STUDENT NAME MD ATIQUR RAHMAN FAISAL

STUDENT ID SCM-012154

COURSE BACHELOR IN MECHANICAL ENGINEERING

LECTURER DR. THAM

SUBMISSION DATE 7th May 2012

SUBJECT THERMODYNAMICS (EAT 106)

Bernoulli’s Principle Lab Report

Title : Bernoulli’s Principle

Introduction : A Swiss scientist name Daniel Bernoulli has discovered this principle which was named after him. Among his all discoveries concerns about the fact pressure in a moving fluid (either liquid or gas) is less than the pressure in stationary fluid. Even the ability of the airplane wings to lift the airplane off the ground is partially responsible of Bernoulli’s name principle. The shape of the airplane wings causes the air on the top moves faster than the air on the bottom of the wings. This causes the air to exert more pressure down the wings, than up the wings, which lets the airplane to lift.

In reality this is a partial explanation, the wings also exerts forces on air to move it downward. The major part of the forces involves Newton’s third law, which helps airplane to fly upside down.

Abstract : The experiment was conducted in order to find the time taken to collect 10 liter of water, to volumetric flow rates of the water, the pressure difference at all manometer tube (static head), velocity, dynamic head and also total head. The data was collected at six adjusted head difference. The experiment was run based on Bernoulli’s principle states that for an invincible flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or decrease in fluid potential energy.

Objective : Firstly this experiment was done to investigate the validation of the Bernoulli’s equation and secondly to measure flow rates and both static and total pressure heads of known geometry for a range of steady flow rates.

Theory : Assumption made in Bernoulli’s Equation:

The fluid is incompressible. The fluid is non-viscous. The flow is steady and velocity of fluid is less than the critical velocityfor

fluid. There is no loss of energy due to friction.

Bernoulli’s Equation for constant head h,

[ (P1)(ρ)+(W 1

2)(2)

=(P2)(ρ)

+(W 2

2)(2)

=Constant ]Allowance for friction looses and conversions of the pressure P1 and P2 into static

pressure head h1 and h2 yields:

¿

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Bernoulli’s Principle Lab Report

Where,

P1→ Pressure at cross-section A1 h1→ Pressure head at cross-section A1 W 1→ Flow velocity at cross-section A1

P2→ Pressure at cross-section A2 h2→ Pressure at cross-section A2 W 2→ Flow velocity at cross-section A2

ρ→ Density of the medium. hv→ Pressure loss head

Technical Data :

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Bernoulli’s Principle Lab Report

Apparatus :

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Bernoulli’s Principle Lab Report

Procedure :

1. A quick inspection was done to ensure that the unit was in proper operating

condition.

2. A hose connection was made to connect the unit to the nearest power supply.

3. The discharge pipe was then opened.

4. The cap nut of the probe compression gland was set to such condition, that the

slight resistance could be felt on moving the probe.

5. The inlet and outlet valve was then opened.

6. The pump was then switched on and the main cock was then slowly opened.

7. The vent valve on water pressure gauze was opened and outlet cock was closed

with great care until pressure gauze was flushed.

8. By simultaneously setting the inlet and outlet cock, the water level pressure

gauze was regulated, so that neither upper or lower range limit was overshot or

undershot.

9. Pressure at all point were measured and recorded. The overall pressure probe

was moved to corresponding measurement level and the overall pressure was

noted down.

10. The volumetric pressure flow was determined, by using stopwatch to

established time required to raise the water level in the volumetric tank from 20

to 30 liters.

Results :

Set-1

h1

(mmWs)

h2

(mmWs)

h3

(mmWs)

h4

(mmWs)

h5

(mmWs)

h6

(mmWs)

Time,

10liters

V, (L/s)

(h (stat . ))260 240 10 145 170 180 63 1.59×10-4

(h (total))298.67 298.67 298.67 298.67 298.67 298.67

(h (dyn ))38.67 58.67 288.67 153.67 128.67 118.67

(W (means ))0.87 1.07 2.38 1.74 1.59 1.53

(W (calc ))0.47 0.68 1.88 0.93 0.63 0.47

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Bernoulli’s Principle Lab Report

%difference 46% 36% 71.4% 46% 60.4% 69.3%

Set-2

h1

(mmWs)

h2

(mmWs)

h3

(mmWs)

h4

(mmWs)

h5

(mmWs)

h6

(mmWs)

Time,

10liters

V, (L/s)

(h (stat . ))250 235 40 150 170 180 70 1.43×10-4

(h (total))373.33 373.33 373.33 373.33 373.33 373.33

(h (dyn ))123.33 138.33 333.33 223.33 203.33 193.33

(W (means ))1.56 1.65 2.56 2.09 2.00 1.95

(W (calc ))0.42 0.61 1.69 0.84 0.56 0.42

%difference 73.1% 63% 33.9% 59.8% 72% 78.5%

Set-3

h1

(mmWs)

h2

(mmWs)

h3

(mmWs)

h4

(mmWs)

h5

(mmWs)

h6

(mmWs)

Time,

10liters

V, (L/s)

(h (stat . ))225 215 80 155 170 175 82 1.22×10-4

(h (total))385.28 385.28 385.28 385.28 385.28 385.28

(h (dyn ))160.28 170.28 305.28 230.28 215.28 210.28

(W (means ))1.8 1.8 2.4 2.1 2.0 2.0

(W (calc ))0.36 0.52 1.44 0.72 0.48 0.36

%difference 80% 71.1% 40% 65.5% 76% 82%

Equation Used

(h(dyn ))=(h(total ))−(h( stat . ))

(W (means ) )=√ (2 )× (g )×(h (dyn )×10−3)

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Bernoulli’s Principle Lab Report

V=( Lρ )×( 1T )

(W (calc ) )=(VA )

%difference=( (W (means ) )−(W (calc ))

(W (means )) )×100%Sample Calculation

From set-1

(h1 (dyn) )=298.67−260=38.67mmWs

(W 1 (means ) )=√(2 )× (9.81 )×(38.67×10−3)=0.87

(hdyn was found in mmWs, so to convert it into mWs, multiply hdyn with 10-3)

V=( 101000 )×( 163 )=1.59×10−4m/s

A1=(338.6)(106)

=3.386×10− 4 (given area was in mm, so multiply with 10-6 to convert into m)

(W 1 (calc ) )=( VA1 )=¿

%Difference=( (0.87 )−(0.47)(0.87) )×100%=46%

Discussion : As we know water is a fluid, and all fluid have the properties to take the

shape of the container or wherever they flow or stored. Since the fluid flow

through a given path for a duration of time, there must a pressure loss during the

path. Bernoulli’s principle says that if the rate of flow of the fluid is high, the

pressure will be low and the slower rate of flow of the fluid exerts more

pressure.

From the experiment it has been found that the Bernoulli’s principle is

valid for steady flow of fluid in tapered duct and velocity increases along same

channel.

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Bernoulli’s Principle Lab Report

Conclusion : From the experiment it is found that the difference between the

experimental and the calculated value are too high. This could happen due to

some factors like:

The reading was not taken on meniscus level, parallel eye reading.

Bubbles those were trapped and were couldn’t be removed before running the

experiment.

The record time might not be accurate.

The internal resistance of the water, those were not taken into account during

calculation.

The pressure at each manometer tube might not be stable before the reading were

taken.

All the above factors might be responsible for the results to get

difference. The experiment can be improved by repeating the experiment taking

the above factors into account.

Overall considering all the factors and the comparison between the

values, the experiment can be accepted as a successful one, because it proves the

Bernoulli’s principle of fluid motion pressure.

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