report hydrostatic fluid

7/28/2019 REPORT Hydrostatic Fluid

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Introduction

Fluid pressure is the pressure on an object submerged in a fluid, such as water. The

pressure can be provided from a number of sources which are the sheer weight of the fluid, such

as in scuba diving, when the diver goes deeper into the water, the water pressure increases; or in

the earth's atmosphere, as a plane goes higher, the air pressure decreases. Then, a pump, such as

when water "pumped" into a water tower. Perhaps, a compressor, such as in a small water supply

system in a rural well for a house connected to an air compressor. Water pressure is used in our

daily lives to control the flow of water coming from any mechanical water source. Fluid pressure

occurs in one of two situations in both an open condition, such as the ocean, or a swimming pool,

and a closed condition, such as a water line or a gas line.

Pressure in open conditions usually can be approximated as the pressure in "static" or

non-moving conditions (even in the ocean where there are waves and currents), because the

motions create only negligible changes in the pressure. Such conditions conform to principles of

fluid statics. The pressure at any given point of a non-moving (static) fluid is called the

hydrostatic pressure. Fluid statics (also called hydrostatics) is the science of fluids at rest, and is

a sub-field within fluid mechanics. The hydrostatic force on any surface is due to the fluidpressure acting on that surface, as shown in Fig. 1. Pressure is a normal stress which is positive

when in compression. Since the pressure is everywhere normal to the surface, the resultant

pressure force (Fp) is also normal to the surface.


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ObjectivesThe objectives of this experiment are:

1. To determine experimentally the magnitude of the force of pressure ( hydrostatic pressure)

and its point of action ( centre of pressure ) on a plane surface,

2. To compare the experimentally results with the theoretical values.

Theoretical backgroundConsider a plane surface submerged in a liquid as shown below.

Figure 3.1: Hydrostatic force and centre of pressure


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Total pressure

It is the resultant force exerted by a static fluid on a surface when the fluid comes in contact with

the surface. It is also called hydrostatic pressure.

F = g A (1)

Where

F is the total pressure (hydrostatic pressure)

is the mass density of the liquid

g is the gravitational acceleration

is the submerged area of the plane surface

is the vertical distance from the liquid surface to the centroid of the

submerged plane surface ( )

Centre of pressure

It is the point of application of the total pressure (hydrostatic force ) on the surface.

(2)

Where

is the vertical distance from the liquid surface to the centre of pressure

is the moment of inertia of the plane about its centroid G


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3.3 There are another calculation method to find both total pressure and centre of pressure

This is based on figure 1. Since the pressure is everywhere normal to the surface, the resultant

pressure force (Fp) is also normal to the surface. The magnitude of Fp is

where p = ysin , = specific weight of the fluid, y = distance measured from level of zero

pressure and measured in the plane of the surface, and = angle which the plane of the surface

makes with the horizontal. For constant and ,

where = y coordinate of the centroid of the surface and is the pressure at the centroid of the

surface. Fp acts at ycp, called the center of pressure. The resultant pressure force acting at this

center of pressure must give the same moment as the distributed pressures, so ycp can be found

from

where Io = moment of inertia about the level of zero pressure for the surface on which the

pressure force is acting and = moment of inertia about the horizontal centroid axis. Notice that


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Fp is calculated using the pressure at the centroid of the surface but the resultant pressure force

acts at ycp which is lower than the centroid.

3. Apparatus

Figure 4.1

4.1 Specification

[1] Apparatus for investigating the hydrostatic pressure in liquids

[2] l x w x h 400x500x360mm, 10kg

[3] Determination of the resulting compression force using weights on lever


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[4] Lever 250mm

[5] Measuring tank with water level scale

4.2 Technical Data

Set of weights: 1x 2.5N, 1x 2N, 2x 1N, 1x 0.5N

Length of lever: 250mm

Tank with angular scale: 90

Capacity: 2ltr

Water level scale: 200cl

Experimental Procedures

Part A: Vertical plane surface ( = 0)

1. Counterbalancing the water vessel

1. By using the detent, the water vessel was set to an angle of =0.

2. The unit was counterbalanced with the rotating slider. The stop pin was precisely in the

middle of the hole.

3. The water, rider and appended weight were removed during the counterbalancing

process.

2. Measurement

1. The rider was mounted and the lever arm was set to any position. The lever arm was

recorded which was the distance from the rider to the centre of rotation of the water

vessel.


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II.is the mass density of the liquid

III. g is the gravitational acceleration

IV.is the submerged area of the plane surface

*A will change according to the value of s

V.is the vertical distance from the liquid surface to the centroid of the

VI. submerged plane surface ( = )

6.1.1Theoretical Part A = = 0

No. 1

= 1.0727 N

No. 4

= 4.950 N

6.1.2 Theoretical Part B = = 20


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No. 1

= 0.847 N

No. 3

= 3.25 N

6.2 Centre of pressure

+

=

Where:

is the vertical distance from the liquid surface to the centre of pressure


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is the moment of inertia of the plane surface about its centroid G

is the submerged area of the plane surface

is the vertical distance from the liquid surface to the centroid of the

Submerged plane surface ( = )

6.2.1 Centre of pressure for part A

Triangle profile

= where h = 0.054 m

=

= 9.84

+

= + 0.027 =0.036 m

Trapezoidal profile

= where h = 0.116 m


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=

= 9.76

+

= + 0.058

= 0.078 m

6.3 Centre of pressure part B: =10

Triangle profile

= where h = 0.057 m

=

= 1.157

+ Where = 0.0285 m


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= + 0.0285

= 0.038 m

Trapezoidal profile

= where h = 0.125 m

=

= 1.22

+

= + 0.0625

= 0.083 m

6.4 Calculation of hydrostatic force and centre of pressure from

experimental data

Case 1 : Triangular profile of pressure distribution


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*All units are in mm

figure 6.1

Case 2 : Trapezoidal profile of pressure distribution

*All units are in mm


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Figure 6.2


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Data and Calculation

Part A: = 0

Table 7.1

No. Lever Arm AppendedWeight

Water level Centre of Pressure

HydrostaticForce

L(mm) FG(N) S1(mm)

S2(mm)

S(mm)

(mm

)

h*(mm)

F(N)

1 200 1 0 54 54 182.00

36.00 1.099

2 200 2 0 78 78 174.00

52.00 2.299

3 200 3 0 98 98 167.30

65.30 3.586

4 200 4 0 116 116 162.63

78.60 4.919

5 200 5 0 134 134 159.92

93.90 6.253


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Part B : = 20

Table 7.2

No.

Lever ArmAppendedWeight

Water levelCentre ofPressure

HydrostaticForce

L(mm) FG(N) S1(mm)

S2(mm)

S(mm)

(mm)

h*(mm)

F(N)

1 200 1 14 62 48 182.97

32.00 1.093

2 200 2 14 88 74 173.40

49.30 2.307

3 200 3 14 108 94 166.66

62.67 3.600

4 200 4 14 126 112 162.83

77.07 4.913

5 200 5 14 144 130 159.43 91.88 6.272


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7.1Example of calculation of Part A: =0

For Triangular case;

For trapezoidal case;


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7.2 Example of calculation of Part B: =20

For Triangular case;

For trapezoidal case;


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Conclusion

As the conclusion, this experiment is successfully because the result that we got from experiment

are not far and precise to theoretical result. We also want to thank to lecturer, En. Mohd Redza

bin Dollah Sajat that gives us a guidance and knowledge about hydrostatic pressure on plane

surface and operating the tools that need many steps and procedures with fulfilled the safety

aspect.

Referenceshttp://www.nationmaster.com/encyclopedia/Fluid-pressure#Applications

http://www.onlineconversion.com/density_all.htm

http://en.wikipedia.org/wiki/Hydrostatic_pressure#Hydrostatic_pressure time 3.00

15/1/09

Yunus A. Cengel and John M. Cimbala, Fluid Mechanics Fundamental and Its

Applications, 6th ed, McGraw-Hill.

Finnemore, E.J., and Franzini, J.B. Fluid Mechanics with Engineering Applications, 10th ed.

McGraw-Hill, Singapore, 2006.
http://www.nationmaster.com/encyclopedia/Fluid-pressure#Applicationshttp://www.onlineconversion.com/density_all.htmhttp://en.wikipedia.org/wiki/Hydrostatic_pressure#Hydrostatic_pressurehttp://www.nationmaster.com/encyclopedia/Fluid-pressure#Applicationshttp://www.onlineconversion.com/density_all.htmhttp://en.wikipedia.org/wiki/Hydrostatic_pressure#Hydrostatic_pressure


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Thermodynamics: An Engineering Approach, Sixth Edition in SI units. Author by Cengel and

Boles.

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