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Lab Manual 2.3 - Level 1 Determination of Metacentric Height
civi; engineering (Universiti Teknologi MARA)
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FACULTY OF CIVIL ENGINEERING
UNIVERSITI TEKNOLOGI MARA
COURSE
COURSE CODE
LEVEL OF OPENNESS
CATEGORY
DEGREE OF OPEN
ENDED
PERIOD OF ACTIVITY
LAB NO
TITLE
DIPLOMA IN CIVIL ENGINEERING
LABORATORY MANUAL
WATER ENGINEERING LABORATORY
ECW341
33%
Traditional
1
1 WEEK
2.3
DETERMINATION OF METACENTRIC HEIGHT
INTRODUCTION
The traditional methods of conducting laboratory activities (assigned as Level
0) will not be able to provide the avenue for students to enhance independent
learning activities and inculcate creativity and innovation. The traditional
method is fully prescriptive where the three elements namely problem, ways &
means and answers are provided/fully given to the students.
OBJECTIVES
The objective of the test is:
To identify the position of the metacentre (M) of a floating body, by referring the
distance from the centre of gravity (G).
PREAMBLE
LEARNING OUTCOMES
At the end of the laboratory works, students should be able to:
i)
Conduct and construct the metacentric height laboratory experiments.
(CO1 – PO4)
ii) Analyze and interpret the data based on obtained data. (CO2 – PO6)
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FACULTY OF CIVIL ENGINEERING
UNIVERSITI TEKNOLOGI MARA
DIPLOMA IN CIVIL ENGINEERING
LABORATORY MANUAL
THEORETICAL BACKGROUND
In these laboratory activities students will be exposed to the equipment that
used to measure the metacentric height of pontoon. For static equilibrium of
the pontoon, the total weight, 𝑊, (which acts through the centre of gravity, 𝐺)
must be equal to the buoyancy force which acts through the centre of buoyancy
𝐵, which is located at the centroid of the immersed cross-section. When the
pontoon heels through a small angle, the metacentre 𝑀 is identified as the point
of intersection between the lines of action of the buoyancy force (always
vertical) and 𝐵𝐺 extended. For stable equilibrium, 𝑀 must be above 𝐺.
There are two methods to measure the metacentric height, GM.
FOR ADJUSTABLE POSITION TRAVERSED WEIGHT EXPERIMENT
When the traversing weight is moved to one side, the centre of gravity, 𝐺, shifts
to a new position, 𝐺 ′ , and the centre of buoyancy, 𝐵, also shifts to a new
position, 𝐵′ as shown in Figure 1.
Since the shift in the centre of gravity was caused by moving the weight, 𝑃
through a distance 𝑥, then:
Px = W(GG′ )
(5.1)
Figure 1: Movement of adjustable weight from the centerline
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(5.2)
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FACULTY OF CIVIL ENGINEERING
UNIVERSITI TEKNOLOGI MARA
DIPLOMA IN CIVIL ENGINEERING
LABORATORY MANUAL
𝐺𝐺 ′ = 𝐺𝑀 𝑡𝑎𝑛𝜃
𝐺𝑀 =
𝑃𝑥
𝑐𝑜𝑡𝜃
𝑊
(5.3)
Where
𝑃 = weight of movable mass
𝑥 = distance between the movable mass and the mast of the pontoon
BASED UPON GEOMETRY AND DEPTH OF IMMERSION
The metacentric height, 𝐺𝑀, is defined as
𝐺𝑀 = 𝐵𝑀 − 𝐵𝐺
(5.4)
The metacentric radius, 𝐵𝑀, can be defined as
𝐵𝑀 =
𝐼
𝑉
(5.5)
where
𝐼= the second moment of area of the plane of floating about an axis through
the centroid perpendicular to the plane of rotation, as the pontoon heels.
𝑉= the immersed volume
The immersed volume, 𝑉 can be determined by calculation. Since the buoyant
force (upthrust) is equal to the total weight, 𝑊, of the pontoon and its load then,
𝜌𝑔𝑉 = 𝑊
The depth of immersion, 𝑑𝑖 can then be found from
𝑉 = 𝐿𝑏𝑑𝑖
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(5.6)
(5.7)
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FACULTY OF CIVIL ENGINEERING
UNIVERSITI TEKNOLOGI MARA
DIPLOMA IN CIVIL ENGINEERING
LABORATORY MANUAL
The point 𝐵 is the centroid of immersed area. It is at distance 𝑑𝑖 ⁄2 from the
base. The centre of gravity 𝐺 is at a distance 𝑦 above the base (Figure 2). By
substitution from above, the following result is obtained.
𝐺𝑀 =
𝑏2
𝑑𝑖
(𝑦 − )
12𝑑𝑖
2
(5.8)
M
G
y
di
di/2
B
b
Figure 2: Section through a floating pontoon
An important application of the buoyancy concept is the assessment of the
stability of immersed and floating bodies when being placed in a fluid. Knowing
metacentre, M location is vital and great importance in the design of ships and
submarines. The body is said stable if M is above G and unstable if otherwise.
PROBLEM STATEMENT
Students are required to perform a relevant experiment to fulfil the objective
stated above using both method namely adjustable position traversed weight
experiment and based upon geometry and depth of immersion. For
computation purpose, the students are asked to find the equations from the
literature or existing manual for fluid and hydraulic laboratory
APPARATUS
WAYS AND MEANS
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FACULTY OF CIVIL ENGINEERING
UNIVERSITI TEKNOLOGI MARA
DIPLOMA IN CIVIL ENGINEERING
LABORATORY MANUAL
Metacentric height apparatus, hydraulic bench, weigh balance, ruler, knife
edge or fine string. The following dimensions from the equipment are used in
the appropriate calculations. If required these values may be checked as part
of the experimental procedure and replaced with your own measurement.
Pontoon data width 200 mm, length 400 mm, height 100mm. Jockey weight
200 g, adjustable weight 500 g and total weight is 2520 g.
PROCEDURE
i)
Weight a) the assembled pontoon, b) the traversed weight (horizontal)
and measure pontoon dimensions.
ii) Each group should have difference centre of gravity compare to
others. In order to change the centre of gravity, slide the traverse
weight on mast to the desired location. Below are the suggested
locations of the traversed weight to determine the centre of gravity.
Group 1 = 16 cm from base
Group 2 = 17 cm from base
Group 3 = 18 cm from base
Group 4 = 19 cm from base
iii) Locate the pontoon’s centre of gravity, y by balancing the mast of
pontoon on a knife edge.
iv) Place the pontoon in the water.
v) Adjust the traverse weight (horizontal) to its middle position. The
plumb bob should now read “0” tilt angle. If not, adjust the line
accordingly.
vi) Move the traverse weight slightly to right side (1 cm) and record the
angle of tilt. (Note: observe the line marked by the plumb bob.
Measure height of mast in order to calculate the angle of tilt)
vii) Repeat step 5 until maximum tilt or until the pontoon is unstable.
viii) Repeat step 5 and 6 by moving the traverse weight to the left side.
RESULTS
The group is required to submit the technical report of the laboratory results
highlighting the apparatus used, the procedures undertaken for the test, data
acquisition process, analysis carried out and the relevancy of the set-out output
to address the given problem.
In your discussion, explain experimental factors which could have contributed
to variation of results compare to theoretical calculation.
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