Post on 03-Apr-2018
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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_pressure7/28/2019 REPORT Hydrostatic Fluid
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Thermodynamics: An Engineering Approach, Sixth Edition in SI units. Author by Cengel and
Boles.