1) The document describes an experiment to determine the stability of a floating body. It involves measuring the angle of tilt caused by moving a jockey weight along a submerged apparatus at different heights. 2) Calculations are shown to determine values like the metacentric height, center of gravity, and the distance between the center of buoyancy and center of gravity. 3) The results show that as the jockey weight height increases, the center of gravity rises and the horizontal movement causes a greater angle of tilt. The metacentric height was found to be greater than the distance between the center of buoyancy and center of gravity, indicating the body is stable.

1. University of Duhok
College of Engineering
Civil Department
Fluid Mechanics – Practical
Fluid Laboratory
A Report About :
Stability of a Floating Body
Student Name : Jameel Masoud Jameel
Class : B
Date of Experimental : 4 / 1 / 2018
Date of Submitting : 11 / 1 / 2018
Experiment No. : 5

2. Procedure :
1) Make sure stability apparatus is correct, all dimension and
weight that may be needed in calculation must be noted, if not
given.
2) Move the jockey weight to the center of the bottom of sall, then
put the stability apparatus into water.
3) Wait until apparatus don’t move in the water (oscillating), then
from plumb line and angular scale read the angle of rotation.
4) Repeat the procedure but just change the position of the jockey
weight two unit from center to the right and left side.
5) After all reading from a bottom's row are finished, then rise the
jockey weight (60 mm) from the bottom row (second row from
bottom) and put it to the center of the row.
6) Repeat the procedure (3 and 4) until the jockey weight gain to
the highest row in the sall.

3. Calculations and Results :
Note:[
Mass of Pontoon (WP) = 2.43 kg , mass of jockey (Wi) = 0.391 kg
Total mass of apparatus = 2.43 + 0.391 = 2.821 kg
Length of pontoon (L) = 360.1 mm
Breadth of Pontoon (B) = 201.8 mm
Area of pontoon (A) = 0.3601 × 0.2018 = 0.07267 m2
Volume displacement (V) =
2.821 kg
1000 kg/m3
= 0.002821 m3
Moment of inertia (IC.G) =
0.3601×0.20183
12
= 0.0002466 m4
Depth of immersion (OC) =
0.002821
0.07267
= 38.8 mm
Height of center of buoyancy B above O (OB) =
38.2
2
= 19.4 mm
Table of Angle of tilt caused by jockey displacement Average
Jockey
Height
(deg.)
Jockey
Height
yi (mm)
Jockey Displacement from Center Xi (mm)
-45 -30 -15 0 15 30 45
105 -7.8 -5.2 -2.7 0 2.6 5.2 7.8 2.60
165 -6.2 -3.1 0 3.2 6.2 4.13
225 -7.7 -3.8 0 3.9 7.8 5.17
285 -5.2 0 5.2 5.20
345 -7.5 7.4 7.45
- Making Average Jockey Height
For example : When Jockey height 105 mm
7.8 - 5.2 = 2.6 5.2 - 2.6 = 2.6 2.6 – 0 = 2.6
7.8 - 5.2 = 2.6 5.2 - 2.7 = 2.5 2.7 - 0 = 2.7
Average Jockey height (dθ) =
2.6+2.6+2.6+2.6+2.7+2.5
6
= 2.60 deg.
- The ratio between Horizontal movement to the average angle (
dx
dθ
) when Jockey
height 105 mm is : :
dx
dθ
=
15
2.6
= 5.77
mm
deg.
×
180 deg.
π rad
= 𝟑𝟑𝟎. 𝟔 𝐦𝐦
𝐫𝐚𝐝⁄
- Note : All our calculation we just use dx = Xi = 15mm

4. - Metacentric (GM) height when jockey weight 105 mm height will be :
GM =
Wi
W
∗
dx
dθ
=
0.391 × 330.6
2.821
= 45.8 mm
- Center of Gravity (OG) for all movement of Jockey Weight :
For Example : For all Changing of 60mm (∆yi) from vertical :
OG =
WJockey × ∆yi
Wall
=
0.391 × 60
2.821
= 8.3162mm
Table of Heights OG of G above base O of Pontoon
yi (mm) 105 165 225 285 345
OG (mm) 58.7 67.0 75.3 83.6 92.0
- (BM) will be determined by using this formula :
BM = OG + GM – 19.4
For Example : OG = 58.7 mm ,GM = 45.8 mm
BM = 58.7mm + 45.8mm – 19.4mm = 85.1 mm
Metacentric Height Derived Experimentally
yi (mm) OG (mm) Xj θ⁄ (mm/rad) GM (mm) BG (mm) BM (mm)
105 58.7 330.6 45.8 39.3 85.1
165 67.0 207.9 28.8 47.6 76.4
225 75.3 166.3 23.1 55.9 79.0
285 83.6 165.3 22.9 64.2 87.2
345 92.0 115.4 16.0 72.6 8 8.6
Note : in this table just Xj = 15mm is used.
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
BG(mm)
Xj/ɵ (mm/degree)

5. Discussion and Conclusion :
In this test we determine the metacentric height and the distance between
center of volume displaced by the body and the center of gravity of
submerged body, and finally we got a result after doing all procedure
accuracy, which is the (BM) and (BG) and (GM). as shown in result,
with increasing the height between bottom of platform and jockey weight
the center of gravity will increase from bottom and the horizontal
movement will increase the angle of tilt. All of result shows that (BM)
is greater than (BG) and it mean's that our body that we submerged will
stable and don’t sink down, we don’t say we have some errors because
our angle of tilt is given because the our apparatus doesn’t work
correctly, therefore we use an available reading which is angle of tilt for
all movement of horizontal and vertical.
In conclusion the purpose of this test is to determine the stability of an
submerged body, to know what's buoyancy, and how we can calculate
the center of buoyancy and volume displacement. finally we will get and
determine the center of buoyancy and stability of submerged body, to
know our body will float or sink down.