Stability of A Floating Body | Jameel Academy

#Jameel_Academy_Fluid Mechanics_Tests

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 m
2


Volume displacement (V) =
2.821 kg
1000 kg/m
3
=0.002821 m
3

Moment of inertia (IC.G) =
0.3601×0.2018
3
12
=0.0002466 m
4


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
y
i (mm)
Jockey Displacement from Center X
i (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
=??????????????????.??????
????????????
??????????????????
⁄

- Note : All our calculation we just use dx = X
i = 15mm

4. - Metacentric (GM) height when jockey weight 105 mm height will be :

GM=
W
i
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 (∆y
i) from vertical :

OG=
W
Jockey×∆y
i
W
all
=
0.391×60
2.821
=8.3162mm

Table of Heights OG of G above base O of Pontoon
y
i (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) X
jθ⁄ (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
00.511.522.533.544.555.566.5
BG (mm)
X
j/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.