The document provides an overview of fluid flow principles in pharmaceutical engineering, covering topics such as types of manometers, Reynolds number, Bernoulli's theorem, and applications in measuring fluid pressure. It explains various devices like piezometers and U-tube manometers, detailing their construction, working mechanisms, advantages, and disadvantages, as well as size reduction and separation principles in fluid dynamics. Additional emphasis is placed on the importance of understanding laminar and turbulent flows in engineering applications.

1. BP 304 T. PHARMACEUTICAL
ENGINEERING (Theory)
Unit: 1 Flow of fluids
Presented by : Jagruti Marathe

2. Unit : 1
Flow of fluids: Types of manometers, Reynolds number and its significance,
Bernoulli’s theorem and its applications, Energy losses, Orifice meter, Venturimeter,
Pitot tube and Rotometer.
Size Reduction: Objectives, Mechanisms & Laws governing size reduction,
factors affecting size reduction, principles, construction, working, uses, merits and
demerits of Hammer mill, ball mill, fluid energy mill, Edge runner mill & end runner
mill.
Size Separation: Objectives, applications & mechanism of size separation,
official standards of powders, sieves, size separation Principles, construction,
working, uses, merits and demerits of Sieve shaker, cyclone separator, Air separator,
Bag filter & elutriation tank
2

3. Flow of fluids

4. 4
Selected Definitions:
• Fluid Flow: It is define as the flow of substances that are not permanently resistant to distortion.
• Fluid Statics : It study the behaviour of liquid at rest.
• Manometers : these are the devices used to the measurement of pressure.
• Fluid Dynamics: It deals with study of fluid in motion.
• Laminar Flow: It is the flow in which the fluid particles move in straight layers or laminae.
• Turbulent Flow : It is the flow in which fluid particles move in random manner instead of straight
path on increasing the velocity.
• Transition Flow: It is a mixture of laminar and turbulent flow , with turbulence at the center of the
pipe and laminar flow near the edges.
• Reynolds number : It is the ration of inertial forces to viscous forces.

5. 5
Selected Definitions:
•Bernoulli's theorem : This states that Total energy (which consist of pressure energy , kinetic energy
and potential energy) per unit mass in steady are constant.
•Potential energy : It is define as the energy processed by the body by virtue of its position
•Kinetic energy : it is define as the energy possessed by the body by virtue of its motion.
•Vena contracta: The point at which diameter of fluid stream get less than initial volume of diameter.
•Flow meters: a flow meter is a device used to measure the flow rate or the amount of a gas or liquid
moving through pipe

6. 6
Introduction:
• A fluid is a substance that under an applied shear stress continuously flows. The term fluids are
a subset of the phases of matter and include both liquids and phases can be defined as the flow
of substances that are not permanently resistances to distortion. The study of fluid can be
divided into fluid statics and fluid dynamics.
• Fluid Statics: study the behaviour of liquid at rest.

7. Measurement of Pressure

9. 9
•A manometer is an instrument used to measure and indicate pressure.
Basic principle Manometer:
A manometer works on the principle of hydrostatic equilibrium and is used for measuring the
pressure (static pressure) exerted by a still liquid or gas. Hydrostatic equilibrium states that the
pressure at any point in a fluid at rest is equal, and its value is just the weight of the overlying fluid.
Manometers:

10. 10
Manometers:
Manometer
Simple Manometer
Differential Manometer
Inclined Manometer
Piezometer
U-Tube
Single Colum
U-tube differential
Inverted U-tube

11. 11
 A simple manometer consists of a tubular arrangement where one end of the tube is connected
to the point in the fluid, whose pressure is to be determined and the other end is kept open to
the atmosphere. Simple manometers can be used to determine the gauge pressure or
vacuum pressure.
 Types of Simple Manometers
Common types of simple manometers are:
• Piezometer
• U-tube Manometer
• Single Column Manometer
Simple Manometers:

12. 12
Piezometer :
Piezometer are the simplest form of simple manometers that can be employed to measure the
gauge pressures. As shown in the figure-1 below, one end of the tube is connected to the point
where the pressure is to be found out and the other end is open to the atmosphere.
Simple Manometers:

13. 13
Let us consider we have one container filled with a liquid and we need to measure the pressure of
liquid at point A in the container. Let us consider that we are using the pressure measuring device
“Piezometer” here to measure the pressure of liquid at point A as displayed here in following figure.
Simple Manometers:
Rise of liquid in the glass tube of Piezometer will provide us the pressure head
at point A and could be written as mentioned here. Rise of liquid in the glass
tube of Piezometer will also be termed as Piezomteric head.
Gauge pressure at point A = ρ x g x h
Where,
ρ = Density of liquid
g = Acceleration due to gravity
h = Rise of liquid in Piezometer glass tube
Absolute pressure at Point A = Pa + ρ x g x h
Where, Pa is the atmospheric pressure

14. 14
Advantages of Piezometer tubes
There are following advantages of using Piezometer tube for measuring the pressure at a point of
fluid in a container and these are as mentioned here.
Technique of using Piezometer is very simple
Pressure measurement with Piezometer tube is quite economical
Piezometer tube will provide the accurate pressure reading
Simple Manometers:

15. 15
Disadvantages of Piezometer tubes
There are following disadvantages of using Piezometer tube for measuring the pressure at a point of
fluid in a container and these are as mentioned here.
Piezometer tube will only be used for measuring the pressure at a point of liquid. It could not be used
to measure the pressure at a point of gas. In simple, Piezometer tube will not be used to measure the
pressure of gas.
Piezometer tube will not be used to measure the negative pressure. Therefore pressure at point A,
where we are measuring the pressure, must be greater than the atmospheric pressure.
Liquid will be exposed to atmosphere in Piezometer tube and therefore liquid must be clean and non-
toxic.
Simple Manometers:

16. 16
U-tube Manometer:
A U-tube manometer, in which differential pressure is measured as the difference h between
the high-pressure reading and the low-pressure reading, multiplied by the density of the liquid in
the tube. ... The tube straightens slightly under pressure to a degree measured by a pointer
In its simplest form the manometer is a U-tube about half filled with liquid……When positive
pressure is applied to one leg, the liquid is forced down in that leg and up in the other. The
difference in height, “h”, which is the sum of the reading above and below zero, indicates the
pressure.
Simple Manometers:

17. 17
U-tube Manometer:
Simple Manometers:
3h
2h
h H
2ϱ
3ϱ
ϱ
 Jumping method
Gauge pressure at point A=Pxgxh
ϱxgx3h+2ϱxgx2h+3ϱxgxh-3ϱxgxH=0
3h+2h+h-3H=0
6h - 3H=0
[
𝐻
ℎ
=3]
Absolute pressure at Point A = Pa + ρ x g x h
Patm +ϱxgx3h+2ϱxgx2h+3ϱxgxh-3ϱxgxH - Patm
3h+2h+h-3H
6h - 3H
[
𝐻
ℎ
=3]

18. 18
U-tube Manometer:
Simple Manometers:
3h
2h
h H
2ϱ
3ϱ
ϱ
 Datum line method
Gauge pressure at point A=Pxgxh
ϱxgx3h+2ϱxgx2h+3ϱxgxh-3ϱxgxH=0
3h+2h+h-3H=0
6h - 3H=0
[
𝐻
ℎ
=3]
Absolute pressure at Point A = Pa + ρ x g x h
Patm +ϱxgx3h+2ϱxgx2h+3ϱxgxh = Patm-3ϱxgxH
3h+2h+h-3H
6h - 3H
[
𝐻
ℎ
=3]
x x

19. 19
Simple Manometers:
19
Single column Manometer
Vertical single Inclined single
It is modified from of a U-tube manometer in which one side is a large reservoir and the outer
side is a small tube , open to the atmosphere.

20. 20
Differential Manometers:
20
U-tube differential manometer:
A U tube differential manometer is a type of a differential manometer which is used to
measure the difference of pressure between the two points of the pipes. U tube
manometer's connected pipes may be at the same level and the different level lets see both
one by one.
𝑃𝐴 − 𝑃𝐵= gxhx(𝑝𝑔 - 𝑝1)
Where,
H= difference in mercury level in the U-tube
𝑝𝑔 = Density of heavy liquid
𝑝1= Density of the liquid A

21. 21
Differential Manometers:
21
Inverted U-tube differential manometer:
Inverted U-tube manometer is used for measuring pressure differences in liquids.
The space above the liquid in the manometer is filled with air which can be admitted or
expelled through the tap on the top, in order to adjust the level of the liquid in the
manometer.
Pa-Pb= P1.g.h1-P2.g.h2-Pg.g.h
Where, P1= density of the liquid at A
P1=density of the liquid at B
Pg= density of the light liquid.
h = difference of light liquid.
h1= height of the liquid A(left limb)
h2= height of the liquid B(right limb)

22. 22
Inclined Manometers:
22
It is an slant manometer. This is used to measure very small pressure difference. Inclination is
done to improve sensitivity .The angle of the measuring leg is appropriately 10˚.

23. 23
Fluid Dynamics:
Fluid Flow
Laminar
Turbulent
Transient

24. 24
24
Reynolds Number
The Reynolds number helps predict flow patterns in different fluid flow situations. At low
Reynolds numbers, flows tend to be dominated by laminar flow, while at high Reynolds
numbers flows tend to be turbulent.
Re=
𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒
𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑣𝑒
Reynolds number formula is given by :
Re=
𝐷𝑢𝑝
𝜂
Where,
D= diameter of the pipe
u=velocity of the fluid(m/s)
P=density of the fluid(kg/m3)
𝜂=viscosity of the fluid

25. 25
25
Reynolds Number
.

26. 26
26
Reynolds Number
Apparatus Required
•A Tank filled with water
•A small reservoir filled with colored fluid or dye
•A glass tube with bell mouth entrance
•A measuring tank
•Regulating valve at the outlet of glass tube
and at inlet of dye injector
•A stopwatch

27. Bernoulli’s theorem