Pharmaceutical Engineering: Flow of fluids

FLOW OF FLUIDS
Parag Jain
Assistant Professor

Chhattrapati Shivaji Institute
of Pharmacy

Durg, Chhattisgarh
Presented by

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

FLUID DYNAMICS
Ø Fluid dynamics deals with the study of
fluids in motion
Ø This knowledge is important for liquids, gels,
ointments which will change their flow behavior
when exposed to different stress conditions
FLOW THROUGH PIPES
FILLED IN CONTAINER
MIXING

Importance Identification
of type of flow is important in ü Manufacture
of dosage forms
ü 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 O R VI S C O U S FLOW
TURBULENT FLOW

TYPES OF FLOW
è Laminar flow is one in
which the fluid particles
move in layers or laminar
with one layer sliding with
other
è There is no exchange of
fluid particles from one
layer to other
è Avg velocity = 0.5 Vmax
è Re < 2000
è When velocity of the water
is increased the thread of
the colored water
disappears and mass of
the water gets uniformly
colored
è There is complete mixing
of the solution and the flow
of the fluid is called as
turbulent flow
è Avg velocity = 0.8 Vmax
è Re > 4 0 0 0
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
Ø Diameter of pipe
Ø Average velocity Ø
Density of liquid
Ø Viscosity of the fluid
This four factors are combined in one way as Reynolds
number
Re=
Ø Inertial forces are due to mass and the velocity of the fluid
particles trying to diffuse the fluid particles
Ø 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 in nature
¬ 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 I said to be laminar
¬ If Re > 4000 the flow is said to be turbulent
¬ If Re lies between 2000 to 4000 the flow
change between laminar to turbulent

APPLICATIONS
Ø Reynolds number is used to predict the nature of
the flow
Ø 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
Ø The flow of fluid in the middle of the pipe is faster
then the fluid near to the wall
Ø At the actual surface of the pipe – wall the velocity
of the fluid is zero

Pipe wall
Relativedistancefrom
thecenterofthepipe
U /U max
Turbulent flow
Viscous flow

BERNOULLI'S THEOREM
When the principals of the law of energy is applied to the flow
of the fluids the resulting equation is a Bernoulli's theorem
Ø Consider a pump working under isothermal conditions between
points A and B
Ø 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

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 the liquid
Potential energy of a body is defined as the energy possessed by the
body by the virtue of itsposition
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 /2g2
Total energy at point A = Pressure energy + Potential energy + K. E
Total energy at point A = PaV + XA + UA /2g
2

According to the Bernoulli's theorem the total energy at point A
is constant
Total energy at point A = PAV + X A + (UA /2g) = Constant2
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 = PBV + X B + UB2 /2g
PAV + X A + (UA 2 / 2g) + Energy added by the pump
= PBV + X B + (UB / 2g)2
V is specic volume and it is reciprocal of density.
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 + X A + UA2 /2g – F + W = PB /ρ B + X B +
UB /2g2
This equation is called a s Bernoulli's equation

Application of
BERNOULLI'S THEOREM
Ø Used in the measurement of rate of fluid
flow using flowmeters
Ø It applied in the working of the
centrifugal pump, in this kinetic energy
is converted in topressure.

ENERGY L O S S
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
Ø Frictional losses
Ø Losses in the fitting
Ø Enlargement losses
Ø Contraction losses

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

Ø This manometer is the most
commonly used one
Ø 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 densityρB
Ø The liquid A and B are immiscible
and the interference can be seen
clearly
Ø If two different pressures are
applied on the two arms the
meniscus of the one liquid will be
higher than the other
SIMPLE M A N O M E T E R

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

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

INCLINED TUBE M A N O M E T E R S
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
Ø Direct weighing or measuring
Ø Hydrodynamic methods
Orifice meter
Venturi meter
Pitot meter
Rotameter
Ø Direct displacement meter
Ø Disc meters
Ø Current 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
Ø Orifice meter is a thin plate containing a narrow and
sharp aperture.
Ø When a fluid stream is allowed to pass through a
narrow constriction the velocity of the fluid
increase compared to up stream
Ø This results in decrease in pressure head and the
difference in the pressure may be read from a
manometer

CONSTRUCTION
Ø It is consider to be a thin plate containing a sharp aperture
through which fluid flows
Ø Normally it is placed between long straight pipes
Ø For present discussion plate is introduced into pipe and
manometer is connected at points A and B
Working
ü 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.
ü Difference in the pressure is measured by manometer
ü Bernoulli's equation is applied to point A and point B for
experimental conditions

Applications
§ Velocity at either of the point A and B can
be measured
§ Volume of liquid flowing per hour 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 √ 2 g . ∆H

Why Venturi meter ifOrifice
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. Vd Orif Ventury

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

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

Construction
Ø It is also known as insertion meter
Ø The size of the sensing element is small
compared to the flow channel
Ø One tube is perpendicular to the flow
direction and the other is parallel to the
flow
Ø 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.

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

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

Working
Ø As the flow is upward through the tapered
tube the plummet rises and falls depend
on the flow rate
Ø Greater the flow rate higher the rise of
plummet.

Use
• To measure flow rate of gas as well
as liquid
• Easy to use and allow direct visual
inspection

Costruction
• It has a propeller which is
rotated when water hits it and
is connected to magnets which
actuates recorders when the
propeller rotates.
• T h e v e l o c i t y o f w a t e r
increases the propeller rotation.

Website: www.probecell.com Email: probecellinfo@gmail.com
Ph: 7415211131
Ofﬁce: Smriti Nagar, Bhilai, Chhattisgarh - 490020
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Pharmaceutical Engineering: Flow of fluids

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