International Journal of Research in Advent Technology, Vol.4, No.
3, March 2016
E-ISSN: 2321-9637
Available online at www.ijrat.org
Modification, Maintenance and Investigation of
Bernoulli’s Apparatus
Mr. Shakti Prasanna Khadanga1, Shankar Prasad Nayak2, Parsuram Pradhan3, Dibyajyoti Panda4
Mechanical Engineering Department 1 2, 3, 4 , GIET,Gunupur ,BPUT, Odisha1 2, 3, 4
Email: shaktiprasanna@gmail.com1,shankar.ursmile@gmail.com2, parsuram365@gmail.com3,
juvin72@gmail.com4
Abstract- Present work gives idea about the investigation and modification of Bernoulli’s apparatus. It includes
the details study of Bernoulli’s Theorem and Integration of Euler’s Equation for One Dimensional Flow. This
paper also prove the Bernoulli’s equation by using the Bernoulli’s apparatus to know the exact behavior of
operating conditions of Bernoulli’s apparatus at some varying condition. Some necessary test on Bernoulli’s
apparatus in hydraulic machine lab. Some experiments are done to know about the possible problems and errors
which can appear during the numerical analysis of the Bernoulli’s theorem by using the Bernoulli’s apparatus.
Some works are also focused on flow through the horizontal duct for which both experimental and numerical
have been discussed clearly. This paper gives report on modification, Maintenance and details investigation of
Bernoulli’s apparatus in order to increase the efficiency of the apparatus at different operating conditions.
Index Terms- Bernoulli’s theorem, Vary Cross-section, Various Fluids, Analysis and modification of flaws in
Bernoulli’s apparatus.
2.1. Ideal fluids
1. INTRODUCTION
Ideal fluids are those fluids which does not exist
Bernoulli’s equation is based on the concept of
practically, which does not have the properties like;
conservation of energy and energy equation that is
viscosity, compressibility and surface tension.
described from Euler’s force equation .[1] When it is
Resistance is irrespective to these fluids. [4]
applied to a fluid passing through a pipe at first it is
considered the fluid is ideal [5] i.e. viscosity of the 2.2. Real fluids
fluid is zero. The velocity of every liquid particle
across any cross section of pipe, is uniform, ir- Real fluid are those fluids which imbibes the
rotational and incompressible.[6] Secondly the properties like; viscosity, compressibility and surface
Bernoulli’s apparatus demonstrate the increase in the tension. They really exist in nature and are
speed of the fluid occurs simultaneously with a mathematical analyzed of fluid flow problems. [4]
decrease in pressure of the fluid passing through the
duct. [2] There will be no loss of energy of the liquid 2.2.1. Newtonian fluid
particle while flowing. It can also be used to examine Newtonian fluid are the types of fluid which obeys
the turbulence in the fluid stream. Necessary test has Newton’s law of viscosity. They have a linear
been conducted to analysis most problems in relationship between shear stress and velocity
mechanics of fluid with the help of Bernoulli’s gradient. E.g.; water, air, etc. [4]
equation and continuity equation as essential
analytical tools. [3] 2.2.2. Non-Newtonian fluid
In this paper we verify Bernoulli’s equation by Non Newtonian fluids: non Newtonian fluids are the
varying the cross-section of horizontal duct tube of type of fluids which do not obey Newton’s law of
Bernoulli’s apparatus also investigate by using various viscosity. The behavior of viscosity is given by the
fluids like alkaline, acid, kerosene, diesel, and petrol. power law equation. e.g.: milk, blood, liquid cement.
[4]
2. TYPES OF FLUIDS
Fluids are classified into two types and they are ideal
fluids and real fluids.
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International Journal of Research in Advent Technology, Vol.4, No.3, March 2016
E-ISSN: 2321-9637
Available online at www.ijrat.org
3. BERNOULLI’S PRINCIPLE 4. BERNOULLI’S APPARATUS
It states in a steady, ideal flow of an incompressible
fluid, the total energy at any point of the fluid is
constant. The total energy mainly consists of
summation of pressure energy, kinetic energy and
potential or datum energy.
Mathematically, the Bernoulli’s theorem is written as:
..(1)
Where,
Pressure Head =
Kinetic head =
Datum head = Z
Bernoulli’s theorem is the principle of energy Fig. 1. Bernoulli’s Apparatus
conservation for ideal fluids in steady and streamlines
flow and it is the basis for many engineering
applications. This apparatus basically used in the hydraulic machine
lab to verify the Bernoulli’s theorem, to check whether
different head remain constant or not. [3]
3.1 Bernoulli’s Equation For Real Fluid 4.1 Apparatus
Equation (1) represent the Bernoulli’s Different apparatus needed for conducting this test
equation for ideal fluid flow and it was derived on the are:
assumption that fluid is non-viscous in nature and 1. Base Frame
therefore frictionless. But all the real fluid are viscous. 2. Sump tank
Thus there are always some losses in fluid flows and 3. Water pump set
hence in the application of Bernoulli’s equation these 4. Measuring tank
losses have to be taken into concern.[6] Thus the 5. Gate valve
Bernoulli’s equation for real fluids between point 1 6. Hose pipe
and point 2 is given as below: 7. Supply tank
8. Delivery tank
9. Test section
The equipment is designed as a self-sufficient
Where, unit it has a sump tank, measuring tank and 0.5 HP
hL = Loss of energy between 1 and 2 pump for water circulation. The apparatus consists of
a supply tank and delivery tank which are connected
3.2 Practical Application of Bernoulli’s Equation to a Perspex flow channel. The channel tapes for a
length of 25 cm and then are fixed at a distance of 5
This is one of the most used equations which cm center to center for measurement of pressure head.
applied in all types of problems related to
incompressible fluid flow where energy considerations 4.2 Problems in the Apparatus:
are involved.
It’s applied over measuring devices as below: 1. System was not in running condition since
1. Venturimeter four.
2. Orificemeter 2. Piezometer tubes were broken.
3. Pitot-tube 3. Inlet and outlet fluid flow pipes were
destroyed.
4. Water supply line was disturbed.
5. Apparatus was corroded due to ageing.
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International Journal of Research in Advent Technology, Vol.4, No.3, March 2016
E-ISSN: 2321-9637
Available online at www.ijrat.org
6. The horizontal duct was destroyed and
leakage are there.
7. The discharge measurement bucket was not
in good condition.
4.3 Analysis of Components:
Steps achieved during analysis of the components are:
1. The apparatus was cleaned and get painted.
2. Discharge bucket was repaired and painted.
3. The piezometer tubes are installed on the
apparatus.
4. New water supply lines are fitted correctly.
4.4 Technical Specification
Cross-sectional area of different piezo metric
tubes: Fig: 2 General Test section of a Bernoulli’s apparatus
Tube No Cross Tube No Cross The piezometer tubes are fitted on the duct at equal
Sectional Sectional intervals for measuring the pressure heads at different
Area (mm2) Area (mm2) gauge points.[6] The duct is connected in between two
1 3.6 8 2.6 tanks, one at the upstream end (inlet tank) and the
2 3.2 9 2.8 other at the downstream end. The inlet tank is fitted
3 2.8 10 3.0 with a piezometer for showing the water level in the
4 2.4 11 3.2 tank. The outlet tank is provided with an outlet valve
5 2.0 12 3.4 for controlling the outflow. The set-up is placed on a
6 2.2 13 3.6 hydraulic bench. Water is supplied to the inlet tank
7 2.4 through the inlet valve or supply valve and connected
Table: 1 to a constant overhead water tank.
6. PROCEDURE
Centrifugal pump:
1. Keep the bypass valve open and start the pump and
Power Frequency Speed slowly start closing the valve.
1 HP, 370w 50Hz 2800 RPM 2. The water shall start flowing through the flow
Table: 2 channel. The level in the piezometer tubes will start
rising. [1]
Measuring tank: 60L capacity. 3. Open the valve in the delivery tank side and adjust the
head in the piezometer tubes to steady position.
5. EXPERIMENTAL SETUP
4. Measuring the heads at all the points and also
discharge with the head of diversion pan and
Bernoulli's apparatus consists of a two dimensional
measuring tank.
rectangular section convergent divergent duct
5. Charge the discharge and repeat the procedure .[1]
designed to fit in between constant head inlet tank and
outlet tank which is variable in nature. An eleven tube
static pressure manometer bank is attached to the 7. OBSERVATION AND CALCULATION
convergent divergent duct.
7.1 Observation-1
W=5 lt T=171sec Q= = 29.23 cm3/sec
V = Q/A = 29.23/A
195
International Journal of Research in Advent Technology, Vol.4, No.3, March 2016
E-ISSN: 2321-9637
Available online at www.ijrat.org
Table: 3 Table: 4
Graph: 1 Graph: 3
Graph: 4
Graph: 2
7.3 Observation-3
7.2 Observation-2
W=5 lt T=12sec Q= = 416.66 cm3/sec
W=5 lt T=18.03sec Q= = 277.17 cm3/sec
V = Q/A = 416.66/A
V = Q/A = 277.17/A
196
International Journal of Research in Advent Technology, Vol.4, No.3, March 2016
E-ISSN: 2321-9637
Available online at www.ijrat.org
REFERENCES
[1] IOSR Journal of Mechanical and Civil
Engineering (IOSR-JMCE) e-ISSN: 2278-
1684,p-ISSN: 2320-334X, Volume 12, Issue 3
Ver. II (May - Jun. 2015), PP 116-146
[2] IOP PUBLISHING EUROPEAN JOURNAL OF
PHYSICS Eur. J. Phys. 32 (2011) 517–520
doi:10.1088/0143-0807/32/2/022.
[3] Megan F. Dunn, W. Roy Penney and Edgar C.
Clausen Ralph E. Martin Department of
Chemical Engineering University of Arkansas.
[4] Dr. R.K.Rajput,A Text Book of Fluid Mechanics,
S.Chand Company Limited,200.
[5] A.K.Jain,Fluid Mechanics,Khanna Publishers,
Table: 5 1993.
[6] Dr.D.S.Kumar Fluid Mechanics and Fluid Power
Engineering Sixth Edition: Jan 1998,S.K. Kataria
& Sons Publishers & Distributers,
Reprinted:2003.
Graph: 5
Graph: 6
8. CONCLUSION
From the above we have concluded that total head of
the streamline flow remains constant by varying the
cross-section of the duct tube. Hence, the Bernoulli’s
equation is verified and the apparatus is justified to be
working properly. Further the extension work can be
done for the different categories of fluids.
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