HH2 CENTRE OF HIDROSTATIC PRESSURE.

1.0 Introduction

Hydraulic structures constructed for the purpose of retaining water are subjected to hydrostatic forces as long as water is at rest. Therefore, it is important to determine the magnitude, the direction and the location of these forces.

2.0 Principles

Resultant force, F on submerged flat surface is given by,

_ F = ρghA (1)

ρ = fluids density (kg/m³).g = gravitational acceleration (m/s²)._h = the vertical distance from centroid of the area (CG) to the fluid surface.A = area of submerged surface (m²).

The force, F is acting through centre of pressure, CP and it is at yp is distance from O (Fig. 1). O is interception point of the surface water line and the plane surface. The distance of yp is measured in the direction of the plane surface.

Fig. 1 Schematic of Centre of Pressure Apparatus

From theory, yp is : _

Yp (theory) = y + ΙPG Ay (2)Where, ΙPG = 2nd moment of area of the submerged surface. For the rectangular shape, ΙPG is, = bd³/12 (m4) (3) A = area of plane section, = bd (4) ӯ = distance from the centre of gravity (CG) to O (Fig. 1)

Refer to Fig. 1, y is given by, _ _ y = h / cos θ (5) _where h is the vertical distance from centre of gravity of the submerged surface to (CG) to the water surface. But the magnitude of h is given by,

_ h = (h1 + h 2 ) / 2 (6)

By taking moment at P,

Fy = Wgs (7)

But y = yp + R1 – (h1 / cos θ) (8)

where R1 is the radius of the water container. Thus the value of experimental yp is

yp (experiment) = y – R1 + (h1 / cos θ) (9)3.0 Objective

1. To determine the magnitude of hydrostatic force which acting on vertical and inclined

plane submerged surface.

2. To determine the location of hydrostatic force, yρ (both theoretical and experimental

by experimental and theoretical, yρs)

3. To compare theoretical and experimental yρ values.

4.0 Apparatus

Hydrostatic pressure equipment

5.0 Procedure

1) The container of the hydrostatic pressure is adjusted to make sure its plane surface is

in vertical section.

2) (a) Width of the plane surface, (b) height of the plane surface, (c) radius of the water

and (d) the length of lever arm, is measured.

3) The water is poured into the balancing container.

4) The load of 350 g is attached to the container arm.

5) The amount of water is added as in step (3) to balance up the load attached in step (4)

and to be making sure the lever arm is in horizontal position.

6) h1 and h2 is measured recorded.

7) Step (4) to (6) is repeated for loads 400 g and 450 g.

8) Step (2) to (7) is repeated by adjusting the plane surface to make an angle of 20˚ to

vertical.

6.0 Data and Result

Data:

Width of flat surface = 0.075m

1. Inner radius, R1 = 0.100m2. Outer radius, R2 = 0.200m3. Length of lever arm, R3 = 0.200m4. Height of flat surface, d = R1 - R2 = 0.100m5. Area of flat surface, A (eqn. 4) = 0.0075m2

No. Angle θ

(data)

h1

(mm)

(data)

h2

(mm)

(data)

ĥ (mm)

(eqn. 6)

F (N)

(eqn. 1)

Ŷ (mm)

(eqn.5)

IPG

Ay

Yp (theory) (mm)

(eqn. 2)

Mass, W (g)

(data)

Y (mm)

(eqn.7)

h1

cos θ

Yp (exp) (mm)

(eqn. 9)

% error

1 0 20 120 70 5.150 70 0.012 82 350 133 20 53 35

2 0 28 128 78 5.739 78 0.011 89 400 137 28 65 27

3 0 32 132 82 6.033 82 0.010 92 450 146 32 78 15

4 20 8 98 53 3.899 56 0.015 71 350 176 9 85 20

5 20 14 100 57 4.194 61 0.014 75 400 187 15 102 36

6 20 20 106 63 4.635 67 0.012 79 450 190 21 111 41

6. 2nd moment area, IPG = 6.25 x 10-6 m4

7.0 Calculation

Example :

Equation 1: (No:1)

F = ρgĥA

=(1000)(9.81)(70x10^-3)( 7.50x(10^-3)

=5150N

Equation 2: (No:1 )

Yp (theory) = ý + ΙPG Ay

= (70x10^-3) + (6.25x10^-6) / (( 7.50x10^-3) (70x10^-3))

= 82mm

Equation 3 :

IPG = bd³/12

= (75 mm )(100 mm)3 / 12

= (6.25x10^-6) m4

Equation 4:

Area of flat surface ,A = bd

= 0.075(0.1)

=7.50x(10^-

Equation 5 : (No.1)

_ _

y = h / cos θ

= (( 70x10^-3) / cos 0)

= 70mm

Equation 6 : (No.1)

_ h = (h1 + h 2 ) / 2

= (20mm+120mm)/2

= 70mm

Equation 7 : (No.1)

Fy = Wgs

y = Wgs/F

= ((350kg)(9.81)(0.2m))/(5150)

= 133m

Equation 8 and 9 : (No.1)

y = yp + R1 – (h1 / cos θ)

yp (experiment) = y – R1 + (h1 / cos θ)

=(133x10^-3)-0.1+((20x10^-3)/cos0)

=53mm

Presentage of the error : (No.1)

= (yp (theory) – yp (experiment)) x 100 %

yp(theory)

=((82-53)/82)x100%

=35%

8.0 Discussion

GOPI S/O VESUVAPATERANAB07006

My group experiment was success and correct but there is also error on the result for example yp(experiment) we get is different from yp(theory) which suppose to be same. This maybe cause by the error or mistake occurs along the experiment. The error maybe contributed from the equipment its self. We cannot get the correct reading because of the difficulty to get the distance reading, the ruler at behind is not clear, when look from front. Beside that there also many factors that maybe have cause the error like, eye of observer are not parallel to the hydrostatic pressure equipment while taking the measurement, blurry while taking the measurement, the angle maybe change while taking the measurement because of wind. The average of the error happen along this experiment is about 29 %.

The error can be reduced, if we follow this precaution:

1. The water have colour, may be blurry can be avoid.2. Eye of observer parallel to the hydrostatic pressure equipment while taking the

measurement, prevent parallax error.3. Make sure the water container is not shaking while measure. 4. Take more than 1 reading, and make average.5. Make sure the angle is correct.

NOR HASLINDA BINTI MOHAMAD ZAINUDIN

AB07063

Hydrostatic pressure is what is exerted by a liquid when it is at rest. The height of a liquid column of uniform density is directly proportional to the hydrostatic pressure. The hydrostatic properties of a liquid are not constant and the main factors influencing it are the density of the liquid and the local gravity. Both of these quantities need to be known in order to determine the hydrostatic pressure of a particular liquid.

From the result we can see different value between experimental and theory.

Cause and error during the experiment:-

Maybe we make mistake in calculate the result.

Make mistake when taking the reading.

The reading is not accurate.

Difficult to take reading because the color of water is close to the color of apparatus.

Careless during handle apparatus.

Error when set the scale at zero.

Precaution:-

Carefully when take a reading.

Make sure your eyes perpendicular with the reading.

Add the color of water, to see the different color to get more good result.

TENGKU NUR ZULAIKHA BT TG CHEK

AB07070

From the experiment that we had done we had managed to determine the yd. There are many errors that may had contributes to the error for the value of yd. Which are those because of the parallax errors that happen while reading the data. The eyes of the observer are not parallel with the water level. The data should be taken three times to avoid the parallax errors. If the water is coloured, this may had help us to read the data better which avoids error. The values that we had from the theoretical and experimental are different and had so many percentages of error. The value of yd for the theoretical at an angle of 0̊ are 82, 89, and 92 while at angle of 20̊ are 71, 75, and 79. For the experimental value of yd at angle 0̊ are 53, 65, and 78 while at angle of 20̊ are 85, 102, and 111. The errors of the value of yd at 0̊ are 35, 27, and 15. At 20̊ are -20, -30, and -41.

There are many possible precaution while the experiment it’s been carried out which is to hold the container carefully while inserting the water inside the container and coloured the water inside the container so that we are able to read the exact value.

KHAIRUL HAZWAN BIN MD KHALID

AB07099

After doing this experiment we have discuss whether we have made the experiment correctly or not but although we have follow the procedure correctly there are still high error from the result that we get. We have manage to determine the magnitude of the hydrostatic force which acting on vertical and inclined plane submerged surfaces which is using calculation of magnitude of h= (h1+h2)/2 . We also have determine the location of hydrostatic force, Yp and Yps with using both theoretical equation and experimental values. We have made the table to compare the experiment and theoretical values of result:

Although we have follow the procedure correctly we still have a large amount of error that occur so we have list all the error that may contribute to this problem.

The precaution step that we must take to overcome the error is to:

1. Avoid parallax error while take the reading.2. Make sure we take the right angle.3. Water should be filling carefully and slowly.4. Make sure the hydrostatic pressure equipment is stable when taking a reading.5. Using colour liquid for easy to take reading.

MUHAMMAD KHAIROL BIN MOHD KHIZAM

AB07026

Angle Theorical Yp Experiment Yps0 82 530 89 650 92 7820 71 8520 75 10220 79 111

During this experiment, we have encounter a several matters that may effect to our result. A precaution and a suitable action must be taken in order to minimize the error occur during the data reading. Below this is the several things that may effecting our result ;

1. Parallax Error is the main and a big problems for us to get a precise readings. The measurement is difficult thing when we cannot see the line of the surface water clearly. Hence, a colorant have to be used in order to provide us a clear line.

2. The procedure during handling the apparatus have to done carefully. The apparatus are quite sensitive during the process of applying load and adding the water. Any careless mistake will earn to the error in our result.

3. Correct technique during taken the readings. As the tester, one should have learn and study the process and technique to take the measurement. It is better if there are two people working to take the measurements.

9.0 Conclusion

GOPI S/O VESUVAPATERAN

AB07006

We had determined the magnitude of hydrostatic force which acting on vertical and inclined plane submerged surface. The total average error occurs are 29%. Yp

(experiment) we get for No.1,2 and 3 with 350g,400g and 450g weight at 00 angle is 53mm,65mm and 78mm, and yp (theory) for No.1,2 and 3 is 82mm, 89, and 92. The percentage of error for No.1,2 and 3 is 35%,27% and15%. While, yp (experiment) we get for No.4,5 and 6 with 350g,400g, and 450g at 200 is 85mm,102mm,and 111mm and yp (theory) for No.4,5 and 6 is 71mm,75mm,and 79mm. The percentage of error occur for No.4,5 and 6 is 20%,36% and 41%. The error can be reduce by taking more than 1 reading for each and make average. Other than that, if the water used have colour, may be blurry can be avoid which can reduce the error. Purpose of this experiment is to determine the centre of hydrostatic pressure which used to design structure for dam, water tank and much more.

NOR HASLINDA BINTI MOHAMAD ZAINUDIN

AB07063

From this experiment we can determine the magnitude of hydrostatic force which acting on vertical and inclined plane submerged surface. We also can determine the location of hydrostatic force, yρ (both theoretical and experimental by experimental and theoretical, yρs). And lastly we can compare theoretical and experimental yρ values. For 0 angle we get yρ 82mm, 89mm and 169mm. for 20 angle we get yρ 71mm,75mm and 79mm. in this experiment we must carefully when take a reading and make sure your eyes perpendicular with the reading. Add the color of water, to see the different color to get more good result. This experiment also very useful to determine the total forces acting at the dam. With this, the dam can be design correctly to support all of the water forces safely.

TENGKU NUR ZULAIKHA BT TG CHEK

AB07070

For the conclusion we had obtained the values of yd and the errors are bigger that it was supposed to be not more than 10% to get the exact value of yd. we can avoid errors while reading the data by colouring the water inside the container and stay at the position where observer eyes at the exact same level to make sure that we get the exact value. Lastly after the experiment is done we managed to archived the objectives of this experiment.

KHAIRUL HAZWAN BIN MD KHALID

AB07099

After doing this experiment we have manage to achieve all the objective given. We have managed to determine the magnitude of hydrostatic force which acting on vertical and inclined plane submerged surfaces. We also managed to determine the location of hydrostatic force with theoretical and experimental value. And lastly we have manage to compare the theoretical and experimental values. Although there are error that occur when doing this experiment we are learning and have list the precaution that must be take in doing this experiment.

MUHAMMAD KHAIROL BIN MOHD KHIZAM

AB07026

For the conclusion, we conclude as this experiment we make is successful and achieved the objectives for this experiment. We also are getting a small error in this experiment as the error cannot be avoided during the test.We have some suggestions we can give to improve the accuracy reading such as the method from manual can change it into digital reading version and the liquid that we use to fill the mould is colored in darkness color so we can more easily to take a reading. This experiment is to find the equilibrium of force. This experiment also very useful to determine the total forces acting at the dam. With this, the dam can be design correctly to support all of the water forces safely.

FACULTY OF CIVIL ENGINEERING & EARTH RESOURCES

HYDRAULIC & HYDROLOGY LABORATORY

ENGINEERING LAB 2 SUBJECT CODE ENGINEERING LAB II (DAA 2931)

EXPERIMENT TITLE CENTRE OF HYDROSTATICS PRESSURE

DATE OF EXPERIMENT 15TH JANUARI 2009

GROUP NUMBER GROUP 1

GROUP MEMBER NAME & ID NUMBER

1. GOPI S/O VESUVAPATERAN (AB07006)2. MUHAMMAD KHAIROL BIN MOHD KHIZAM

(AB07026)3. KHAIRUL HAZWAN BIN MD KHALID (AB07099)4. TENGKU NUR ZULAIKHA BT TG CHEK(AB070)5. NOR HASLINDA BINTI MOHAMAD ZAINUDIN

(AB07063)LECTURER PN. WAFTY BINTI ABD RAHMAN

REMARKS

ENDORSEMENT

TABLE OF CONTENT

10.0 Appendix

NO. TITLE PAGE

1.0 INTRODUCTION AND PRINCIPLES

2.0 OBJECTIVE

3.0 APPARATUS

4.0 PROCEDURE

5.0 RESULT AND CALCULATION

6.0 DISCUSSION

7.0 CONCLUSION

8.0 APPENDIX