# Stability of Floating Body (E2)

**Topics:**Buoyancy, Archimedes, Fluid statics

**Pages:**10 (2747 words)

**Published:**April 23, 2013

SKPU 1711

FLUIDS MECHANICS LABORATORY

2012 / 2013 - SEM 2

TITLE OF EXPERIMENT

STABILITY OF FLOATING BODY (E2)

SECTION 04

NO.| TEAM MEMBERS| MATRIC NO.|

1.| KHAIRUL AIZAT BIN SALEH| A11KP0088|

2.| HAZIQ FIKRI BIN AHMAD ZUHARDI| A11KP0052|

3.| FATIN FARHANA BT MOHD FADLULLAH| A11KP0070|

LECTURER NAME: DR GOH PEI SEAN

DATE OF EXPERIMENT: 28th February 2013

DATE OF SUBMISSION: 7th March 2013

1.0 TITLE

The title of this experiment is stability of floating body.

2.0 REPORT SUMMARY

The report is prepared for the sake of discussing about the principle in fluid mechanics which is the stability of floating body which relates to the concept of centre of gravity and the location centre of buoyancy. The appropriate location these two are matters since they will determine whether or not a random floating body is either stable or not when placed in water. By theory, we know that when the centre of buoyancy point of the body is higher/same than the centre of gravity, hence the body is in neutral stability while if the case is opposite, otherwise will happen. Hence, the experiment is conducted to prove this theory and according to the analysis prepared in Section 7.0 (p. 11), the theory is proven to be correct.

3.0 INTRODUCTION

In physics, buoyancy is an upward acting force, caused by fluid pressure, which opposes an object's weight. If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat. This can occur only in a reference frame which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction (that is, anon-inertial reference frame). In a situation of fluid statics, the net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body. This is the force that enables the object to float.

3.1 Objective

The objective of this experiment is to determine the height of meta-center using tilting method.

4.0 THEORY OF EXPERIMENT

The knowledge on the stability of pontoon such as a floating ship is important. Whether the ship is stable, unstable or at critical condition, it is determined by the height of the centre of gravity. In this experiment, the stability of a pontoon is determined with the centre of gravity at different heights. A body in a fluid, whether floating or submerged, is buoyed up by a force equal to the weight of the fluid displaced. The results obtained from the experiment can be compared mathematically by Archimedes` principle as follows: Fb = γfVd

Fb =Buoyant force γf = Specific weight of the fluid Vd =Displaced volume of fluid

When a body is floating freely, it displaced a sufficient volume of fluid to balancing their own weight. The analysis of problems dealing with buoyancy requires the application of the equation of static equilibrium in the vertical direction.

The condition for the floating bodies is different for the completely submerged bodies. The reason is show in the figure 3.1 and figure 3.2.

Figure 4.1 shows that the floating body is at equilibrium orientation and exhibit neutral stability. In this case, the centre of gravity (CG) is above centre of buoyancy (CB). In the other hand, figure 4.2 shows when the body rotates slightly, the centre of buoyancy shift to a new position because the geometry of the displaced volume has changed. The buoyant force (Fb) and weight (W) now produce the righting couple to return the body to its original position.

The meta-centre (MC) defined as the intersection of the vertical axis of a body when in its equilibrium position and the...

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