# Buoyancy & Floatation Highlights

## Buoyancy & Floatation in points :

1- The upward force exerted by a liquid on a body when the body is immersed in the liquid is known as buoyancy or force of buoyancy.

2- The point through which force of buoyancy is supposed to act is called center of buoyancy.

3- The point about which a body starts oscillating when the body is tilted is known as meta-center.

4- The distance between the meta-center and center of gravity is known as meta-centric height.

5- The meta-centric height GM is given by :

$GM = \frac{I}{V} - BG$

where :

I : moment of inertia of the floating body (in plan) at water surface about the axis Y-Y

V : volume of the body submerged in water

BG : distance between center of gravity and center of buoyancy

6- Conditions of equilibrium of a floating body are :

• Stable equilibrium occurs for a floating body when M is above G
• Unstable equilibrium occurs for a floating body when M is below G
• Neutral equilibrium occurs for a floating body when M and G coincide

7- Conditions of equilibrium of a submerged body :

• Stable equilibrium occurs for a submerged body when B is above G
• Unstable equilibrium occurs for a submerged body when B is below G
• Neutral equilibrium occurs for a submerged body when B and G coincide

8- The value of meta-centric height GM experimentally is given by :

$GM = \frac{{{w_1} \times x}}{{W \times \tan \theta }}$

where :

w1 : movable weight

x : distance through which w1 is moved

W : weight of the ship or floating body including w1

θ : angle through the ship or floating body is tilted due to the movement of w1

9- The time period of oscillation or rolling of a floating body is given by :

$T = 2\pi \sqrt {\frac{{{K^2}}}{{GM \times g}}}$

where :

GM : meta-centric height

T : time of one complete oscillation

You can also check other Fluid Mechanics Highlights on the following links :

Fluid Mechanics - Fluid Properties Highlights

Fluid Mechanics - Fluid Statics Highlights

Fluid Mechanics - Hydrostatic Forces on Surfaces Highlights

Fluid Mechanics - Fluid Kinematics Highlights

Fluid Mechanics - Dynamics of Fluid Flow Highlights