1. The document describes an experiment conducted to determine hydrostatic pressure and the center of pressure acting on a plane surface using a hydrostatic pressure apparatus. 2. The experiment involved setting the apparatus at an angle, balancing it by adding weights, and measuring the water level as more weights were added. 3. Calculations were done to find theoretical and practical hydrostatic pressures using equations for the area, height, resultant force, and center of pressure. The results showed some difference between theoretical and practical pressures.

1. Soran University
Faculty of Engineering
Department of Petroleum Engineering
Fluid Mechanic
Title: Hydrostatic Pressure
Experiment No.: 3
Name: Muhammad Sulaimon Rasul
Group: B2
Date: 15 OCT 2019
Supervisors: Ms Marriam, Mr. Shahab, Mr. Sarkar

2. Contents
Aim………………………………………………………………………………………….…….1
Theory…………………………………………………………………………………….…….…1
Apparatus…………………………………………………………...…………………………..…2
Procedure………………………………………………………………………………………….3
Calculation………………………………………………………………………………...………4
Result and Discussion……………………………………………………………………………..6
Conclusion………………………………………………………………………………………...6
References…………………………………………………………………………………………7
List of Figures
Figure 1 Hydrostatic pressure apparatus ………………………………………………………….2
Figure 2 Schematic image of hydrostatic force apparatus………………………………..……….3
List of Tables
Table 1: Experimental and Theorical Results……………………………………………………..5

3. Aim
The objective is to determine:
1. The hydrostatic pressure acting on a plane surface either surface is fully submerged or
partially.
2. The center of pressure acting on the plane surface by the experiment and theorical position
Theory
Building and evaluating fluid system is necessary to know hydrostatic force and the center of
pressure equations and a device for performing the tests before the designing a fluid system.
Hydrostatic pressure is a force exerted by a fluid to an area at rest because of its weight against the
surface area. Hydrostatic pressure has a wide variety application, thus its very important to know
the equations and how to measure and develop them for hydrostatic force and the center of pressure
when this force acting on the surface area (Çengal et al., 2014).
A device used to measure hydrostatic force named hydrostatic pressure apparatus. The concept of
the device (fig. 1) is the sum of the moments about the pivot should equals zero. The moment of
hydrostatic force which acting on the vertical rectangular quadrant should equals to the weight of
the masses applied to the left. When masses added to the system, the pivot rotates in order to
equivalent the moment which caused by the mass and return the system to equilibrium, water
added to the chamber. The height of water, center of pressure, hydrostatic force and the weight of
masses can be determined using series of equations, however the equations for partially or fully
submerged surface are different (Humpherys, 1991).
Equations are used in order to determine the hydrostatic pressure, Resultant force.
𝐴 = 𝐵 ∗ ℎ/𝑠𝑖𝑛Ө …………………………………….………..…………………….….……… ..(1)
ℎ′
=
ℎ
2
……………………………………………………………………………...…………..(2)
ICG = (B.H3
)/12 ………………………………………………………………………….…….....(3)
F= ϒ. ℎ′
. 𝐴 ……………………………………………………………………………………….(4)
HPth =
𝐼𝑐
ℎ′ 𝐴
Sin2
Ө+ℎ′ ……………………………………………………………………………(5)
Po= 𝐹𝑔.
𝐿
𝐹
……………………………………………….………………………………………..(6)
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4. Hp Practical = h-(1.2-Po)sin Ө …………………………………………………………………(7)
Apparatus and Materials
Materials: Water.
Apparatus and Equipment’s:
• Hydrostatic pressure apparatus which is a device used to measure hydrostatic force and
center of pressure. (Figure 1)
• Weights: are used to balance the system. (Figure 1 - Weights)
Figure 1 Hydrostatic pressure apparatus system with weights applied to the arm on the left, the
provide in equilibrium (right) and the chamber or vessel filled with water.
4. Water Vessel
2. Rotary pin1. Slider
6. Weights
5. Rider (Pivot)
2
3. Detent7. Stop pin

5. Procedure
1. The water vessel (4) at fig.1 should set the angle to Ө=70o
using the detent (3).
2. Balance the system by rotating the slider (1). The stop pin should be exactly fixed on the
arm.
3. Move the rider (5) and set it on a scale.
4. Fill the vessel with water until it gets balanced.
5. Read the water level and record it to the table 1.
6. Now increase the weights on the left (6) in increment of 50-100g and repeat the procedure
until it gets balanced again.
Figure 2 Schematic image of hydrostatic pressure apparatus with the measurement parameters and
the locations of resultant force, center of pressure.
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6. Calculation
4

7. 5

8. Result and Discussion
Table 1: Experimental and Theorical Results for angle Ө=70o
.
For X
gms.
Level
Arm (L)
in m
Mass
in kg
Weigh
(Fg) in
N
Water
Level (h)
in m
Resultant
Force (F)
in N
Hp (th) in
cm
Hp(pr)
in cm
50 0.33 0.050 0.4905 0.05 1.3 3.3 15.61
150 0.33 0.1 0.981 0.08 3.33 5.33 16
250 0.33 0.1 0.981 0.1 0.127 56.7 247.9
The calculated results for Hp in theorical way and Hp in practical are something different from
each other which the Hp for theorical has first calculated the area using the eq.1 then calculating
the h` using the eq. 2, by putting h which equals to H for the partial submerged water H=h for the
first case which the level of water is partially submerged but if it was totally submerged then H=0.1
m. It should be notice that if the water was totally submerged; then the calculation for h` will be
calculated with another equation which its h`=h-105sin Ө. The calculation for Ic will be executed
on the eq. 3 by putting B and H to the equation. The resultant force has to be calculated also using
the eq. 4 in N s, then by putting Ic, h`, Ө, and A into the HP theorical eq. 5; the theorical hydrostatic
pressure can be calculated. For the result Hp(pr) in the table 1 which stands of “practical
hydrostatic pressure” as the eq.7 which Po should be calculated before using the eq.6, after Po has
been calculated the practical HP can be measured using eq.7. The same procedure of calculation
should be applied for No. 2 and No. 3 in the Table 1.
Conclusion
Practical and theorical hydrostatic pressure have measured using a hydrostatic pressure apparatus
and calculating the resultant force acting on the plane addition to the center of pressure Po using
some formulas which was one the objectives in this experiment.
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9. References
Cengel, Y.A., & Cimbala, J.M. (2014). In Fluid mechanics: Fundamentals and Applications
(3rded., pp.38--‐59). New York, NY: McGraw--‐Hill Higher Education.
Humpherys, A. S. (1991). Center-of-Pressure Gates for irrigation. Applied Engineering in
Agriculture, ppt 185-192.
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