CEE320 _ LAB 2_Vergara,Kailah
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CEE 320 Fluid Mechanics Fundamentals Lab
POPPING PLUG TEST
Kailah Vergara
University of Hawaii at Manoa
CEE 320L Fluid Mechanics
(Date)
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
EXECUTIVE SUMMARY
In the experimental setup, we began by inserting a plug and placing a weight on it.
Following this, a hose was introduced into the tank, along with a ruler to measure the
water's height. As the hose was introduced, the tank started filling with water. When the
water level exceeded the position of the weight on top of the plug and filled the tank, we
removed the weight. Subsequently, we turned off the hose and opened the valve at the
bottom of the tank, allowing the water to drain. The tank continued to drain until the
pressure eventually forced the plug out of its position. We recorded the water level at
the moment of the plug's expulsion. After all the water had drained from the tank due to
the absence of the plug, we repeated this test two more times.
The investigation yielded equations for determining "h," buoyancy, equilibrium, and
area when the height is set to zero. The computed measurement for "h" was found to be
5.22 inches, whereas the experimental "h" values were recorded at 16.0 inches, 16.1
inches, and 16.05 inches, revealing a notable difference between the two sets of values,
which defines the position of "h." Figure 2.1 illustrates how "h" corresponds to the
vertical distance between the top of the plug and the water level. Throughout the
experiment, "h" measurements were taken from the tank's bottom to the water level.
The value of A was determined to be 6.424 square inches. Additionally, the Free Body
Diagram of the test and the Pressure Distribution Diagram are presented for reference.
Page
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
TABLE OF CONTENTS
EXECUTIVE SUMMARY………………...……………………………………………………………...i
1
INTRODUCTION
.............................................................................................................................
1
1.1
B
ACKGROUND
..............................................................................................................................
1
1.2
R
EASON
FOR
E
XPERIMENT
...........................................................................................................
1
1.3
T
HEORY
........................................................................................................................................
1
1.4
O
BJECTIVE
...................................................................................................................................
1
2
APPROACH
......................................................................................................................................
2
2.1
T
EST
S
ETUP
AND
I
NSTRUMENTATION
...........................................................................................
2
2.2
T
EST
S
PECIMENS
..........................................................................................................................
3
2.3
T
EST
P
ROCEDURE
.........................................................................................................................
3
3
CALCULATIONS/ EQUATIONS
....................................................................................................
5
4
RESULTS
...........................................................................................................................................
6
4.1 E
XERCISE
1
........................................................................................................................................
6
4.2 E
XERCISE
2
........................................................................................................................................
6
4.3 E
XERCISE
3
........................................................................................................................................
7
4.4 E
XERCISE
4
........................................................................................................................................
7
5
ANALYSIS/ERROR
..........................................................................................................................
9
5.1 C
OMPARING
THE
H
CALCULATED
VALUE
TO
THE
H
EXPERIMENTAL
VALUE
........................................
9
5.2 E
RROR
A
NALYSIS
...............................................................................................................................
9
6
CONCLUSIONS/RECOMMENDATIONS
...................................................................................
10
7
REFERENCES
................................................................................................................................
11
APPENDIX
TABLE OF FIGURES
Figure 2-1:
Popping Plug Lab Test Diagram
............................................................................................
2
Figure 2.3-1: Popping Plug Lab Test Set Up
...............................................................................................
4
Figure 4.1: Pressure Distribution Diagram
..................................................................................................
6
Figure 4.2: Free Body Diagram
...................................................................................................................
6
Figure 4.5: Popping Plug Lab Test Results
.................................................................................................
8
Page
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CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
1
Introduction
1.1
Background
In the case of an incompressible fluid, characterized by its consistent density,
pressure is determined by the product of the fluid's density and the acceleration it
experiences. When the fluid is at rest, pressure is solely influenced by the depth of the
fluid and remains unaffected by the volume of the container housing the fluid, a
phenomenon commonly referred to as hydrostatic distribution.
1.2
Reason for Experiment
When crafting watercraft such as ships or canoes, it is crucial to factor in buoyancy
to prevent them from sinking. To address this concern, the vessel's volume is adjusted
in a manner that minimizes the impact of any weight changes. Additionally, pressure
alterations play a role in ensuring the pipes remain securely in place, preventing
potential issues like popping out and causing complications.
1.3
Theory
The buoyant force arises when an object is immersed in a fluid, creating an upward
vertical force. This upward pressure force escalates with greater depths, implying that
the forces exerted beneath the object exceed those from above it. This force is
equivalent to the weight of the displaced fluid and is commonly known as Archimedes'
principle. If the object's weight is lower than the weight of the displaced fluid, it will
remain afloat.
1.4
Objective
The aim of this laboratory experiment was to investigate the pressure exerted on a
cylindrical plug, leading to its ejection as the water levels in a tank decreased. By
Page
1
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
closely observing this phenomenon, valuable insights can be gained regarding
fundamental fluid mechanics principles, including buoyancy and pressure fluctuations.
2
Approach
(Briefly describe the approach used for this experiment using the following sections)
2.1
Test Setup and Instrumentation
In this experimental setup, we employed a cubic tank, a cylindrical plug with
specified dimensions and mass, and a steel object. The diagram below illustrates the
apparatus when the water level reaches a height 'h' above the inserted cylindrical plug.
Additionally, it provides information about the plug, including 'h1,' the height of the top of
the plug, and the location within the tank where water is discharged.
Figure 2.1: Popping Plug Lab Test Diagram
2.2
Test Specimens
Page
2
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
Given Data: Dimensions of the hollow cylindrical plug.
h
1
=
5
∈
.
D
=
3.5
∈
¿
D
0
=
2
∈
¿
Mass
=
269
g
2.3
Test Procedure
In the test setup, a plug was inserted, and a weight was positioned on top of it.
Subsequently, a hose was introduced into the tank, accompanied by a ruler to gauge
the water's height. As the hose was introduced, the tank commenced filling with water,
and once the water level surpassed the position of the weight atop the plug and filled
the tank, the weight was removed. Consequently, the hose was shut off and the valve at
the bottom of the tank was released allowing the water to drain. The tank continued to
drain the water until the pressure ultimately expelled the plug from its location. The
water level measurement was documented now of the plug's expulsion. Once all the
water had drained from the tank due to the lack of plug, this test was replicated two
more times.
Page
3
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CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
Figure 2.3-1: Popping Plug Lab Test Set Up
Page
4
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
3
Calculations/Equations
P
1
=
¿
h
1
P
2
=(
h
+
h
1
)
F
2
−
F
1
=
hA
+
h
1
(
A
−
A
0
)
−
h A
0
−
hA
=
(
A
−
A
0
)
−
h A
0
=
F
B
−
F
'
F
B
=
Buoyancy
=
h
1
(
A
−
A
0
)
=
¿
Ɐ
B
Ɐ
B
=
h
(
A
−
A
❑
0
)
F
'
=
P
1
∗
A
=
h A
0
F
P
=
F
B
−
F
'
=
h
1
(
A
−
A
0
)−
hA
0
Equilibrium
:
F
0
−
W
=
0
→ F
B
−
F
'
−
W
=
0
h
1
(
A
−
A
0
)
−
h A
0
−
mg
=
0
Height
:
h
=
?
, { h} rsub {1} =5
, D
0
=
2, m=269 g=
9.4887 oz, g=32.2 ft/s^2 = 386.4 in/s^2
:
h
=
h
1
(
A
−
A
0
)
−
m
A
0
=
(
1000
) (
0.127
)
(
(
0.0889
2
π
4
)
−
(
0.0508
2
π
4
)
)
−(
0.269
)
(
1000
)(
0.0508
2
π
4
)
=
0.129
m
=
5.22
∈
¿
h
=
0, { h} rsub {1} =5
,D
0
=
2, m=269 g =
9.4887 oz , g=32.2 ft/s^2 = 386.4 in/s^2
0
=
(
1000
) (
0.127
)
(
A
−
(
0.0508
2
π
4
)
)
−(
0.269
)
(
1000
)(
0.0508
2
π
4
)
→ A
=
0.00414494
m
2
=
6.424
in
2
Page
5
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
4
Results
4.1
Exercise 1
Figure 4.1: Pressure Distribution Diagram
4.2
Exercise 2
Figure 4.2: Free Body Diagram
4.3
Exercise 3
The expression for the equilibrium for the plug:
Page
6
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CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
o
γ h
1
(
A
−
A
0
)
−
γh A
0
−
mg
=
0
The expression for the buoyant force. Show on the diagram, by shading, the
portion of the volume equivalent to the effective buoyant volume:
o
F
B
=
Buoyancy
=
γ h
1
(
A
−
A
0
)
The expression for the height h at which the plug pops up. Also, give the
numerical value in inches and compare with the experimental result:
o
h
=
mg
−
γ h
1
(
A
−
A
0
)
γ A
0
o
h
=
5.22
∈
¿
o
The experimental result showed that the h value for the 3 tests were:
16.0 in, 16.1 in, and 16.05.
4.4
Exercise 4
For what value of A will the plug pop up when h =0?
o
A
=
6.424
in
2
4.5
Lab Test Results
Page
7
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
Figure 4.5: Popping Plug Lab Test Results
Page
8
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
5
Analysis/Error
5.1
Comparing the H calculated value to the H experimental value.
The computed "h" measurement was determined to be 5.22 inches, while the
experimental "h" values yielded measurements of 16.0 inches, 16.1 inches, and 16.05
inches. The disparity between these two sets of values determines the position of "h."
As depicted in the Figure 2.1, the "h" measurement represents the vertical distance
between the top of the plug and the water level. During the experiment, the "h"
measurements are taken from the bottom of the tank to the level of the water.
5.2
Error Analysis
In the experiment, students employed a ruler to gauge the water level's height when
the plug emerged. Errors could potentially arise when the observer's line of sight and
the water level were not perfectly aligned on the same horizontal plane. Furthermore, a
delay of approximately half a second consistently occurred when recording data at the
moment the plug popped up, contributing to potential inaccuracies. However, it is worth
noting that the heights obtained in all three trials closely resembled the theoretical
height, and there were no outliers or problematic data points in the experiment.
Page
9
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CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
6
Conclusions/Recommendations
In this experiment, a hollow cylindrical plug was submerged in a tank filled with
water. As water was gradually drained from the tank, the water level decreased.
With the decreasing water level, the pressure began to decrease while the
buoyancy force acted to push the plug upward.
The moment when the cylindrical
plug dislodged from its position was noted as a water level 'h' which averaged 16.05
inches. Using net force and pressure equations, a theoretical 'h' value was
computed, yielding 5.22 inches.
The cylindrical plug dislodged at a water height 'h' of 16.05 inches.
The theoretical 'h' value was determined to be 5.22 inches.
When h=0 inches the Area is estimated to be 6.424 inch^2.
The expression for the equilibrium for the plug:
o
γ h
1
(
A
−
A
0
)
−
γh A
0
−
mg
=
0
The expression for the buoyant force.
o
F
B
=
Buoyancy
=
γ h
1
(
A
−
A
0
)
The expression for the height h at which the plug pops up.
o
h
=
mg
−
γ h
1
(
A
−
A
0
)
γ A
0
Page
10
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
7
References
Munson, B.R. Okiishi, T.H., Huebsch, W.W., Rothmayer, A.P. Fundamentals of Fluid Mechanics,
9th ed., John Wiley & Sons, NY. ISBN-9781119686545
Page
11
CEE 320L Fluid Mechanics
Fall 2023
Laboratory (No.)
Appendix
A-1
Equations and Sample Calculations
h
avg
=
16
+
16.1
+
16.05
3
=
16.05
inches
A-2
Raw Data
h= 16,16.1, 16.05 in
h
1
=
5
∈
.
D
=
3.5
∈
¿
D
0
=
2
∈
¿
Mass
=
269
g
Page
12
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ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
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