Pharmaceutical Engineering

Flow of Fluids
Aditya DGS
(Asst. Professor, Bharati Vidyapeeth’s College of Pharmacy,
Navi Mumbai)
Important Aspects
● Fluid Statics (Manometers, Pressure gauge)
● Fluid Dynamic (Reynolds Experiment)
● Bernoulli’s Theorem
● Energy Losses
● Measurement of Rate of Flow of Fluids (Orifice meter, venturi meter,
Rotameter)
Pharmaceutical
Industrial
Processing &
Basic Principles
Flow of Fluids
Fluid flow may be defined as the flow of substances that do not permanently resist
distortion.
Fluid includes both liquids and gases.
● Fluids may be defined as a substance that does not permanently resist
distortion. an attempt to change the shape of a mass of fluid will result in layers
of fluids sliding over one another until a new shape is attained.
● During the change of shape shear stresses will exist, the magnitude of which
depends upon the viscosity of the fluid and the rate of sliding. But when a final
shape is reached, all shear stresses will disappear. A fluid at equilibrium is free
from shear stresses.
● The density of a fluid changes with temperature and pressure. In case of a liquid
the density is not appreciably affected by moderate change of pressure.
Flow of Fluids
In case of gases, density is affected appreciably by both change of
temperature and pressure.

● The science of fluid mechanics includes two branches:

(i) fluid statics and (ii) fluid dynamics.

Fluid statics deals with fluids at rest in equilibrium.

Fluid dynamics deals with fluids under conditions where a portion is in

motion relative to other portions.
Fluid Statics
The behaviour of liquid at rest, the nature of pressure it exerts and variations
of pressure at different layers in the liquid are some of the relevant aspects in
Pharm. Engg.

The study of fluids at rest is based on 2 principles:

a. Pressure at a point is same in all directions.

b. Pressure is same at all points in a given horizontal line in a continuous
fluid.
Fluid Statics

In a stationary column of
static fluid the pressure at
any one point is the same
in all directions. The
pressure will also remain
constant in any
cross-section parallel to
the earth’s surface, but will
vary from height to height.
Fluid Statics
Let us consider, that the column of fluid in the
figure is remaining at equilibrium. If the orifice D is
open then the fluid will try to flow away.
So either D is closed or a pressure is applied such
that the liquid column stand at any desired height.
The cross-section of the column is S metre square
(let).
Now, say the pressure at the height X2 = P2 (in
gravitational unit). At equilibrium all the forces
acting on point B will be the same.
i.e. Upward force =P2S
Fluid
Statics
Manometers
Manometers are the devices used for measuring the pressure difference.

Manometers are used in measuring flow of fluid

Different type of manometers are there they are

·Simple manometer
·Differential manometer
·Inclined manometer
Simple Manometer Diagram
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 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 and point 5 will be P2 Pascal's
•The pressure at point 2 can be written as = P1+ (m + R ) ρB

*(m + R ) = distance from 3 to 5

Simple Manometer
Since the points 2 and 3 are at same height the pressure at 3 can be written
as, Pressure at 3 =P1+ (m + R ) ρ B
Pressure at 4 can be written as, = P1 + (m + R ) ρ B- R.ρA
(At Point 5) we have, P2 = P1+ ρB ( m + R )- R.ρA- m.ρB
P1-P2=∆P = R (ρA- ρB)

Pressure difference can be determined by measuring R

Differential Manometer
Differential Manometer
•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 C 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
Hence smaller the difference between ρC and ρA larger will be R
Inclined Tube Manometer
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 = R (ρ A - ρ B) sin α
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
Types of Flow
Identification of type of flow is important in
•Manufacture of dosage forms
•Handling of drugs for administration
The flow of fluid through a closed channel can be
viscous or turbulent and it can be observed by
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
Types of Flow- Laminar v/s Turbulent 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
When velocity of the water is increased the thread of the colored water
disappears and mass of the water gets uniformly colored, indicates
complete mixing of the solution and the flow of the fluid is called as
turbulent flow
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
·Average velocity
·Density of liquid
·Viscosity of the fluid
This four factors are combined in one way as Reynolds number is obtained by
the following equation
Reynolds Number contd.
•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.
•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
 Reynolds Number- Applications
•Reynolds number is used to predict the nature of the flow
•Stoke’s 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 than the fluid near
to the wall
•The velocity of fluid approaches zero as the pipe wall is approached
•At the actual surface of the pipe wall the velocity of the fluid is zero
•The velocity of the fluid is zero at the wall surface there should be
some layer in viscous flow near the pipe wall which acts as stagnant
layer
•if the flow is turbulent at the center and viscous at the surface a
buffer layer exist, this buffer layer changes between the viscous to
turbulent flow
Bernoulli’s Theorem
•When the principles of the law of energy are 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
•At point a one kilogram of liquid is assumed to be
entering at this point, pressure energy at joule can be Kinetic energy= u2/2g
written as Pressure energy= Pa/ⲣAg
Pressure energy = Pa /g ρ A
Where Pa = Pressure at point a , g = Acceleration due to
gravity, ρA = Density of the liquid
Bernoulli’s Theorem
Potential energy of a body is defined as the energy possessed by the body by the virtue of its
position

Kinetic energy of a body is defined as the energy possessed by the body by virtue of its motion,

According to the Bernoulli's theorem the total energy at point A is constant.

After the system reaches the steady state, whenever one kilogram of liquid enters at point A, and
another one kilogram of liquid leaves at point B
Bernoulli’s Theorem
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
During the transport some energy is converted to heat due to frictional Forces

Loss of energy due to friction in the line = FJ

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.
Energy Losses
According to the law of conservation 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
·Contraction losses
Frictional Losses
The fluid flow could be either viscous or Turbulent.
However, Fanning Equation is used to calculate the friction loss whether the flow is
viscous or turbulent.
Fanning equation ∆Pf = 2 fu2Lρ / D
∆Pf= Loss in pressure due to friction, f = frictional factor, L= Length of pipe, ρ= Density
of liquid, D= diameter of the pipe

The value of f solely depends on the nature of flow of fluid and roughness of the pipe
internal surface. For smooth to badly rusted pipe, it may vary from 0.9-2.5.
*Reduction of friction loss in turbulent flow of newtonian liquids can be achieved by addition
of soluble high molecular weight polymers in extremely low concentrations.
Loss 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
*Due to the very widely varying types of fittings, it is difficult to specify the loss due

to each type. Instead, it is customary to express this loss as the equivalent length

of the straight pipe which is given as certain number of pipe diameters.

 Enlargement Loss
If the cross section of the pipe enlarges gradually, the
fluid adapts itself to the changed section without any
disturbance & no energy loss.
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
Therefore, For sudden enlargement,
∆ He = (u1 – u2)2 / 2g
∆ H = loss of head due to sudden enlargement, u1 &
u2- velocities in smaller & larger cross sections resp.
Contraction Loss
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
∆Hc = K u22 / 2g
Where, u2 is the velocity in the smaller cross
section and K is a constant, the value of which
depends on the relative areas of two sections
Measurement of Rate of Flow of Fluids
Whenever fluid are used in a process it is necessary to measure the rate at
which the fluid is flowing through the pipe. Those methods of measurement
are,

1.Direct weighing or measuring

2.Hydrodynamic methods
a.Orifice meter
b.Venturi meter
c. Pitot meter
d. Rotameter
3.Direct displacement meter, a. Disc meters, b. Current meters
Orifice Meter Diagram
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 (u) increases, and hence increase in KE at the point of constriction.
• As per Bernoulli’s Theorem (BT) there must be reduction in pressure at B.
• This results in decrease in pressure drop and the difference in the pressure
may be read from a manometer
• Also, as per BT between pt. A & B, Xa=Xb (Horizontal pipe), Friction loss=0
and the fluid is same, ⍴a=⍴b. Then BT reduces to,
uB2-uA2= 2gc (PA-PB)/⍴ =2gc ΔP/⍴ = 2gc ΔH

• Diameter of liq. at pt. B would be less than constriction diameter, called as

Vena Contracta.
Orifice Meter
•Hence a constant C0 (Coefficient of orifice) to correct the difference in
velocities at pt. B & orifice. (u0=velocity through orifice)
√u02-uA2= C0 √2gc ΔH

•Value of C0 depends upon orifice to pipe diameter, position of orifice taps &
reynolds number of the liquid. (Normal C0 value=0.61)
• If the diameter of orifice is 1/5th or less to diameter of pipe then uA2 is
negligible as compared to u0 & therefore neglected. Then final equation
becomes,
u0= C0 √2gc ΔH
• Since ratio of cross sectional area of orifice to pipe is known, ratio between
u0 & uA is known and therefore final eq. Can be solved for both for volumetric
flow of liquid.
Orifice Meter
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 measure the
variation in the pressure across a fixed construction placed in the path of
flow.
•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
Venturi Meter
•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
•The same eq. of orifice meter could be
applied here, (Normal Cv value=0.98)
√uB2-uA2= Cv √2gc ΔH
Orifice meter v/s Venturi meter
Orifice Meter Venturi Meter

•Cheap •Expensive
•Easy to install •Fabrication is highly technical
•Construction can be made •It should be purchased from a
•Head losses are more dealer
•Power losses are more, particularly •Head losses are insignificant
coefficient of discharge is high •Power losses are less
•Normally used for testing purpose
•Used in online installation
•Greater flexibility
•Not flexible ,permanent
•Reading is larger under identical
•The reading is comparatively
condition
smaller under identical conditions
Pitot Tube
● A pitot tube is a pressure measurement instrument used to measure fluid
flow velocity
● It is widely used to determine the airspeed of an aircraft, water speed of a
boat, and to measure liquid, air and gas velocities in industrial
Applications
● The pitot tube is used to measure the local velocity at a given point in the
flow stream and not the average velocity in the pipe.
● pt. A measures both KE & PE of flowing liq., whereas pt. B measures only
pressure head. Thus, manometer measures velocity head as per the eq.
(derived from BT), ΔHP=u2/2gc (ΔHP=Velocity head of fluid corres. to R)
Pitot Tube
● While orifice & venturi meters
measure average velocity of the
whole stream of fluid, pitot tube
measures velocity at one point only.
● Since the velocity has to be
calculated either from the max.
Velocity or by taking readings at
different points in the cross section,
and determining the mean velocity
by graphic integration ultimately.
Advantages & Disadvantages of Pitot Tube
Advantages:
•Pitot tubes measure pressure levels in a fluid
•They do not contain any moving parts and routine use does not easily damage them
•Also, pitot tubes are small and can be used in tight spaces that other devices cannot fit
into
Disadvantages:
•Foreign material in a fluid can easily clog pitot tubes and disrupt normal readings as a
result
•This is a major problem that has already caused several aircraft to crash and many
more to make emergency landings
Rotameter
Variable area meter
•A device used to measure fluid flow, in which a float rises in a
tapered vertical tube to a height dependent on the rate of flow
through the tube
•It is a variable area meter which works on the principle of
upthrust force exerted by fluid and force of gravity
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
•Graduated tapered metering glass tube
•Float
Rotameter
Float:
•Floats may be constructed of metals of various densities from lead to aluminum or from
glass or plastic.
•Stainless-steel floats are common ones
•Float shapes and proportions are also varied for different applications
•For small flows floats are spherical in shape
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
Fluid enters the tapered tube, some of the fluid strikes directly the float. Some of the fluid
passes from sides Two forces are acting in this case:
·Upthurst Force (Buoyancy), Weight of the float, Annular space increases due to increase in
area of the tube When equilibrium is established the float comes to rest
Rotameter
Rotameter
Measurement of flow rate
The flowrate is measured directly from calibrated scale.
The reading is noted generally from ending point of cap of the float.
Advantages:
•No external power or fuel
•Manufactured of cheap materials
•Since the area of the flow passage increases as the float moves up the tube, the scale is
approximately linear.
Disadvantages:
•Accuracy of rotameter
•Uncertainty of the measurement
•Impact of gravity
Summary
● A fluid is a substance that continually deforms (flows) under an applied shear
stress
● Fluid statics deals with the fluids at rest in equilibrium
● Fluid dynamics deals with the study of fluids in motion
● The flow of fluid through a closed channel can be viscous or turbulent and it can
be observed by Reynolds experiment
● Bernoulli's theorem states that in a steady state the total energy per unit mass
consists of pressure, kinetic and potential energies are constant
● According to the law of conservation of energy, energy balance have to be
properly calculated
● Manometers are the devices used for measuring the pressure difference
● Differential manometers are suitable for measurement of small pressure
differences
● Inclined manometer enables the measurement of small pressure changes with
increased Accuracy
Summary
● Orifice meter is referred as the variable head meter, i.e it measure the variation
in the pressure across a fixed construction placed in the path of flow
● When fluid is allowed to pass through narrow venturi throat then velocity of
fluid increases and pressure decreases
● Main disadvantage of orifice meter is power loss due to sudden contraction with
consequent eddies on other side of orifice plate
● A pitot tube is a pressure measurement instrument used to measure fluid flow
velocity
● Rotameter is a device used to measure fluid flow, in which a float rises in a
tapered vertical tube to a height dependent on the rate of flow through the
tube