Game Development Reference

In-Depth Information

where
P
is the pressure at a point in the fluid volume under consideration, γ is the specific

weight of the fluid,
z
is the elevation of the point under consideration,
V
is the fluid

velocity at that point, and
g
is the acceleration due to gravity. As you can see, if the

expression on the left is to remain constant, and assuming that
z
is constant, then if

velocity increases the pressure must decrease. Likewise, if pressure increases, then ve‐

locity must decrease.

As you can see in
Figure 6-5
, the pressure will be greatest at the stagnation point,
S
l
, and

will decrease around the leading side of the sphere and then start to increase again

around the back of the sphere. In an ideal fluid with no friction, the pressure is fully

recovered behind the sphere and there is a trailing stagnation point,
S
t
, whose pressure

is equal to the pressure at the leading stagnation point. Since the pressure fore and aft

of the sphere is equal and opposite, there is no net drag force acting on the sphere.

The pressure on the top and bottom of the sphere will be lower than at the stagnation

points since the fluid velocity is greater over the top and bottom. Since this is a case of

symmetric flow around the sphere, there will be no net pressure difference between the

top and bottom of the sphere.

In a real fluid there is friction, which affects the flow around the sphere such that the

pressure is never fully recovered on the aft side of the sphere. As the fluid flows around

the sphere, a thin layer sticks to the surface of the sphere due to friction. In this
boundary

layer
, the speed of the fluid varies from 0 at the sphere surface to the ideal free stream

velocity, as illustrated in
Figure 6-6
.

Figure 6-6. Velocity gradient within boundary layer

This velocity gradient represents a momentum transfer from the sphere to the fluid and

gives rise to the frictional component of drag. Since a certain amount of fluid is
stick‐

ing
to the sphere, you can think of this as the energy required to accelerate the fluid and

move it along with the sphere. (If the flow within this boundary layer is laminar, then

the viscous shear stress between fluid “layers” gives rise to friction drag. When the flow

is turbulent, the velocity gradient and thus the transfer of momentum gives rise to

friction drag.)