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Flow fluid:- PDF / PPT



      Presented by:
      Asst. Professor

Faculty of Pharmaceutical Sciences,
Maharana pratap college
Of Pharmacy
Fluid flow



Orifice meter


Pitot tube

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 static’s deals with the fluids at rest in equilibrium

Behaviour of liquid at rest

Nature of pressure it exerts and the variation of pressure at different layers

Fluid dynamics deals with the study of fluids in motion

This knowledge is important for liquids, gels, ointments
which will change their flow
behaviour when exposed to different stress conditions

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.


Prof. Osborne Reynolds conducted the experiment in the year 1883.

This was conducted to demonstrate the existence of two

Types of flow

  1. Laminar Flow 2. Turbulent Flow 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.
    Reynold’s experiment-
    2 types of flow- turbulent
    laminar Types Of Flows Based On Reynold Number – If Reynold number, RN < 2000 the flow is laminar flow. If Reynold number, RN > 4000 the flow is turbulent flow.


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

   Re= D u ρ           INERTIAL FORCES
       ƞ             VISCOUS FORCES

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.

Reynolds number have no unit

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 the principals 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”
At point a one kilogram of liquid is
assumed to be entering at point a,
Pressure energy = Pa /g ρA

Where Pa = Pressure at point a

    g = Acceleration due to gravity

    ρA = Density of the liquid

Potential energy of a body is defined as the energy possessed by the body by the virtue of its

    Potential energy = XA

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

    motion, kinetic energy = UA2 / 2g

Total energy at point A = Pressure energy + Potential energy + K. E

Total energy at point A = PaV + XA + UA2 / 2g
According to the Bernoulli’s theorem the total energy at point
A is constant Total energy at point A = PAV +XA + (UA2 / 2g) =

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 +XB + UB2 / 2g

PAV +XA + (UA2/2g) + Energy added by the pump = PBV +XB

  • (UB2/2g) V is volume and it is reciprocal of density.
    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 + UA2 / 2g – F + W = PB /ρ B
    +XB + UB2 / 2g
    This equation is called as Bernoulli’s
    equation 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 /ρA +XA + UA2 / 2g – F + W = PB /ρ B +XB + UB2 / 2g

This equation is called as Bernoulli’s equation.


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
Used in the measurement of rate of fluid flow using flowmeters
It applied in the working of the centrifugal pump, in this kinetic energy is
converted in
to pressure

Manometers are the devices used for measuring the
pressure difference . Different type of
manometers are

Simple manometer

Differential manometer

Inclined manometer
Simple manometer

This manometer is the most commonly used one
It consists of a glass U shaped tube filled with a
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 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 ρA g

Pressure at 5 is still less than pressure at point 4 by mρ B g


This can be summarise as

P1 + (m + R ) ρ B g – R ρA g –
mρ B g= P2

∆P= P1-P2=R (ρ A- ρ B )g


Pressure difference can be
determined by measuring R

Manometers are use in
measuring flow of fluid.
These manometers are suitable for measurement of
small pressure differences

It is also known as two – Fluid U- tube manometer

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It contains two immiscible liquids A and B having
nearly same densities

The U tube contains of enlarged chambers on both


Using the principle of simple manometer the
pressure differences can be written as

∆P =P1 –P2 =R (ρc – ρA)g
Differential manometer

Many applications require accurate
measurement of low pressure such as drafts
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  
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 head and the difference in the
pressure may be read from a manometer

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

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 Aand point B for

experimental conditions Total energy at point A = Pressure energy +

Potential energy + K. E

Total energy at point A = PaV + XA + UA2 / 2g

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Bernoullis eqn… Pa /ρ A +XA + UA2 / 2g – F + W = PB /ρB +XB + UB2 / 2g



Pipeline is horizontal A and B are at same position Therefore XA=XB

Suppose friction losses are negligible 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 After
applying assumptions Bernaoulis eqn…

PA /ρ A +XA + UA2 / 2g – F + W = PB /ρ B +XB + UB2 / 2g

Change to—

PA /ρ + UA2 / 2g = PB /ρ + UB2 / 2g
UA2 / 2g – UB2 / 2g = PB /ρ – PA /ρ


Multiply both sides by -2g

U 2 – U 2 = 2g.PA /ρ – 2g.PB/ρ

√UB2 – UA2 = √2g/ρ . (PA – PB)
√UB2 – UA2 = √2g∆H …….. as (PA – PB)/ρ=∆H
√UB 2 – UA2 = √2g∆H
diameter of vena contracta is not known practically

There are friction losses so above equation is modified to—

√U02 – UA2 =C0 √2g. ∆H


If the diameter of orifice is 1/5th of the diameter of pipe then UA 2 is
The velocity of the fluid at thin constriction may be written as –
U0 = C0 √ 2g ∆H

∆H = Difference in pressure head, can be measured by manometer
C0 = constant c-oefficient of orifice (friction losses)
U0 = velocity of fluid at the point of orifice meter
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

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

Venturi meter consist of two tapperd (conical
section) inserted in pipeline

Friction losses and eddies can be minimized by this
For permanent installations

Power loss is less

Head loss is negligible


Need technical export

Not flexible it is permanent
Fig. Venturi meter
A pitot tube is a pressure measurement instrument used to measure
fluid flow velocity. The pitot tube was invented by the French
engineer Henri Pitot in the early 18th century and was modified to
its modern form in the mid-19th century by French scientist Henry
Darcy. 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 or conduit
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


A pitot tube is simply a small cylinder that faces a fluid so that
the fluid can enter it. Because the cylinder is open on one side
and enclosed on the other, fluid entering it cannot flow any
further and comes to a rest inside of the device. A diaphragm
inside of the pitot tube separates the incoming pressure (static
pressure) from the stagnation pressure (total pressure) of a
system. The difference between these two measurements
determines the fluid’s rate of flow.


In industry, the velocities being measured are often those flowing in ducts
and tubing where measurements by an anemometer would be difficult to
obtain. In these kinds of measurements, the most practical instrument to
use is the pitot tube. The pitot tube can be inserted through a small hole in
the duct with the pitot connected to a U-tube water gauge or some other
differential pressure gauge for determining the velocity inside the ducted
wind tunnel. One use of this technique is to determine the volume of air
that is being delivered to a conditioned space.


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.

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


It is a variable area meter which works on the
principle of upthurst force exerted by
fluid and force of gravity



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 plummet rise due to variation in flow

The upper edge of the plummet is used as an index to note the
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.

Impact of gravity.
Accuracy of rotameter.
Uncertainty of the measurement

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