BDA FLUID MECHANICS
GROUP PROJECT : HYDROSTATIC FORCE
GROUP 3
LECTURER : DR SAHRUL AMIR SECTION
:1 NAME
MATRIX NUMBER
1
JOSHUA REYNOLDS BIN JAPAR
CD 140046
2
AIMY SHAH BIN MARBEK
CD 140091
3
MOHD ARDY BIN ABDUL RAZAK
CD 140074
4
LIM JUN MING
DD 140003
MARK
CONTENT
CONTENT
PAGE 3
1.0 TITLE 3 2.0 OBJECTIVES 4 3.0 HYDROSTATICS 5 4.0 INTRODUCTION THE HYDROSTATICS PRESSURE ( MODEL: FM 35) 6 5.0 EXPERIMENTAL THEORY
Figure 5.1 Hydrostatics force Figure 5.2 Water Level above the Quadrant Scale Figure 5.3
5 6 10
5.1Determination of Centre of Pressure, CP ( Theoritical Method )
7
6.0 EXPERIMENT PROCUDURE
10
7.0 RESULT
11
8.0 CALCULATION
12
9.0 DISCUSSION Graph
14
ℎ() For graph ℎ ()
10.0 CONCLUSION
17
11.0 REFERENCE
18
12.0 APPENDIX
19
2
1.0 TITLE
HYDROSTATIC PRESSURE
2.0 OBJECTIVES
2.1 To determine the center of pressure on both submerged and partially submerged a plane surface. 2.2 To compare the center of pressure between experimental result with the theoretical values. 2.3 To determine experimentally the magnitude of the force of pressure hydrostatic force.
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3.0 HYDROSTATICS
Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics, the study of fluids in motion. Hydrostatics are categorized as a part of the fluid statics, which is the study of all fluids, incompressible or not, at rest. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always flat and horizontal whatever the shape of its container.
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4.0 INTRODUCTION THE HYDROSTATICS PRESSURE ( MODEL: FM 35)
The Hydrostatic Pressure (Model: FM 35) apparatus has been designed to introduce students to the concept of centre of pressure of an object immersed in fluid. It can be used to measure the static thrust exerted by a fluid on a submerged surface, either fully or partially, and at the same time allowing the comparison between the magnitude and direction of the force with theory. The apparatus consists of a specially constructed quadrant mounted on a balance arm. It pivots on knife edges, which also correspond to the centre of the arc of quadrant. This means that only the hydrostatic force acting on the rectangular end face will provide a moment about the knife edges (SOLTEQ, n.d.). The force exerted by the hydraulic thrust is measured by direct weighing. With no water in the tank, and no weights on the scale, the arm is horizontal. As weights are added one by one to the scales, water can be added to the tank so that the hydrostatic force balances the weights and bring the arm back to horizontal. Figure 1 is a sketch of the Hydrostatic Pressure (Model: FM 35).
Figure 4.1: Hydrostatic Pressure (Model: FM 35).
The design of many engineering systems such as water dams and liquid storage tanks requires the determination of the forces acting on the surfaces using fluid statics. The complete description of the resultant hydrostatic force acting on a submerged surface requires the determination of the magnitude, the direction, and the line of action of the force (Fluid Mechanics, Cengel & Cimbala, 2010).
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5.0 EXPERIMENTAL THEORY
Figure 5.1 Hydrostatics force
The hydrostatic force on submerged surface is given by,
= ρ gℎ A Where,
= hydrostatic force ℎ = depth of the centroid from fluid free surface A = Submerged surface At any given depth, h, the force acting on the element area Da is given by dF = γh d A and is perpendicular to the surface. Thus, the magnitude of the resultant force acting on the entire surface can be determine by summing all the differential forces.
= ∫ ℎ = ∫ sin With h = y sin θ. For constant γ and θ
= γ sinθ ∫ yd A But the term ∫ yd A is the first moment of area with respect to axis x where
∫ yd A = yc A Thus
= γAyc sin θ or = γhc A 6
Where ℎ is the vertical distance from the fluid surface to the centroid of the area. 5.1Determination of Centre of Pressure, CP (Theoritical Method)
Point or location where resultant force FR act i s known as center of pressure of pressure, CP. Position of this point usually is explained by a vertical distance free surface, hR or distance from axis x, yR (or sometimes known as ycp). This yR distance can be determined by summation of moments around x axis. That is moment of resultant force must equal the moment of the distributed pressure force, or Therefore, ∫ =
=
∫
=
∫
But dA is the second moment of area (moment of inertia), ix with respect to an axis formed by the plane containing the surface and the free surface (x axis). Thus, we can write
=
Or,
=
Where,
= distance from point 0 to center of pressure, CP (m) = distance from point 0 to centeroid of surface area (m) = second moment of area about the centroid (m) A= area of submerged surface ( )
Or in a vertical distance
ℎ = ℎ
7
Hydrostatic pressure on the circular side of the quadrant exerts no turning moment on yhr fulcrum. The same is hydrostatic pressure on the radial side of the quadrant. The only pressure exerting turning moment on the fulcrum is that a pressure actin on the 100mm x 75mm surface which is maintained at vertical.
Submerged surface, A= 100mm x 75mm (width) Quadrant inner radius, R1= 100mm Quadrant outer radius, R2= 200mm Fulcrum is located at the same centre of the quadrant block.
Under static balance conditions, FY= mgL Thus, Y=
a. When water level is above the quadrant scale :
ℎ() = ℎ +
Theorytically,
ℎ = ( ℎ + 50) mm Where,
75 X 100 = = = 6.25 12 12
= 75 X 100 = 7500 From Figure 5.2,
= ℎ ( ℎ )
Thus,
ℎ = ℎ
Experimentally,
ℎ() = ℎ =
8
ℎ
=
1 0 0 ℎ
=
100 ( +)
ℎ
ρ = 1000 /
Where,
L = 280 mm A = 100 mm x 75 mm =
7500
Figure 5.2 Water Level above the Quadrant Scale b. When water Level is within the Quadrant Lower Scale :
Theoretically,
ℎ() = ℎ
Where,
ℎ = = =
From Figure
5.3,
Experimentally,
= 75ℎ
= ( ℎ ℎ ) ℎ() = ( ℎ )
9
=
=
200
ℎ ℎ
=
2 200 ℎ ℎ
Figure 5.3
6.0 EXPERIMENTAL PROCEDURE
1. make sure all equipment is in good condition 2. Add water until the container is full column 3. Adjust the balance so that the plane in balance , showing the value of '0'. 4. Put a weight of 500g 5. Remove the water so the plane back in balance. 6. Measuring the level of water is left in the container. 7. Reduce the weight of 50g up to 450g it. The experiment was repeated starting from step 5 to 7. The reduced weight of 50g for each test so that the water is at a point below the latter.
all data collected and verified by calculation.
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7.0 RESULTS
Table 7.1 Water level above the Lower Quadrant
NO.
Mass, m
h
ℎ = (ℎ +50)
Ic
Unit
g
mm
mm
mm
1
500
73
123
2
450
60
3
400
4
hR(teory)
hR(ep)
mm
mm
6.25 x 10 922.5 x 10
123.10
129.15 x 10
110
6.25 x 10
825 x 10
117.58
103.95 x 10
98
98
6.25 x 10
735 x 10
106.50
82.32 x 10
350
36
86
6.25 x 10
645 x 10
95.69
63.21 x 10
5
300
23
73
6.25 x 10
547.510
89.92
45.99 x 10
6
250
11
61
6.25 x 10 457.5 x 10
74.66
32.02 x 10
A x hc
Table 7.2 Water level within the Lower Quadrant
NO. Mass, m
h
ℎ =
Ic
A
A x hc
hR(teory)
hR(ep)
mm
mm
(ℎ +50) unit
g
mm
mm
mm
mm
1
200
98
49
5.882 x 10
7350
360.15 x 10
65.33
40.34 x 10
2
150
84
42
3.704 x 10
6300
264.6 x 10
56
22.27 x 10
3
100
69
34.5
2.053 x 10
5175
178.54 x 10
46
10 x 10
4
80
63
31.5
1.563 x 10
4725
148.84 x 10
42
6.67 x 10
5
60
55
27.5
1.039 x 10
4125
113.44 x 10
36.66
3.811 x 10
6
40
48
24
6.91 x 10
3600
86.4 x 10
24.08
1.94 x 10
7
20
38
19
342.95 x 10
2850
54.15 x 10
25.33
0.606 x 10
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8.0 CALCULATION
Table 7.1,
ℎ = 73
= 7500 x 100 = 7500
ℎ = (ℎ 50)
To find area = x ℎ
= 73 50
= 7500 x 123
ℎ = 123
= 922.5 x 10
=
=
=
= 6.25 x 10 100 +)
ℎ() = ( =
() ( )
ℎ
10073
= 129.15 x 10
ℎ() = ℎ
. = 123 + ()()
= 123.10 mm
12
Table 7.2
h = 98 =
ℎ =
= 49 mm
=
=
=
= 5.882
x 10
= 75 x 98 = 7350 mm
A x hc = 7350 x 49 = 360.15 x 10
ℎ() = ℎ
. = 49 + .
= 65.33
ℎ () = =
200 ℎ
()() 20098 ( . )
= 40.37 mm 13
9.0 DISCUSSION
m=
−
−
= .−. =
.
m = 4.68 g/mm For graph ℎ()
m=
− = − . −.
=
.
= 3.673x 10 g/mm
For graph ℎ ()
For graph ℎ() show that a straight line with m = 4.608 g/mm. We can see that most of point is near and touch on the point and data we know increased evenly
For graph ℎ () show that a straight line with m =
3.673x 10 g/mm. This is
because we take a point on average to know the change that occurred.
14
For graph ℎ()
15
For graph ℎ ()
16
10.0
CONCLUSION
The conclusion about the Hydrostatic force is, all the objective of the experiment is successful. From that we know the hydrostatic force is the branch of fluid mechanics that studies incompressible fluids at rest. It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics, the study of fluids in motion. Hydrostatics are categorized as a part of the fluid statics, which is the study of all fluids, incompressible or not, at rest. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always flat and horizontal whatever the shape of its container. Besides that, all the theory we can prove that from the experiment and we know that the hydrostatic force is not affected by the volume of water. The hydrostatic force is influenced by the depth, gravity and mass (type of liquid). Hydrostatic power system is widely used in our daily lives. It can be seen as the system of water tanks, dams and more. This system helps in saving energy and costs especially in the industrial and electricity generating sources. All these involve knowledge of fluid mechanics
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11.0
REFERENCES
1. Y.A. Cengel & J. M. Cimbala, . Fluid mechanics: fundamental and applications. Third Edition In SI Unit : McGraw-Hill. 2. Centre of pressure. [Online] Available at: https://en.wikipedia.org/wiki/Hydrostatics. 3. Penerbit UTHM, Engineering Laboratory IV Book
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12.0
APPENDIX
19
