RESULT%
Student number(s):
2
Surname and initials:
KGENGWE KT
Programme:
Dip Eng Tech (Mechanical Engineering)
Module name:
FLUID MECHANICS I
Module code:
0
M
Assignment/project
number:
2
0
3
M
1
Graduate Attribute (GA)
assessment:
Due date:
2
2
2
C
4
6
4
1
0
9
1
A
9
1
0
2
3
0M
M5
0D
3D
Mr L Masheane
Lecturer:
DECLARATION OF OWN WORK:
I,
_____KGOTSO
THEODOCIUS
KGENGWE_________________________________________________________, student
number_______220032409_______________________________, hereby declare that the
content of this assignment/project is my own work, as defined and constituted in the Rules
and Regulations of the Central University of Technology, Free State (Please consult the
Programme Guide of the Department).
Signed:
_______K .T KGENGWE_________________________
Date:
_____17 March 2023___________________________
Table of Contents
Aim: ......................................................................................................................................................... 3
Apparatus: ............................................................................................................................................... 3
Procedure: ............................................................................................................................................... 4
Theory: .................................................................................................................................................... 4
Experimental Data................................................................................................................................... 7
Results: .................................................................................................................................................... 8
Graphs: .................................................................................................................................................... 9
Causes for Error..................................................................................................................................... 10
Conclusion ............................................................................................................................................. 11
Reference .............................................................................................................................................. 11
Aim:
This experiment aims to determine the hydrostatic force acting on a partially or fully
submerged surface in water and the depth of centre of pressure at which forces are acting.
Furthermore, to determine and analyse the relationships of hydrostatic force and canter
of pressure with respect to the height of the water in the pressure system chamber.
to confirm that these relationships are represented in the given equations, and to
assess the accuracy of the measurements produced by the Edibon Hydrostatics Pressure
System.
Apparatus:
1)
7)
2)
8)
3)
4)
5)
6)
9)
10)
Figure 1: Edibon Hydrostatics Pressure system
1- Level Indicator
7- Spirit Level
2- Balance Arm
8- Weight Hanger
3- Clamping Screw
9- Quadrant
4- Scale
10- Adjustable Feet
5- Knife Edge Pivot
11- Drain Valve
6- Counterbalance
12- Water
11)
12)
Procedure:
Begin the experiment by measuring the dimensions of the quadrant vertical end face (B and
D) and the distances (H and L) and also measure the radius of the arc, and then perform the
experiment by taking the following steps:
A) Clean the quadrant with a moist rag to eliminate surface tension and prevent the
formation of air bubbles.
B) When the built-in circular spirit level indicates that the base is horizontal, position the
apparatus on a level surface and adjust the screwed-in feet as necessary. Using the spirit
level to adjust the feet until the air bubble is in the centre of the black circle.
C) Balance the arm by adjusting the counterbalance until the central index mark on the
beam reaches the level indicator.
D) Place the weight hanger on the end of the balance arm and level the arm, using the
counterweight, so that the balance arm is horizontal.
E) The practical consists of two cases, Partially and fully submerged surface in water, both
consist of different masses(given) to be added separately on weight hanger.
F) After adding required mass as prescribed (mass is given to be added consecutively
separately per case)
G) Add water to the tank and allow time for the water to settle
H) Close the drain valve at the end of the tank, then slowly add water until the hydrostatic
force on the end surface of the quadrant is balanced. This can be judged by aligning the base
of the balance arm with the top or bottom of the central marking on the balance rest.
I) Record the water height, which displayed on the side of the quadrant in mm. If the
quadrant is partially submerged, record the reading in the partially submerged portion of
the Raw Data Table.
J) Repeat the steps, adding 50 g weight each time, until the final weight of 500 g is reached.
When the quadrant is fully submerged, record the readings in the fully submerged part of
the Raw Data Table.
K) Repeat the procedure in reverse by progressively removing the weights.
L) Release the water valve, remove the weights, and clean up any spilled water.
Theory:
Hydrostatic force is the pressure exerted by a fluid due to the weight of fluid above the
surface. Hydrostatic pressure and its resulting force have a wide variety of applications.
Thus, it is important to be able to measure and develop equations for hydrostatic
force due to pressure as well as the canter of pressure at which this force acts.
One device used to measure hydrostatic force is an Edibon Hydrostatics Pressure system.
This device (fig. 1) is based on the principle that the sum of the moments about
the pivot must be equal to zero. Thus, the moment due to the weight of the masses
applied to the left end must be equal to the moment due to the hydrostatic force acting on
the vertical rectangular quadrant. When known masses are applied to the end of the system,
the pivot rotates. In order to balance the moment caused by the weight of the masses
and return the pivot to equilibrium, water is added into the chamber of the pressure system.
In this experiment, when the quadrant is immersed by adding water to the tank, the
hydrostatic force applied to the vertical surface of the quadrant can be determined by
considering the following:
• The hydrostatic force at any point on the curved surfaces is normal to the surface and
resolves through the pivot point because it is located at the origin of the radii. Hydrostatic
forces on the upper and lower curved surfaces, therefore, have no net effect – no torque to
affect the equilibrium of the assembly because the forces pass through the pivot.
• The forces on the sides of the quadrant are horizontal and cancel each other out (equal
and opposite).
• The hydrostatic force on the vertical submerged face is counteracted by the balance
weight. The resultant hydrostatic force on the face can, therefore, be calculated from the
value of the balance weight and the depth of the water.
• The system is in equilibrium if the moments generated about the pivot points by the
hydrostatic force and added weight (=mg) are equal.
Partial immersion: (y < d)
Resultant force=
Centre of pressure=D
(Theoretical)
Moment of
(Experimental)
Moment of 𝑅𝑒𝑥𝑝 = Moment of weight = mgl
=mgl
Fully immersion: (y > d)
Resultant force=R = 𝜌𝑔𝑏𝑑𝑦̅ (Theoretical)
Centre of pressure=
Moment of
(Experimental)
Moment of 𝑅𝑒𝑥𝑝 = Moment of weight = mgl
= mgl
Experimental Data
Partially sub-merged
Mass(g)
Y(cm)
1.
40
4
2.
60
5
3.
4.
5.
80
100
120
5,8
6,6
7,3
6.
140
7,9
Fully sub-merged
Mass(g)
Y(cm)
1.
240
10,7
2.
260
11,1
3.
280
11,7
4.
300
12,1
5.
320
12,75
6.
340
13,2
Calculations
Partial immersion: (y < d)
= (0.5)(1000)(9.81)(0.075)(0.04)2
= 588.6× 10−3N
= mgl
= (0.04) (9.81) (0.275)
= 107.91× 10−3N
=mgl
=
107.91×10−3 𝑁
(0.1)+(0.1)−
(0.04)
3
= 578.089× 10−3N
Fully immersion: (y > d)
Resultant force=R = 𝜌𝑔𝑏𝑑𝑦̅ (Theoretical)
= (1000) (9.81) (0.075) (0.1) (0.057)
= 4193.775 N
= (0.107) -
0.1
2
= 0.057m
= mgl
=
(0.24)(9.81)(0.275)
0.1
(0.1) 2
)−
2
12(0.057)
(0.1)+(
= 4782.5× 10−3N
Results:
Partially immersed:
y
(m)
R
−3
(× 10 N)
a+d-
𝑦
3
(m)
m
(kg)
mgl
R(experimental)
(× 10−3N)
0.04
588.6
0.1867
0.04
0.1079
578.1
0.05
919.688
0.1833
0.05
0.1619
882.9
0.058
1237.532
0.1807
0.058
0.2158
1194.6
0.066
1602.464
0.178
0.066
0.2658
1515.6
0.073
1960.406
0.1757
y (m) R (× 10−3N)
0.073


d
d2 

a
+
+
_ 

2
12 y 

0.3237
m
1842.9
mgl
Rexp
(× 10−3N)
(m)
0.107
4193.8
0.1501
0.107
0.6475
4782.5
0.111
4488.1
0.1501
0.111
0.7014
5144.6
0.117
4929.5
0.1501
0.117
0.7554
5491.1
0.121
5223.8
0.1501
0.121
0.8093
5853.5
0.1275
5702.1
0.1501
0.1275
0.8633
6199.6
0.132
6033.15
0.1501
0.132
0.9199
6578.6
0.079
2295.908
0.1737
0.079
0.3777
2174.8
Fully immersed:
Graphs:
Theoretical resultant force
Experimental resultant force
Resultant vs y
2500
2000
1500
1000
500
0
0
0,01
0,02
0,03
0,04
Series1
0,05
Series2
0,06
0,07
0,08
0,09
Partially submerged surface
Experimental Resultant force
Theoretical Resultant force
Radius vs y
7000
6000
5000
4000
3000
2000
1000
0
0
0,02
0,04
0,06
Series1
0,08
0,1
0,12
0,14
Series2
Fully submerged surface
Causes for Error.
While in general the results seem to be in line with what is expected, the big impact seems
to be occurred in the graph of fully submerged surfaces there is still the possibility of error.
This may be due to a variety of mistakes in the experiment. For example, there is the
possibility of human error in reading when the balance bridge arm is level. This would lead
to an inaccurate water height reading, which would consequently affect everything height
was used to calculate. There may also have been human error in reading the height of the
water in the chamber: also affecting the height measurement and all subsequent
calculations. Experimentally, a source of error may be in the possibility of water splashing
onto the balance bridge arm while it was poured. This would cause an artificial increase in
weight beyond the weight due to the applied masses. As a result, the hydrostatic force to
counteract the
Masses moment would also be artificially high, and an artificially high-water height would
be read off the pressure system. Finally, the applied masses were not weighed prior to their
application onto the balance bridge arm. Thus, the applied mass may weigh more due to
accumulation of oils from being handled. As a result, an artificially high mass would be
recorded, resulting in what appears to be a water height that it too high. However, these
errors are so minor that it is likely that, even if they were present in the experiment, they
would have little, to no, effect on the results.
Conclusion
The Edibon Hydrostatic Pressure system accurately measures the hight of the water in the
chamber needed to calculate both hydrostatic force acting on the vertical rectangular
quadrant and the canter of pressure at which this force acts, with a low standard deviation
from the theoretical water height for both partially and fully submerged surfaces. This is
confirmed by the linear plots of theoretical versus measured water height in which the slope
is approximately on of the partially and fully submerged surfaces. The data gathered from
the pressure system also supports the relationship between variables as they are presented
in the equations given to calculate hydrostatic force, canter of pressure, and mass. In other
words, the hydrostatic force acting on both partially and fully submerged vertical rectangular
surface increases as the height of fluid (water) in the chamber increases.
Reference
Çengel, Y. A., & Cimbala, J. M. (2014). In Fluid mechanics: Fundamentals and
Applications (3rd ed., pp. 38-‐59). New York, NY: McGraw-‐Hill Higher
Education.