the validity of bernoulli's theorem as applied the flow of water in a tapering circular duct

1. Investigatory project
ThevalidityofBernoulli'sTheoremas
appliedtotheflowofwaterin atapering
circularduct.
SUBMITTED BY;
k.kajaa lakshmie
Roll no.11ao7
CLASS – XI

2. Physics
KENDRIYA VIDYALAYA DHARMAPURi
Certificate of originality
This is to certifythatk.kajaa lakshmie

3. Of class-xihas donetheproject to investigatethevalidity ofBernoulli's
Theorem as applied to theflow ofwaterin a taperingcircularduct in
physics forthe partialfulfillment ofaissce2018-19.
Internalexaminer externalexaminer
Principal
Acknowledgement

4. I wouldlike toexpress myspecial thanksofgratitudeto my physics teacher
MS.s.SUNITAas well as ourprincipal shri.k.raghavendra raowho gaveme
thegolden opportunitytodo this wonderfulproject onthis topic, which also
helped mein doinga lot of researchandI cameto knowaboutso manynew
things.I am really thankfultothem.I would alsolike tothankmy parents
andfriends who helped me a lot in finishingthis projectwithin the limited
time.
CONTENT
 Aim of the experiment

5.  Introduction
 Principle
 Requirements
 Procedure
 Observations
 Calculations
 Results
 Precautions
 Conclusion
 Bibliography
Aim of the experiment

6. To investigate the validity of Bernoulli's
Theorem as applied to the flow of water
in a tapering circular duct.
INTRODUCTION

7. Bernoulli’s theorem, in fluid dynamics, relation among the
pressure, velocity, and elevation in a moving fluid (liquid or
gas), the compressibility and viscosity (internal friction) of which
are negligible and the flow of which is steady, or laminar.
First derived (1738) by the Swiss mathematician Daniel Bernoulli,
the theorem states, in effect, that the total mechanical energy of
the flowing fluid, comprising the energy associated with fluid
pressure, the gravitational potential energy of elevation, and the
kinetic energy of fluid motion, remains constant.
Bernoulli’s theorem is the principle of energy conservation for
ideal fluids in steady, or streamline, flow and is the basis for
many engineering applications.
Bernoulli’s theorem implies, therefore, that if the fluid flows
horizontally so that no change in gravitational potential energy
occurs, then a decrease in fluid pressure is associated with an
increase in fluid velocity.
If the fluid is flowing through a horizontal pipe of varying
Cross-sectional area, for example, the fluid speeds up in
constricted areas so that the pressure the fluid exerts is least
where the cross section is smallest.
This phenomenon is
Sometimes it is called the Venturi effect, after the Italian
scientist G.B. Venturi (1746–1822), who first noted the effects of
constricted channels on fluid flow.
PRINCIPLE

8. Bernoulli’s theorem states that in fluid flow, an
increase in velocity occurs simultaneously with
decrease in pressure. This principle is
simplification of Bernoulli’s equation which
states that the sum of all forms of energy in a
fluid flowing along an enclose path (a
streamline) is the same at any two points in
that path. it is names after the Daniel Bernoulli
a mathematician and scientist
REQUIREMENTS

9.  Bernoulli’s test rig
 Pump
 Stop watch
 Beaker
 Measuring cylinder
PROCEDURE

10.  All necessary measuring devices are well connected with
equipment
 The fluid pump is switched on and the tank level is maintained
constant
 Check if the drain valve is open keep it wide open and check the
outlet pipe goes to the drain
 Check that all the tubing are properly connected to the
corresponding pressure taps and are free from air bubble if
needed flush the air bubbles by slowly closing the exit valve and
draining the water(and the air bubbles) through the manometer
tubing
 Measure the time to collect desired volume in a measuring
cylinder to obtain volumetric flow rate
 Note the height of liquid level from the base of the apparatus
(base datum) in different tubing for different pressure heads
 The total head (pressure kinetic and potential) of diverging cone
and covering cone were compared to verify the Bernoulli‘s
theorem

OBSERVATIONS

11. PIEZOMETRIC HEAD IS THE SUM OFDATUM HEAD AND PRESSURE HEAD
S.no TIME
(sec)
PIEZOMETRIC
HEAD
(CM)
INLET
SECTION
PIEZOMETRIC
HEAD
(CM)
THROAT
SECTION
PIEZOMETRIC
HEAD
(CM)
OUTLET
SECTION
VELOCITY
(v)
VELOCITY
HEAD
(cm)
TOTAL
ENERGY
HEAD
(cm)
1
90.4 19.8 17.5 19.3 26.2 0.35 20.1
2
92.90 19.9 17.3 19.2 25.5 0.33 20.1
3 101.26 19.4 17.4 18.8 23.2 0.27 20.1

12. CALCULATIONS
Bernoulli Theorem Equations:
Fluid Mechanics Hydraulic Design Formula
Solving For Head Loss

13. RESULTS
FINALLY,
ON ANALYSING THE BERNOULLI’S THEOREM STATEMENT
“THE SUM OF PRESSURE ENERGY, KINETIC ENERGY , POTENTIAL
ENERGY PER UNIT VOLUME OF AN IN COMPRESSIBLE NON VISCOUS
FLUID IN A STREAMLINED IRROTATIONAL FLOW REMAINS CONSTANT
AT EVERY CROSS SECTION THROUGHOUT THE LIQUID FLOW “
INCOMPARISION TO APPLICATION ON TAPERING CIRCULAR DUCT IN
THIS EXPERIMENT
THE TOTAL ENERGY IS CONTANT THAT IS 20.1 J
THEREFORE;
BERNOULLI’S THEOREM IS VALIDATED IN A TAPERING CIRCULAR DUCT
BY LAW OF CONSERVATION OF ENERGY

14. PRECAUTIONS
• All measuring devices should be well connected with the
equipment
• All the tubing are properly connected to the corresponding
pressure taps and are free from air-bubble
• The height of liquidlevel from the base of the apparatus
(base datum) in different tubing for different pressure heads
should be noted properly

15. CONCLUSION
After the experiment, we can now say that at the
respective position where area is less; there velocity is
more; pressure is less which verifies Bernoulli’s theorem

16. BIBLIOGRAPHY
 WIKIPEDIA.ORG
 https://www.britannica.com/science/Bernoullis-
theorem
 FLUID MECHANICS
 SCIENCE FOR ALL
 PHYSICS HANDBOOK
 SOFTWARE FOR EDUATION
 ENGINEERING HAND BOOK