
➢ The pressure at point 2 can be written as
= P1+ (m + R ) ρB g
(m + R ) = distance from 3 to 5
➢ Since the points 2 and 3 are at same height
the pressure at 3 can be written as
Pressure at 3 =P1+ (m + R ) ρB g
➢ Pressure at 4 can be written as
= P2 + gm ρB
OR
= P1+ ρB ( m + R ) g- ρA R g
Both the equations should be equal
P2 + gm ρB = P1+ ρB ( m + R ) g- ρA R g
P1 – P2 = gm ρB - ρB ( m + R) g + ρA R g
∆P = gm ρB - gm ρB - R ρB g + R ρA
∆P =R (ρA- ρB )g
10

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
11

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,
as in Figure, therefore providing an
expanded scale.
• This enables the measurement of small
pressure changes with increased accuracy.
P1 –P2 = g R (ρ A - ρ B) sin α
12

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
13

Applications of Fluid Dynamics
• Manufacturing of dosage
form
• Handling of drugs for
administration
14

TYPES OF FLOW
15
Flow
Laminar/
Viscous
Transient Turbulent

Laminar flow
• Fluid particles move in straight layers or
laminae.
• No exchange of fluid paticles from one layer to
another
• Streamline flow
• Small pipes & low flow rates are involved
• Shear stress depends exclusively on the
viscocity & is independent of the of the density. 16

Turbulent flow
• When velocity is increased fluid particles in
random manner instead of straight path. This is
called turbulent flow.
• Vortices, eddies & waves make flow unpredictable
• Generally occurs with high flow rates & with larger
pipes.
• Shear stress for turbulent flow is a function of the
density. 17

Transient flow
• It is mixture of laminar & turbulent flow, with
turbulent at center of pipe & laminar flow near
the edges.
• Critical velocity: Velocity at which flow
changes from laminar to turbulent.
18

Reynolds Number & Its Significance
• Osborne Reynolds in 1883
• The fundamental dimensionless parameter that
characterizes the behavior of flowing fluids
known as Reynolds number.
• It was the ratio that shows the effect of viscosity
in a given medium which governs the transition
between laminar and turbulent flow
19

Reynold’s Number (Re)
• It is a dimensionless number.
• Turbulent or laminar flow is determined by the Reynolds
number.
• It gives a measure of the ratio of inertial forces to viscous
forces
Re=
𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒𝑠
𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑐𝑒𝑠
Re=
𝐷𝑢𝜌
𝜂
Where,
𝐷= diameter of pipe (m)
𝑢= velocity of flow (m/s)
𝜌= density of fluid (kg/m3)
𝜂= viscosity of fluid
20

Measurement of fluid flow- Reynold’s
Experiment
• The apparatus consist of glass tank containing water, a
small tank containing color liquid or dye & a glass tube
with regulating valve (to adjust the velocity of flow) at the
end.
• Water is allowed to flow through glass tube. A liquid dye
with same specific weight as water as introduced into
glass tube. 21

❑Observations by Reynold’s
• At low velocity, the dye will move in a parallel to the tube
& also it does not get dispersed (i.e. Laminar flow)
• At velocity little more than before the dye moves in a wave
form (i.e. Transition flow)
• At more velocity the dye will no longer move in a straight
(i.e. Turbulent flow)
• The flow is
- Laminar when Re< 2000
- Transition when Re 2000-4000
- Turbulent when Re > 4000
❑Applications
• To predict nature of flow
• To study flow of incompressible fluid in closed pipes.
• The Stock’s law equation is modified to include the
Reynolds number to study the sedimention rate in
suspension.
• Heat transfer in liquids also depends on flow. 22

Bernoulli’s Theorem
1. Pressure Energy (PE)= PAL
• AL= W/ρg
• PE= PW/ρg
• PE= P/ρg …….. (if we consider this to unit weight of water)….(1)
2. Kinetic Energy = ½ MV2
Where V is the velocity of the body
• M= W/g
Thus,
• KE= ½ WV2/g
• KE= V2/2g……. (if we consider this to unit weight of water)….(2)
3. Potential Energy = Mgh
• M x g= W
• PE= WX
• PE= X………….. (if we consider this to unit weight of water)….(3)
23

➢When the principle of the law of energy is applied to the flow
of the fluids the resulting equation is called Bernoulli's
theorem
➢Consider a pump working under isothermal conditions
between points A and B
➢Bernoulli's theorem states that in a steady state the total
energy per unit mass consists of pressure, kinetic and
potential energies are constant
Pump
Friction energy = F
B
A
XA
XB
25

➢ At point a one kilogram of liquid is assumed to be
entering at this point, pressure energy at joule can be
written as
Pressure energy = PA /g ρ A
Where PA = Pressure at point a
g = Acceleration due to gravity
ρ A = Density of the liquid
➢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 = UA
2 / 2g
Total energy at point A = Pressure energy + Potential
energy+ Kinetic energy
26

➢Total energy at point A = Pa /g ρ A +XA + UA
2 / 2g
➢According to the Bernoulli's theorem the total energy at point A is
constant
Total energy at point A = Pa /g ρ A +XA + UA
2 / 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 /g ρ B +XB + UB
2 / 2g
INPOUT = OUT PUT
Pa /g ρ A +XA + UA
2 / 2g =PB /g ρ B +XB + UB
2 / 2g
➢Theoretically all kids of the energies involved in fluid flow should be
accounted, pump has added certain amount of energy
Energy added by the pump = + wJ
27

➢During the transport some energy is converted to heat due
to frictional Forces
Loss of energy due to friction in the line = FJ
Pa /g ρ A +XA + UA
2 / 2g – F + W = PB /g ρ B +XB + UB
2 / 2g
This equation is called as Bernoulli's equation
❑Applications
➢Used in the measurement of rate of fluid flow
➢It applied in the working of the centrifugal pump, in this
kinetic energy is converted in to pressure.
28

ENERGY LOSSES
• When a fluid through a pipe, the fluid
experiences some resistance due to which part
of energy is lost. This loss of energy is classified
as
• According to the law of conversation of energy,
energy balance have to be properly accounted.
Energy
Losses
Friction
losses
Losses in
fitting
Enlargement
losses
Contraction
losses

Friction Losses
➢ During flow of fluids frictional forces causes a loss in pressure (∆Pf Pascals). The fluid
flow can be either viscous or turbulent, which also influences the losses
In general pressure drop (∆Pf ) will be
PRESSURE DROP α VELOCITY (u), m/s
α Density of fluid(ρ), kg/m3
α Length of the pipe (L), m
α 1 / diameter of the pipe (D), m
➢ These relationships are proposed in Fanning equation for calculating friction losses
Fanning equation ∆Pf =
2fu2Lρ
D
(viscous/turbulent)
where, F = frictional factor
∆Pf = Pressure drop
➢ For viscous flow pressure drop Hagen –Poiseullie equation (Viscous equation):
∆P =
32 Luη
D2
η = viscocity of the liquid,
∆Pf = Pressure drop
30

Losses in Fitting
➢Fanning equation is applicable for the losses in
straight pipe.
➢When fitting are introduced into a straight pipe,
they cause disturbance in the flow, Which result in
the additional loss of energy losses in fitting may
be due to
• Change in direction
• Change in the type of fittings
31

Enlargement Loss
➢If the cross section of the pipe enlarges gradually, the fluid
adapts itself to the changed section without any disturbance. So
no loss of energy.
➢If the cross section of the pipe changes suddenly then loss in
energy is observed due to eddies. These are greater at this point
than straight line pipe
Then u2< u1
➢For sudden enlargement = ∆ H = u1 – u2 / 2g
∆ H = loss of head due to sudden enlargement

Contraction Losses
➢If the cross section of the pipe is reduced
suddenly the fluid flow is disturbed, the diameter
of the fluid stream is less than the initial column
this point is known as vena contracta.
33

MEASUREMENT OF RATE OF FLOW OF FLUIDS
➢Whenever fluids are used in a process it is necessary to
measure the rate at which the fluid is flowing through
the pipe.
➢Methods of measurement are
Measurement
of Fluid Rate
A. Direct weighing
or measuring
B. Hydrodynamic
methods
Orifice
meter
Venturi
meter
Pitot meter
Rotameter
C. Direct
displacement meter
34

A. 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
35

B. Hydrodynamic Methods
1. ORIFICE METER
Principle:
➢ Orifice meter is a thin plate containing a narrow and sharp
aperture.
➢ When a fluid stream is allowed to pass through a narrow
constriction the velocity of the fluid increase compared to
up stream
➢ This results in decrease in pressure drop and the
difference in the pressure may be read from a manometer
➢ The velocity of the fluid at thin constriction may be written
as
U0 =C 0 √ 2g ∆H
∆H = can be measured by manometer
C0 = constant
U0 = velocity of fluid at the point of orifice meter
36

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
➢ Orifice meter is referred as the variable head meter,
i.e it measures the variation in the pressure across a
fixed constriction placed in the path of flow.
➢ Hen fluid stream is allowed to pass through coss-
section of the orifice, the velocity of fluid at point B
increases at the expense of pressure head.
➢ As a result the pressure at point A is higher than at
point B.
➢ The difference in the pssure (∆H) may be read from a
manometer, connected to the points A and B.
37

2. Venturi Meter
Principle:
➢When fluid stream is allowed to pass
through narrow throat , velocity of
fluid increases at venturi as
compared to the velocity of upstream
which results in corresponding
decrease in pressure head.
➢The difference in pressure head (∆H)
may be read from a manometer.
➢The velocity of fluid at narrow
constriction throat may be written as:
Uv = Cv √ 2g . ∆H
Uv = velocity at the throat of venturi,
m/s
Cv =coefficient of venturi meter
∆H = difference in the head of
manometer, m
38

Construction:
➢ Consist of 2 tapered sections inserted in a pipeline
➢ Venturi meter is placed between long straight pipes.
➢ The upper stream cone is normally shorter than the downstream.
➢ A manometer is connected at points A & B as shown in fig.
Working:
➢ Referred as variable head meter, as measures the variable differential
pressure.
➢ The velocity of fluid is increased at throat due to constriction which results
in the decreased pressure in the upstream cone.
➢ This pressure drop is utilized to measure the rate of flow using a
manometer.
Applications:
➢ Used for liquids especially for water.
➢ Also used for measurement of gases
Disadvantages
➢ Expensive
➢ Occupies more space
➢ Not flexible it is permanent
Advantages
➢ Power loss is less
➢ Head loss is negligible

3. Rotameter
Principle:
➢ Consist of vertical tapered & transparent tube in
which a plummet is placed .
➢ During the fluid flow though the tube , the plummet
rises & falls because of variation in flow. As a result,
the area of annular space between the plummet &
the tube varies.
➢ The head loss across the annulus is equal to the
weight of plummet.
➢ The upper edge of plummet is used as index to note
the reading on the tapered tube which indicates the
flow of fluid.
Construction
➢ It consists of vertically tampered and transparent
tube in which a plummet is placed
➢ During the flow the plummet rise due to variation in
flow the upper edge of the plummet is used as an
index to note the reading
40

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
➢ 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
√U0
2 – UA
2 =C0 √2g. ∆H
U0 = velocity of fluid at orifice
UA = velocity of fluid at point A
C0 = constant
➢ If the diameter of the orifice is 1/5 or less of the pipe diameter then UA is
neglected
Applications
➢ Velocity at either of the point A and B can be measured
➢ Volume of liquid flowing per hour can be determined
41

Pitot Tube
Construction
➢ It is also known as insertion tube
➢ 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
∆Hp = u2 /2g
Working
➢Tube are inserted in the flow shown
is the figure
U2 = Cv √2g. ∆H
➢ Coefficient of Pitot tube
42

C. DIRECT DISPLACEMENT METER
➢Used for the measurement
of domestic water supply
PRINCIPLE
➢In this a stream of water
enters meter and strikes the
moving meter, the rate of
rotation of the moving
membrane is proportional to
the velocity of the fluid.
43

Question Bank
1.Write Reynolds equation and describe its terms.
2.Write about types of fluid flow.
3.What is manometer? Explain simple & differential
manometers.
4.Derive & explain Bernaulli’s theorem.
5.Write a note on:
a) Orifice meter
b)Venturi meter
c) Rotameter
44

Thank You….
45

Flow of fluids

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