## Description

FLOW OF FLUIDS

```
Presented by:
Dr.Balajeechari
Asst. Professor
```

Faculty of Pharmaceutical Sciences,

Maharana pratap college

Of Pharmacy

www.remixeducation.in

CONTENT

Fluid flow

Reynold’s

experiment

BeRnoulli’s

theorem

Orifice meter

Venturimeter

Pitot tube

Rotometer

www.remixeducation.in

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 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.

` www.remixeducation.in`

FLUID STATICS

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

`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

MIXING ——— FLOW THROUGH PIPES ———– FILLED

IN CONTAINER

www.remixeducation.in

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.

` www.remixeducation.in`

REYNOLDS EXPERIMENT

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

This was conducted to demonstrate the existence of two

Types of flow

- 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.

www.remixeducation.in

Reynold’s experiment- www.remixeducation.in

2 types of flow- turbulent

laminar`www.remixeducation.in`

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.

REYNOLDS NUMBER

In Reynolds experiment the flow conditions are affected by-

Diameter of pipe

Average velocity

Density of liquid

Viscosity of the fluid

` www.remixeducation.in`

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 www.remixeducation.in

APPLICATIONS

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

` www.remixeducation.in`

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

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”

www.remixeducation.in

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

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 = UA2 / 2g
www.remixeducation.in
```

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) =

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 = 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.

www.remixeducation.in

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`www.remixeducation.in`

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.

` www.remixeducation.in`

ENERGY LOSS –

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

Application of BERNOULLI’S THEOREM

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

www.remixeducation.in

MANOMETERS

Manometers are the devices used for measuring the

pressure difference . Different type of

manometers are

Simple manometer

Differential manometer

Inclined manometer

www.remixeducation.in

Simple manometer

This manometer is the most commonly used one

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 www.remixeducation.in

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
www.remixeducation.in
```

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

Application

Pressure difference can be

determined by measuring R

Manometers are use in

measuring flow of fluid. www.remixeducation.in

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

www.remixeducation.in

Differential manometer

` www.remixeducation.in`

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,

This enables the measurement of small

pressure changes with increased accuracy.

` P1 –P2 = g R (ρ A - ρ B) sin α www.remixeducation.in`

www.remixeducation.in

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 head and the difference in the

pressure may be read from a manometer

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

www.remixeducation.in

Working

`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

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

` www.remixeducation.in`

Assumptions

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

` www.remixeducation.in`

Multiply both sides by -2g

U 2 – U 2 = 2g.PA /ρ – 2g.PB/ρ

B A

√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

` www.remixeducation.in`

If the diameter of orifice is 1/5th of the diameter of pipe then UA 2 is

negligible

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

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

www.remixeducation.in

www.remixeducation.in

VENTURI 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 √ 2g . ∆H

www.remixeducation.in

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

arrangement.

www.remixeducation.in

ADVANTAGES

For permanent installations

Power loss is less

Head loss is negligible

DISADVANTAGES

Expensive

Need technical export

Not flexible it is permanent www.remixeducation.in

Fig. Venturi meter

www.remixeducation.in

PITOT TUBE

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

www.remixeducation.in

CONSTRUCTION

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

` www.remixeducation.in`

WORKING

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.

` www.remixeducation.in`

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.

` www.remixeducation.in`

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

www.remixeducation.in

ROTAMETER

PRINCIPLE

It is a variable area meter which works on the

principle of upthurst force exerted by

fluid and force of gravity

` www.remixeducation.in`

Construction

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

reading

www.remixeducation.in

www.remixeducation.in

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:

Impact of gravity.

Accuracy of rotameter.

Uncertainty of the measurement

www.remixeducation.in

www.remixeducation.in