FLUIDS MECHANICS GROUP PROJECT

8/18/2019 FLUIDS MECHANICS GROUP PROJECT

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BDAFLUID MECHANICS

GROUP PROJECT : HYDROSTATIC FORCE

GROUP 3

LECTURER : DR SAHRUL AMIR

SECTION : 1

NAME MATRIX NUMBER

1 JOSHUA REYNOLDS BIN JAPAR CD 1400462 AIMY SHAH BIN MARBEK CD 140091

3 MOHD ARDY BIN ABDUL RAZAK CD 140074

4 LIM JUN MING DD 140003

MARK


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CONTENT

CONTENT PAGE

1.0 TITLE3

2.0 OBJECTIVES3

3.0 HYDROSTATICS4

4.0 INTRODUCTION THE HYDROSTATICS PRESSURE ( MODEL: FM 35)

5

5.0 EXPERIMENTAL THEORY

Figure 5.1 Hydrostatics force

Figure 5.2 Water Level above the Quadrant Scale

Figure 5.3

5.1Determination of Centre of Pressure, CP ( Theoritical Method )

6

56

10

7

6.0 EXPERIMENT PROCUDURE 10

7.0 RESULT 11

8.0 CALCULATION 12

9.0 DISCUSSION

Graph ℎ() For graph ℎ()

14

10.0 CONCLUSION 17

11.0 REFERENCE 18

12.0 APPENDIX 19


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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


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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 is 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


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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) mmWhere,

=

12

=75 X 100

12

= 6.25

= 75 X 100 = 7500

From Figure 5.2, = ℎ ( ℎ )

Thus, ℎ = ℎ

Experimentally, ℎ() = ℎ

=

- ℎ


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=

1 0 0 ℎ

=

( +) 100 ℎ

Where, ρ = 1000 /

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 =

=

=

= 75ℎ

From Figure 5.3, = ( ℎ ℎ)

Experimentally, ℎ() = ( ℎ)

=

ℎ

=

200 ℎ


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=2

ℎ 200 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 Ax hc hR(teory) hR(ep)

Unit g mm mm mm mm mm

1 500 73 123 6.25 x 10 922.5 x 10 123.10 129.15 x 10

2 450 60 110 6.25 x 10 825 x 10 117.58 103.95 x 10

3 400 98 98 6.25 x 10 735 x 10 106.50 82.32 x 10

4 350 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

Table 7.2 Water level within the Lower Quadrant

NO. Mass, m h ℎ =

(ℎ+50)

Ic A Ax hc hR(teory) hR(ep)

unit g mm mm 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

ℎ() =

( +) 100 ℎ

=()

( ) 100 73

= 129.15 x 10

ℎ() = ℎ

= 123 +.

()()

= 123.10 mm


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Table 7.2

h = 98

ℎ=

=

= 49 mm

=

=

=

= 5.882 x 10

= 75 x 98

= 7350 mm

Ax hc = 7350 x 49

= 360.15 x 10

ℎ() = ℎ

= 49 +.

.

= 65.33

ℎ() =

200 ℎ

=()()

( . ) 200 98

= 40.37 mm


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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.


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For graph ℎ()


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For graph ℎ()


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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 thatstudies 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 costsespecially 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

https://en.wikipedia.org/wiki/Hydrostaticshttps://en.wikipedia.org/wiki/Hydrostaticshttps://en.wikipedia.org/wiki/Hydrostatics


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12.0 APPENDIX

FLUIDS MECHANICS GROUP PROJECT

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