### 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.

**Objective of Bernoulli Theorem**

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

Find the

- Air-flight
- Lift
- Baseball
- Draft
- Sailing

## Theory of Bernoulli's Theorem Experiment

According to Miller, R.W (1996) Law of conservation of energy was the main deriving factor behind the derivation of the Bernoulli’s experiment or Bernoulli principle.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 to make the final sum same as before. According to the Bernoulli'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

1. Place the venture meter on to a horizontal surface and note the height of input valve and output valve and make sure they are same.2. Attach the apparatus with the power supply but keep the supply off

V= 0.865 m/sec

h_n= h_1-[ (v_n^2)/2g- (v_1^2)/2g]

h_2= 0.274-[ 〖1.106529〗^2/2g- 〖0.881013〗^2/2g]

h_2= 0.251131 m

## 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

Aim and objective of this Bernoulli experiment was to discuss the behavior of ideal and real fluid and on the basis of the test result it can be concluded that the experiment was successful because there is difference in measured and theoretical values.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

• R.K. Bansal (n.d) Chapter 8 flow measurement, A Textbook of Fluid Mechanics• Miller, R.W (1996) Flow Measurement engineering Handbook 3Rd ED. McGraw-Hill Book, New York N.Y

• USBR (1996) Flow Measurement Manual. Water Resource Publication LLC Highland Ranch Co

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