bernoulli equation experiment report

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Experiment #2: Bernoulli’s Theorem Demonstration

1. introduction.

Energy presents in the form of pressure, velocity, and elevation in fluids with no energy exchange due to viscous dissipation, heat transfer, or shaft work (pump or some other device). The relationship among these three forms of energy was first stated by Daniel Bernoulli (1700-1782), based upon the conservation of energy principle. Bernoulli’s theorem pertaining to a flow streamline is based on three assumptions: steady flow, incompressible fluid, and no losses from the fluid friction. The validity of Bernoulli’s equation will be examined in this experiment.

2. Practical Application

Bernoulli’s theorem provides a mathematical means to understanding the mechanics of fluids. It has many real-world applications, ranging from understanding the aerodynamics of an airplane; calculating wind load on buildings; designing water supply and sewer networks; measuring flow using devices such as weirs, Parshall flumes, and venturimeters; and estimating seepage through soil, etc. Although the expression for Bernoulli’s theorem is simple, the principle involved in the equation plays vital roles in the technological advancements designed to improve the quality of human life.

3. Objective

The objective of this experiment is to investigate the validity of the Bernoulli equation when it is applied to a steady flow of water through a tapered duct.

In this experiment, the validity of Bernoulli’s equation will be verified with the use of a tapered duct (venturi system) connected with manometers to measure the pressure head and total head at known points along the flow.

5. Equipment

The following equipment is required to complete the demonstration of the Bernoulli equation experiment:

• F1-10 hydraulics bench,
• F1-15 Bernoulli’s apparatus test equipment, and
• A stopwatch for timing the flow measurement.

6. Equipment Description

The Bernoulli test apparatus consists of a tapered duct (venturi), a series of manometers tapped into the venturi to measure the pressure head, and a hypodermic probe that can be traversed along the center of the test section to measure the total head. The test section is a circular duct of varying diameter with a 14° inclined angle on one side and a 21° inclined angle on other side. Series of side hole pressure tappings are provided to connect manometers to the test section (Figure 2.1).

Manometers allow the simultaneous measurement of the pressure heads at all of the six sections along the duct. The dimensions of the test section, the tapping positions, and the test section diameters are shown in Figure 2.2. The test section incorporates two unions, one at either end, to facilitate reversal for convergent or divergent testing. A probe is provided to measure the total pressure head along the test section by positioning it at any section of the duct. This probe may be moved after slackening the gland nut, which should be re-tightened by hand. To prevent damage, the probe should be fully inserted during transport/storage. The pressure tappings are connected to manometers that are mounted on a baseboard. The flow through the test section can be adjusted by the apparatus control valve or the bench control valve [2].

Bernoulli’s theorem assumes that the flow is frictionless, steady, and incompressible. These assumptions are also based on the laws of conservation of mass and energy.  Thus, the input mass and energy for a given control volume are equal to the output mass and energy:

These two laws and the definition of work and pressure are the basis for Bernoulli’s theorem and can be expressed as follows for any two points located on the same streamline in the flow:

P: pressure,

g: acceleration due to gravity,

v : fluid velocity, and

z: vertical elevation of the fluid.

In this experiment, since the duct is horizontal, the difference in height can be disregarded, i.e., z 1 =z 2

The hydrostatic pressure (P) along the flow is measured by manometers tapped into the duct. The pressure head (h), thus, is calculated as:

Therefore, Bernoulli’s equation for the test section can be written as:

The total head (h t ) may be measured by the traversing hypodermic probe. This probe is inserted into the duct with its end-hole facing the flow so that the flow becomes stagnant locally at this end; thus:

The conservation of energy or the Bernoulli’s equation can be expressed as:

The flow velocity is measured by collecting a volume of the fluid (V) over a time period (t). The flow rate is calculated as:

The velocity of flow at any section of the duct with a cross-sectional area of  is determined as:

For an incompressible fluid, conservation of mass through the test section should be also satisfied (Equation 1a), i.e.:

8. Experimental Procedure

• Place the apparatus on the hydraulics bench, and ensure that the outflow tube is positioned above the volumetric tank to facilitate timed volume collections.
• Level the apparatus base by adjusting its feet. (A sprit level is attached to the base for this purpose.) For accurate height measurement from the manometers, the apparatus must be horizontal.
• Install the test section with the 14° tapered section converging in the flow direction. If the test section needs to be reversed, the total head probe must be retracted before releasing the mounting couplings.
• Connect the apparatus inlet to the bench flow supply, close the bench valve and the apparatus flow control valve, and start the pump. Gradually open the bench valve to fill the test section with water.
• Close both the bench valve and the apparatus flow control valve.
• Remove the cap from the air valve, connect a small tube from the air valve to the volumetric tank, and open the air bleed screw.
• Open the bench valve and allow flow through the manometers to purge all air from them, then tighten the air bleed screw and partly open the bench valve and the apparatus flow control valve.
• Open the air bleed screw slightly to allow air to enter the top of the manometers (you may need to adjust both valves to achieve this), and re-tighten the screw when the manometer levels reach a convenient height. The maximum flow will be determined by having a maximum (h 1 ) and minimum (h 5 ) manometer readings on the baseboard.

If needed, the manometer levels can be adjusted by using an air pump to pressurize them. This can be accomplished by attaching the hand pump tube to the air bleed valve, opening the screw, and pumping air into the manometers.  Close the screw, after pumping, to retain the pressure in the system.

• Take readings of manometers h 1 to h 6 when the water level in the manometers is steady. The total pressure probe should be retracted from the test section during this reading.
• Measure the total head by traversing the total pressure probe along the test section from h 1 to h 6 .
• Measure the flow rate by a timed volume collection. To do that, close the ball valve and use a stopwatch to measure the time it takes to accumulate a known volume of fluid in the tank, which is read from the sight glass. You should collect fluid for at least one minute to minimize timing errors. You may repeat the flow measurement twice to check for repeatability. Be sure that the total pressure probe is retracted from the test section during this measurement.
• Reduce the flow rate to give the head difference of about 50 mm between manometers 1 and 5 (h 1 -h 5 ). This is the minimum flow experiment. Measure the pressure head, total head, and flow.
• Repeat the process for one more flow rate, with the (h 1 -h 5 ) difference approximately halfway between those obtained for the minimum and maximum flows. This is the average flow experiment.
• Reverse the test section (with the 21° tapered section converging in the flow direction) in order to observe the effects of a more rapidly converging section. Ensure that the total pressure probe is fully withdrawn from the test section, but not pulled out of its guide in the downstream coupling. Unscrew the two couplings, remove the test section and reverse it, then re-assemble it by tightening the couplings.
• Perform three sets of flow, and conduct pressure and flow measurements as above.

9. Results and Calculations

Please visit this link for accessing excel workbook for this experiment.

9.1. Results

Enter the test results into the Raw Data Tables.

Raw Data Table

  Raw Data Table

9.2 calculations.

For each set of measurements, calculate the flow rate; flow velocity, velocity head, and total head,  (pressure head+ velocity head).  Record your calculations in the Result Table.

Result Table

Use the template provided to prepare your lab report for this experiment. Your report should include the following:

• Table(s) of raw data
• Table(s) of results
• For each test, plot the total head (calculated and measured), pressure head, and velocity head (y-axis) vs. distance into duct (x-axis) from manometer 1 to 6, a total of six graphs. Connect the data points to observe the trend in each graph. Note that the flow direction in duct Position 1 is from manometer 1 to 6; in Position 2, it is from manometer 6 to 1.
• Comment on the validity of Bernoulli’s equation when the flow converges and diverges along the duct.
• Comment on the comparison of the calculated and measured total heads in this experiment.
• energy loss and how it is shown by the results of this experiment, and

Applied Fluid Mechanics Lab Manual Copyright © 2019 by Habib Ahmari and Shah Md Imran Kabir is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Bernoulli Experiment Lab Report

Aim of bernoulli experiment.

Aim of this experiment is to compare the behaviour of ideal fluid and real fluid using Bernoulli experiment.

1. Use the venture meter apparatus to perform Bernoulli experiment and the effect of area of the flow velocity and fluid pressure 2. Use the Bernoulli’s equation /  Bernoulli theorem  to compare the behaviour of ideal and real fluid

Introduction  Bernoulli Experiment

According to the Bernoulli’s experiment when area available for the fluid to flow decrease then flow of fluid increase and at the mean while time the fluid pressure or the fluid potential energy decreases.

Read about the Effect of Sluice Gate on the Flow of Fluid . 

This principle was name after the Daniel Bernoulli who first writes this principle in book named Hydrodynamic.  Following are some of the application of the Bernoulli experiment

Theory of Bernoulli's Theorem Experiment

Bernoulli experiment / principle state that the in a steady flowing fluid the sum of all the mechanical energies including kinetic energy, dynamic head, fluid pressure and potential energy should remain same at all the point of the flow. 

So if any type of energy increase like if kinetic energy increase then the other type of the energy like potential energy, pressure will decrease t o make the final sum same as before.  According to the B ernoulli's theorem experiment or can say  Bernoulli equation a flowing fluid have three things

• Pressure head
• Kinetic Energy
• Potential Energy

So we have P+  1/2×ρ×v^2+ ρgh=C P/ρg+  1/2×v^2/g+h=C According to the law of conservation of energy, energies at the input should be equal to the output so P_1/ρg+  (V_1^2)/2g+h=  P_n/ρg+  (V_n^2)/2g+h In the above equation  P = fluid pressure V = flow velocity Z = height ρ = density

From Bernoulli’s experiment / principle it can be stated that the density and pressure are inversely proportional to each other’s means high density fluid will apply more pressure while moving than the low density fluids. 

In the horizontal pipe where the inlet and outlet of the are at same height, the z quantity can be removed to give the above mention equation of Bernoulli’s principle a new look from where we can calculate the height at any point of the flow if we have the initial height of flow and velocity at respective positions. 

P_1/ρg+  (V_1^2)/2g=  P_n/ρg+  (V_n^2)/2g P_1/ρg=h1 and  P_n/ρg=hn  h_1+  (V_1^2)/2g= h_n+  (V_n^2)/2g h_n= h_1-[  (v_n^2)/2g-  (v_1^2)/2g]

Apparatus for Bernoulli's theorem experiment

• Venture meter
• Supply Hoses
• Measuring Tank

Procedure for Bernoulli experiment

Following is a complete procedure for performing the Bernoulli experiment

Graphs of  Bernoulli's theorem lab report

Following are the main Graphs of  Bernoulli's theorem lab report

Discussion of Bernoulli theorem lab report

Based on the calculation above and graph papers presented a detailed discussion of Bernoulli theorem lab report is as follow

• From the calculation it is very clear that with decrease in area of the flow velocity increase and pressure decrease • As shown in graph of all three test that the decrease in area of flow decrease the height of water in manometer column means they are directly proportional to each other • Difference in the theoretical and measured value it can be said that water is not an ideal fluid  • Height of water in the final column was not equal to the initial values which show that there are friction losses in water particle • This type of information is very use full in the case if nozzles, jets and diffusers

Conclusion of Bernoulli's theorem

This is because of the friction losses in the real fluid; ideal fluid does not have friction losses. From the experiment it can be conclude that with decrease in area of flow there is an increase in velocity and decrease in the flow pressure of the fluid.   

References for bernoulli equation lab report

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Experimental verification of bernoulli’s theorem.

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🕑 Reading time: 1 minute

The procedure of Laboratory experiment to verify Bernoulli’s theorem, required apparatus and calculations to be done are explained in this article.

Bernoulli’s theorem states - For a continuous, steady and frictionless flow the total head (which is the sum of pressure head, velocity head and elevation head) at any section remains constant.

Total Head = pressure head + velocity head + elevation head

H = P/w + V 2 / 2g + Z

According to Bernoulli’ theorem, Total head at any two sections is expressed as :

Apparatus required

Apparatus required to conduct Bernoulli’s experiment are :

• Supply tank
• Tapered inclined pipe with piezometer tubes at different points
• Measuring tank

Test Procedure

Test procedure to verify Bernoulli’s experiment is as follows :

• Open the inlet valve and allow the water to flow from the supply tank to the receiving tank through a tapered inclined pipe.
• Adjust the flow using an outlet valve to make the head constant in the supply tank. At the constant head, head causing inflow and outflow are equal.
• After adjusting the flow, Note down the readings of the water level of each piezometer tube which are nothing but pressure heads at different points of tapered tube.

• Compute the area of cross-section of tapered pipe at points where piezometer tubes are located.
• Now, take the stopwatch and measure the height of water collected for a particular time interval.
• Also, note down the measuring tank dimensions.
• Repeat the same procedure for different discharges for at least two more times.

Observations

Pressure head or Piezometer readings, P/w =

Area of cross section of tapered pipe under piezometer tubes = A 1 , A 2 , A 3 …….

Area of Measuring tank, A =

Height of water collected for “t” interval of time =

Elevation head, Z =

Calculations

Volume of water Collected in measuring tank (V) = Area of measuring tank (A) X height of water collected for “t” interval of time (h)

Discharge Q = volume / time = V/t

Velocity of flow, v = Discharge / Area of cross section of tapered pipe

Velocities under each piezometer tube are v 1 = Q/A 1 ,

v 2 = Q/A 2 ,

v 3 = Q/A 3 ………

Velocity head = v 2 / 2g

Total Head = P/w + V 2 / 2g + Z

Hence, Bernoulli’s theorem is proved and It can be expressed as,

Sadanandam Anupoju

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Bernoullis Lab Report

This experiment is about Bernoulli's theorem. The objective of this experiment is to demonstrate the Bernoulli's theorem. This experiment use the Bernoull's Theorem Demonstration Apparatus. The apparatus contains venture meter, pad of manometer tube, pump, and water tank equipped with pump water controller, water host and tubes. This experiment uses the venturi meter to measure the fluid flow through a pipe.The venturi tube has converging and diverging portion that function of increasing and decreasing the velocity of fluid and lower and higher the static pressure respectively. The experiment is conducted with different flow rates starting the first after the level pressure of each manometer A, B, C, D, E and F is equal and stable. The flow rate was taken as the water indicator reached at 5 liters of water level. Level pressure of each manometer is measured as head loss. From the experiment conducted, we observed than when fluids moves at higher pressure to lower pressure, the velocity increases. There are differences on the speed of the flow and the pressure when we use Bernoull's equation and Continuity equation to calculate velocity. Thus, we concluded that the Bernoull's theorem is accepted. The experiment was a successfully and the objectives are obtained. CONCLUSION

Related Papers

savery chhin

Nithiaprathap Paneerselvam

nkosiyazi mondli

American Journal of Physics

Salvador Gil

Gerald Recktenwald

A series of laboratory exercises has been developed to aid in the teaching of thermal and fluid sciences to undergraduate engineers. The exercises use simple hardware and a guided-inquiry approach to expose student misconceptions and to develop deeper understanding of basic concepts. This paper fo-cuses on one of the laboratory exercises, which uses a simple duct with a sudden expansion to demonstrate the error caused by misapplication of the Bernoulli equation. The apparatus and the laboratory exercise are described. Learning gain measurements and results of attitude surveys are presented. The exercise is successful in causing students to confront their misconceptions and lack of understanding. Student attitudes about the usefulness of the exercise correlate with their grade inthe course. The A students have a less favorable opinion than the B and C students. NOMENCLATURE A area of duct cross section.

IOSR Journals

This thesis aims toDebotteleneck the Bernoulli's apparatus kept in hydraulic machines laboratoryof Mechanical Engineering Department of BIT SINDRI DHANBAD,JHARKHAND,INDIA,which was out of order from more than a decade. Also aims to verify well known Bernoulli's equation with this apparatus.Chapter one gives some insight towards basics of fluid mechanics. Chapter two deals with Bernoulli's theorem and its applications.Chapter three deals with constructional details and experimentation method of Bernoulli's apparatus.Chapter four deals with observations and calculations for verifyingBernoulli'stheorem.Chapter five gives final results which verify Bernoulli's theorem.Chapter six tells about scope for future works.

Bapi Mondal

Lab Report on "Applying Bernoulli equation to determine the orifice throat diameter of the given orifice meter and plotting the following curves." a) Pressure difference vs Reynolds number. b) Log pressure difference vs Log velocity c) Log average velocity vs manometer reading and find the slope of the line.

Water flow Venturi meter

Akorede Oyindamola

The Venturi meter experiment was conducted by using a venturi tube which is a device used for measuring the rate of flow along a pipe. Water, which is the fluid used in this experiment, accelerates in the direction of the contraction of the neck of the device with an increase in velocity in the throat. This leads to a decrease in pressure and this effect on pressure change is referred to as the Venturi effect. In this experiment, the actual flow rate is different from the theoretical flow rate due to frictional and turbulence effects and this is observed by determining the coefficient of discharge for the venturi.

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