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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.)
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