TO VERIFY BERNOULLI’S EQUATION BY EXPERIMENT

S M Mozakkir Quadri 10CES-54(5th SEM) JAMIA MILLIA ISLAMIA

INDRODUCTION

Daniel BernoulliA Swiss scientist born in 1700’s that is most famous for his work in fluid pressure. He died in 1782.

BERNOULLI’S THEOREMBernoulli’s theorem which is also known as Bernoulli’s principle, states that an increase in the speed of moving air or a flowing fluid is accompanied by a decrease in the air or fluid’s pressure or sum of the kinetic (velocity head), pressure(static head) and Potential energy energy of the fluid at any point remains constant, provided that the flow is steady, irrotational, and frictionless and the fluid is incompressible.

BERNOULLI’S EQUATION

If a section of pipe is as shown above, then Bernoulli’s Equation can be written as;

BERNOULLI’S EQUATION

Where (in SI units)      

P= static pressure of fluid at the cross section;ρ= density of the flowing fluid in; g= acceleration due to gravity;v= mean velocity of fluid flow at the cross section in;h= elevation head of the center of the cross section with

respect to a datum.

HOW TO VERIFY?The converging-diverging nozzle apparatus (Venturi meter) is used to show the validity of Bernoulli’s Equation. The data taken will show the presence of fluid energy losses, often attributed to friction and the turbulence and eddy currents associated with a separation of flow from the conduit walls.

APPARATUSES USEDArrangement of Venturi meter apparatus(fig.1)Hydraulic bench(fig. 2). Stop watch(fig.3).

fig. 2 fig. 3

PROCEDURE1.Note down the inlet, throat and outlet section areas.2.Measure the distances of inlet, throat ant outlet

section from origin.3.Switch on the motor attached to hydraulic bench.4.If there any water bubble is present in tube remove it

by using air bleed screw. 5.Fully open the control valve.6.Note down the reading of piezometer corresponding

to the section, simultaneously note down the time required to a constant rise of water in volumetric tank(say of 10).

7.Varying the discharge and take at least six readings.

OBSERVATIONS

1.Volume = 1000 cm3

2.Distance of inlet section from origin= 5.5 cm3.Distance of throat section from origin= 8.1 cm4.Distance of outlet section from origin= 15.6

cm5.Area of inlet section= 4.22 cm2

6.Area of throat section= 2.01 cm2

7.Area of outlet section= 4.34 cm2

OBSERVATIONSS NO. TIME(se

c)

PIEZOMETRIC HEAD(cm)

INLETSECTION

THROATSECTION

OUTLETSECTION

1 90.40 19.8 17.5 19.3

2 92.90 19.9 17.3 19.2

3 101.26 19.4 17.4 18.8

4 106.00 19.4 17.4 18.8

5 110.00 19.6 17.6 19.0

6 115.65 19.2 17.6 18.8

CALCULATED VALUES

Q(cm3/s)

VELOCITY(v)

(cm/sec)

VELOCITY HEAD

(cm)

TOTAL ENERGY

HEAD (cm)

LOSS OF ENERGY

(cm)

v1 v2 v3v1

2/2

g

v22/2

g

v32/2

gE1 E2 E3 E1-E2 E1-E3

110.62 26.2 55.0 25.4 0.35 1.54 0.31 20.1 19.0 19.6 1.10 0.51

107.64 25.5 53.5 24.8 0.33 1.46 0.31 20.2 18.7 19.5 1.47 0.71

98.76 23.4 49.1 22.7 0.27 1.23 0.26 19.6 18.6 19.0 1.04 0.61

94.34 22.3 46.9 21.7 0.25 1.12 0.24 19.6 18.5 19.0 1.13 0.61

90.91 21.5 45.2 20.9 0.23 1.04 0.22 19.8 18.6 19.2 1.19 0.61

86.47 20.4 43.0 19.9 0.21 0.94 0.20 19.4 18.5 19.0 0.87 0.41

RESULTS

It is observed from the calculated value that at section where area is less velocity is high and pressure is low which validates the Bernoulli’s Equation. Graphs are plotted between distance v/s piezometric head and distance v/s total energy but from the graph (B) we can observe that there is dissipation in energy at last point this is because to achieve an ideal condition practically is not possible.

GRAPHS

4 6 8 10 12 14 16 1817

19

21

obs no. 1

Distance x(cm)

piez

omet

ric h

ead(

cm)

4 6 8 10 12 14 16 1817

19

21

obs no. 1

Distance (x) (cm)

Tota

l ene

rgy

(E)(

cm)

APPLICATIONS The Bernoulli’s equation forms the basis for solving a wide variety of fluid flow problems such as jets issuing from an orifice, jet trajectory flow under a gate and over a weir, flow metering by obstruction meters, flow around submerged objects, flows associated with pumps and turbines etc.Apart from this Bernoulli’s equation is very useful in demonstration of various aerodynamic properties like Drag and Lift.

APPLICATIONSDRAG AND LIFT

Fast Moving Air; Low Air PressureAir travels farther

Slow Moving Air; High Air Pressure

airfoilLeading edge

Trailing edge

APPLICATIONS

CONCLUSION

From the result obtained, we can conclude that the Bernoulli’s equation is valid for flow as it obeys the equation. As the area decreases at a section (throat section) velocity increases, and the pressure decreases.

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