Flow of fluids

Ms. Mandakini Sampat Holkar
(M. Pharm.)
For Second Year B. Pharm. Program as
per PCI syllabus, New Delhi
Flow of Fluids

Flow of Fluids
Syllabus-
Types of manometers, Reynolds number and
its significance, Bernoulli’s theorem and its
applications, Energy losses, Orifice meter,
Venturimeter, Pitot tube and Rotometer.

Introduction
ØFluid may be defined as substance that cannot resist deformation or
distortion permanently.
ØIt may be a liquid or a gaseous substance that attempts to change its
shape by making its layers to slide over one another
Until a new shape is attained.
Ø at particular condition of pressure and temperature, every fluid has a
definite density.
Ø In case of liquids the density is not affected by slight changes in
pressure but may change by changing temperature.
ØIn case of gases density get affected with a changes in pressure both
pressure and temperature.
ØWhen fluid is not affected by changes in pressure such fluid is called
as Incompressible fluid.

Flow of Fluids involved in a number of areas of pharmaceutical industries
• Transporting of sterile air and sterile water in the production
of Parenterals
•Mixing of solid and liquid in case of suspension
•Packing of semisolids in containers.
•Filling of liquid dosage forms into the containers.

Flow of Fluids
The subject of fluid flow can be divided in to two parts
1. Fluid statics or hydrostatics-deal with fluids at rest in
equilibrium state.
2. Fluid dynamics or Hydrodynamics-deal with fluids under
motion.

2.Fluid dynamics or Hydrodynamics
Fluid dynamics deals with the study of fluids in motion.
Flow of fluid through a closed channel (pipelines) can be either
Laminar or turbulent. These can be observed in the classical
Reynolds experiment.

Reynolds experiment.

Reynolds Number
The special significance of Reynolds number is that it can be used to
estimate the type of fluid flow in a particular set of conditions. prof.
Reynolds after carrying out a series of experiments, found that if
value of this than 2000,the flow is considered to be streamline or
laminar and if the number exceeds 4000 the flow is said to be
turbulent.
Any intermediate value indicates transitional flow conditions.
Reynolds number is of great help in case of stability studies of
suspensions.
Used to study the sedimentation rate of particles.
Applicable in assessing the rate of heat transfer in liquids.

Bernoulli's Equation and its application
Bernoulli's equation is the application of Bernoulli’s
theorem which works on the principle of conservation of
energy when applied to flow of fluids.
Bernoulli’s theorem states that in a steady state ideal flow
of an incompressible fluid ,the total energy per unit mass
which includes pressure energy kinetic energy and datum
energy at any point of fluid is constant.

Bernoulli's Equation and its application
At point A, one kilogram of liquid is assumed to enter the pipe and experience
pressure energy , Kinetic energy ,potential (datum) energy.
Pressure energy = PA/gρA
....................................... 1
PA is pressure in Pascal's at point A
In g is acceleration due to gravity ,m/s2
ρA is density of the liquid Kg/m3
Point A considered to be placed at a height of XA meters above the
datum plane.
Potential energy= XA.......................................................2

Kinetic energy is the energy possessed by a body by virtue of its motion
Kinetic energy = u2A/2g
....................................... 3
Total energy experienced by liquid at point A
Total energy= pressure energy + potential energy + kinetic energy
= PA/gρA + XA+ u2A/2g............................4

As per Bernoulli’s theorem the total energy at point A is
constant.
Therefore equation no 4 may be written as-
Total energy at point A= PA/gρA + XA+ u2A/2g = Constant ..................5
Once the system reaches the steady state the flow becomes steady at each
point in the pipe and leave the pipe at point B.
Therefore energy content of one kg liquid at point B can be written as
Total energy at point B= PB/gρB + XB+ uB2/2g = Constant ..................6

PB= is pressure in Pascal's at point B
ρB is density of the liquid at point B Kg/m3
XB= height of point B from datum , m
uB=velocity at point B, m/s
If there is no gain loss of energy, principle of conversation of energy may be applied
to point A and B
Input = Out put
Total energy at point A= Total Energy At point B
PA/gρA + XA+ u2A/2g= PB/gρB + XB+ uB2/2g ............7

Since all kind of energies involved should be accounted , therefore energy
provided by pump (W joule) has to be added and energy lost in the form of
friction (F joule) has to be deducted from equation
PA/gρA + XA+ u2A/2g + W- F = PB/gρB + XB+ uB2/2g
This is Bernoulli's equation

Application of Bernoulli's Theorem
It is applied in measuring the flow rate of fluids using head
meters like orifice meter, venture meter.
It is applied in working of centrifugal pumps where kinetic
energy is converted into pressure head to pump the fluid
It is easy to measure heights and use them as energy terms ,
which is a contribution of Bernoulli's theorem

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.
This is required for optimization of process parameters in a chemical
industry.
Methods of measurement may be classified as
1.Direct weighing methods
2.Hydrodynamic methods
a. Orifice meter
b. Venturi meter
c. Pilot tube
d. Rotameter
3.Direct displacement meter

Orifice Meter
Principle-
The orifice meter is a thin plate containing a narrow and sharp
aperture.
When a fluid stream is suddenly allowed to pass through the narrow
constriction , the velocity of fluid at orifice meter increase compared to
the velocity of fluid in the upstream .this result in decrease in the
pressure head.
Bernoulli’s theorem provides the basis for correlating the increase in
the velocity head with the decrease in pressure head between two
points.
The difference in the pressure head (∆H ) may be read from
manometer.
If diameter of orifice is small compared to the diameter of the pipe
velocity of fluid at the point before entering the orifice may be negelible
. in such cases the manometer reading directly gives the velocity of the
fluid.

Velocity of the fluid at the thin constriction can be written
as
u0 =C0√2g. ∆H
U0= is the velocity of fluid at orifice point m/s
C0= constant related to orifice meter
∆H= Difference in pressure head from manometer

Construction-
Orifice meter is a thin plate containing a sharp aperture or hole having
very less diameter as compared to the diameter of the pipe.
It placed in straight pipes of short length so that other fitting do not
affect the flow rate.
Difference in the pressure head can be measured from the attached
manometer between the points a and b.
Working-
Orifice meter is referred to as variable head meter i.e it measures the
variation in the pressures across a fixed constriction placed in the path
of flow consisting of a constant area.

When fluid stream is allowed to pass through the cross section of the
orifice the velocity of fluid at B increases at the expense of pressure head.as
result the pressure at point A higher than at point B.
Bernoulli,s provides the basis for correlating the increase in velocity head
with the decrease in pressure head.
The differenece in pressre may be read from manometer,connected to the
points A nad B
Bernoulli’s equation may be applied for two points (A AND B) for given
experimental conditions as given below
√u02-ua2=C0√2g. ∆H
u0=velocity of fluid at the point of orifice
meter,m/s
uA=velocity of fluid at the point A

If the diameter of the orifice is small and is around 1/5 of the
pipe diameter,ua is small as compared to u0
In such case ua is neglected and equation became
u0= C0√2g. ∆H

Venturimeter
In venturimeter the fluid flow rate is measured by reducing the cross
sectional flow area in the flow path which generates the pressure
head difference.
Principle-
Venturimeter consist of two tapered section in the pipeline with
gradual constriction known as venturi throat , at its centre. When
stream of fluid passes through this throat ,the velocity of fluid
increases as compared to the velocity upstream.
This increases in velocity as per Bernoulli's theorem leads to
corresponding decrease in pressure head.
The difference the pressure head can be obtained from manometer
attached to the assembly .
In case the diameter of venturi is small compared to the diameter of
pipe, velocity of fluid at the point before the orifice can be
considered to be negligible. in such case the manometer reading
directly gives the velocity of fluid .

Velocity of fluid at narrow constriction can be written as
uv=Cv√2g. ∆H
uv=velocity of fluid at throat of venturi ,m/s
Cv=is a constant
∆H= is difference in pressure head from
manometer ,m.

Pitot Tube:
It is an instrument to determine the velocity of the flow at the
required point in a pipe or a stream. In its simplest form, a pitot tube
consists of a glass tub with 90° bent.
It measures the fluid flow velocity by converting kinetic energy of
the flow into potential energy. While orifice meter and venturimeter
measure the average velocity of the whole stream of the fluid, pitot
tube measures the velocity at one point only. Since, the velocity of
fluid varies across
the cross section of pipe, average velocity has to be calculated either
from the maximum velocity or by taking readings at different points
in the cross section and then determining the mean velocity by
graphic integration.

Principle:
Pitot tube consists of a sensing element, which when inserted at
the centre of the stream,
increases the velocity of flow and hence, pressure head
decreases. The tube at right angles to the flow measures the
pressure head only, while the tube that pointed upstream
measures both pressure head and velocity head. The difference
of these two indicates the velocity head.

Construction:
Construction of Pitot tube is as shown in Fig. It is also known as
insertion meter. Point A measures both velocity head and pressure
head of the flowing fluid and point B situated at right angles to the
flow measures only the pressure head. Both the tubes are connected
to a manometer as shown in the figure.

Working:
The two tubes are inserted into the stream of flowing fluid. Point A is
having the sensing element which is small opening as compared to the
size of the flow channel.
It measures both pressure head and velocity head. The velocity of the
fluid increases as enters into this narrow constriction. This results in
decrease of the pressure. Tube at right angles to the flow (point B)
measures pressure head only. The difference in these two readings
indicates the velocity head.
According to Bernoulli's equation, velocity head of the fluid at pitot
(∆Hp) may be obtained as
∆Hp = u2/2g
u2=2g. ∆Hp
This is the theoretical velocity and actual velocity may be given as
u=Cp√2g. ∆Hp

Where Cp is the coefficient of pitot tube.
Application-
1. It is used to determine the amount of cooling that is happening to
a room.
2. It can be inserted through a small hole in a duct with the pitot
connected to a water weight, gauge or differential manometer to
determine the velocity inside the ducted wind tunnels.
different
3. In industry, the velocities being measured are often those flowing
in ducts or tubes, diagonal where measurements by a simple
manometer would be difficult. In such cases, the shows if most
practical instrument to be used is Pitot tube.

Advantages:
1. It is very simple in construction and easy to install and
handle.
2. It can measure the velocity directly at a single point in
the pipe.

Disadvantages:
1. At the point of insertion, pitot tubes themselves cause
disturbances. Eddies within the pressure tube may disturb the
readings.
2. Velocity is given for a single point only and it can not give
the average velocity directly.
3. When the fluid is a gas, the readings are extremely small and
a simple construction does not give accurate results. Therefore,
for gases working on low pressures, some kind of multiplying
gauges should be used.

Rotameter:
A rotameter is a device that measures the volumetric flow rate
of fluid in a closed tube. It
belongs to a class of meters called variable area meters, which
measure flow rate by allowing
the cross-sectional area of the pipe to vary, causing a
measurable effect.

Principle:
The Rotameter's operation is based on the variable area principle.
Fluid flow raises a float in a tapered tube, increasing the area for
passage of the fluid. The greater the flow, the higher the float is
raised. The height of the float is directly proportional to the flow
rate. With liquids, the float is raised by a combination of the
buoyancy of the liquid and the velocity head of the fluid. With
gases, buoyancy is negligible, and the float responds to the velocity
head alone. The float moves up or down in the tube in proportion to
the fluid flow rate and
the annular area between the float and the tube wall. The float
reaches a stable position in the tube when the upward force exerted
by the flowing fluid equals the downward gravitational force exerted
by the weight of the float. A change in flow rate upsets this balance
of forces.

The float then moves up or down, changing the
annular area until it again reaches a position where
the forces are in equilibrium. To satisfy the force
equation, weight of the float. A change in flow rate
upsets this
rotameter float assumes a distinct position for every
constant flow rate.

Construction:
A rotameter consists of a tapered tube, typically made of glass
with a 'float' (a shaped weight, made either of anodized
aluminum or a ceramic), inside that is pushed up by
the drag force of the flow and pulled dawn by gravity (Fig. 1.14).
Floats are made in many different shapes, with spheres and
ellipsoids being the most common. The float may be diagonally
grooved and partially coloured so that it rotates axially as the
fluid passes. This shows if the float is stuck since it will only
rotate if it is free. Readings are usually taken at the top of the
widest part of the float; the center for an ellipsoid or the top for
a cylinder. Some manufacturers use a different standard. The "
float" must not float in the fluid, it has to have a higher density
than the fluid otherwise it will float to the top even if there is no
flow.

Working:
Due to taper tube, as the float moves upwards , the fluid passing area
increseses as result of which the differential pressure decreases.
Upward movement of float stops when the dead load is dynamically
balanced by the differential pressure. Tapering of metering tube is so
designed that the vertical movement of the float becomes linearly
proportional to the rate of flow and the scale is provided to read the
position of the float, thus giving birth to flow rate indication.

A higher volumetric flow rate through a given area increases flow
speed and drag force,so the float will be pushed upwards. However, as
the inside of the rotameter is cone shaped (widens), the area around
the float through which the medium flows increases, the flow
speed and drag force decrease until there is mechanical equilibrium
with the float's weight.
The mechanical nature of the measuring principle provides a flow
measurement device that does not require any electrical power. If the
tube is made of metal, the float position is transferred to an external
indicator via a magnetic coupling. This capability has considerably
expanded the range of applications for the variable area flow meter,
since the measurement can observed remotely from the process or
used for automatic control.

Applications:
1. Rotameters are extensively used in chemical and
pharmaceutical industries.
2. In case of fermentation industry, rotameters are attached to
the fermenters to check and control the flow of various gases
and air.
3. Rotameters are also used in hospitals and clinics for
controlling the oxygen gas intake by the patients.

ENERGY LOSSES
According to the law of conservation or energy, energy
balances have to accounted effectively, Therefore, it is very
much essential to calculate the energy losses occurring during
the flow of fluids.
These losses can occur in several ways and some of them are
as follows:
Frictional losses
Enlargement losses
Contraction losses
Losses in fittings

Frictional LOSSES
Frictional losses cause a loss in pressure, ∆Pf, which is
proportional to the velocity, viscosity and density of
the fluid, and the length of the pipe. It is inversely
proportional to the diameter of the pipe. The fluid
flow can be either laminar (viscous) or turbulent.
However, in practice, fluids are rarely handled in
laminar or viscous flow. Hagen - Poiseuille equation
can be used for calculating the friction drop in case
the flow is viscous.
∆Pf=32 Luμ/D2

Frictional LOSSES
where,
∆Pf is the pressure drop due to friction,
L is the length of pipe,
u is velocity of fluid,
μ is the viscosity of fluid and
D is the diameter of the pipe

Frictional LOSSES
Fanning's equation is employed for calculating the friction losses, irrespective
of the
nature of the flow, whether viscous or turbulent.
∆Pf = 2 f.L.u2.ρ /D
where, f. is the friction factor and ρ is the density of the fluid. Other terms are
same as above. The value of f depends on:
Nature of the flow of the fluid
Roughness of the inner surface of the pipe. This value may vary from 0.6 to
2.5 for asmooth brass, copper or lead pipe to a badly rusted cast iron pipe.
A reduction of friction loss in turbulent flow of Newtonian fluids can be
achieved by
adding soluble high molecular weight polymers in very very low
concentrations and by using the smooth walled pipes which are free from rust.
It is important to note that the friction losses are permanent losses as the
potential and
the kinetic energies get converted into heat energy.

Enlargement LOSSES
If the cross section of the pipe is increased or decreased gradually, the
fluid adapts itself to the changed section without any disturbances
and there are practically no energy loss However, if the cross section
is changed suddenly, loss of energy occurs due to the formation
of eddies. Due to sudden enlargement disturbances, loss of pressure
head is observed sudden enlargement of the section, the velocity of
flow at enlarged section (u2) is less than that at the small cross
section (u1), i.e., U2 < U1. The loss can be calculated as:
∆H =(u1-u2)2/ 29
where, ∆H is the loss in head due to enlargement

Contraction LOSSES
In this case, when the cross section is reduced suddenly, there occurs
a disturbance in flow. The point of minimum cross section is known
as vena contracta. If u1 is the velocity at large section and u2 is the
velocity at small cross section, then in this case u2 > u1 and u1 may
be considered negligible. The lass can be calculated as:
∆Hc= K(u2)2 /2g
where, ∆Hc is the loss in head due to contraction and K is a constant
whose value
depends upon the relative areas of two sections, When this ratio is
0.5, K = 0.3 and there is negligible loss in case of laminar flow.

Fitting LOSSES
Usually a large number of fittings are introduced in pipe during the
flow of fluid for long distances.
This leads to disturbance in the flow and hence loss of energy.
These losses may be either due to change in the direction of flow
or change in the of fitting like union couplings or even some valve
and meters.
Losses in the fittings are expressed in terms of an equivalent
length of straight pipe (ELSP) which is in forms of a number as
per the diameter of pipe.
These numbers are used to convert the fitting in to its equivalent of
straight pipe
Equivalent length of fitting = ELSP * internal diameter of pipe

Flow of fluids

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (20)

Semelhante a Flow of fluids

Semelhante a Flow of fluids (20)

Mais de mandakiniholkar

Mais de mandakiniholkar (15)

Último

Último (20)

Flow of fluids