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If we consider an object moving through air at some point in space, from Newton’s second law of
motion, the aerodynamic force
on the object is directly related to the change in momentum of
the fluid with time . The fluid momentum is equal to the mass
times the velocity .
Since the air moves, defining the mass is difficult. If the mass of fluid were brought to a halt, it
would occupy some volume in space. We can therefore define the density
mass divided by the volume
of the fluid to be the
Since the fluid is moving, we must determine the mass in terms of the mass flow rate. The mass
flow rate is the amount of mass passing a given point during some time interval
and its units
are mass/time. We can relate the mass flow rate to the density intuitively. The mass flow
is equal to the density times the velocity times the area
through which the mass passes.
We can check this using dimensional analysis
With knowledge of the mass flow rate, we can express the aerodynamic force as equal to the
mass flow rate times the velocity.
Again we check the dimensions
We now have a simple equation for the force due to air resistance. In practice this equation is not
very accurate as modelling the drag force is an incredibly complex procedure that is usually
dependent on two complex factors; drag pressure and drag friction. We can however say “As the
size and/or speed of the body increases, in due course the flow of fluid past the body becomes
disorderly and turbulent. For example the, the flow of air past an automobile moving 100 km/h is
quite turbulent. Turbulence leads to a much larger drag. In fact, experiment shows that when
turbulence is present, the magnitude
of the force is approximately proportional to
, the
square of the body’s speed. The experimental results are described as a good approximation by
the empirical law for turbulent flow” [_]:
We see that the coefficient from equation _____ is approximated for objects that have similar
shape to vehicles and the slight variations of shape can be accounted for in the drag
. We note that this equation can only be applied for high velocities. For low
velocities Stokes’ law is used to the calculate drag force. This isn’t necessary for our purpose so