Game Development Reference

In-Depth Information

Buoyancy

You've no doubt felt the effects of buoyancy when immersing yourself in the bathtub.

Buoyancy is why you feel lighter in water than you do in air and why some people can

float on their backs in a swimming pool.

Buoyancy is a force that develops when an object is immersed in a fluid. It's a function

of the volume of the object and the density of the fluid and results from the pressure

differential between the fluid just above the object and the fluid just below the object.

Pressure increases the deeper you go in a fluid, thus the pressure is greater at the bottom

of an object of a given height than it is at the top of the object. Consider the cube shown

in
Figure 3-2
.

Figure 3-2. Immersed cube

Let
s
denote the cube's length, width, and height, which are all equal. Further, let
h
t

denote the depth to the top of the cube and
h
b
the depth to the bottom of the cube. The

pressure at the top of the cube is
P
t
=
ρ
g h
t
, which acts over the entire surface area of

the top of the cube, normal to the surface in the downward direction. The pressure at

the bottom of the cube is
P
b
=
ρ
g h
b
, which acts over the entire surface area of the bottom

of the cube, normal to the surface in the upward direction. Note that the pressure acting

on the sides of the cube increases linearly with submergence, from
P
t
to
P
b
. Also, note

that since the side pressure is symmetric, equal and opposite, the net side pressure is 0,

which means that the net side force (due to pressure) is also 0. The same is not true of

the top and bottom pressures, which are obviously not equal, although they are opposite.

The force acting down on the top of the cube is equal to the pressure at the top of the

cube times the surface area of the top. This can be written as follows:

F
t
= P
t
A
t