So what is pressure drag? In order to understand
that. We have to understand what drag itself
is. This occurs when a body is moving through
a fluid, and when we have drag. We assume
that there is not only pressure forces, but
there are viscous forces as well. So the forces
that oppose movement. Are what is known as
drag, and we have 2 main components of drag.
We have friction drag, which is due to a tangential
force we call tau. We also have pressure drag,
and pressure drag is due to the pressure on
the object and it is a normal force. So lets
take a look at some examples. If we consider
a flat plate, and we are going to incline
this plate, and you have some velocity of
the fluid. Normal to the plate you have your
pressure forces. Tangential to the plate you
have your friction forces. So lets take a
look at a couple of other situations. What
would happen if you had a plate that was parallel
to the direction of the flow. Well there you
will only have tangential forces. We are considering
this a template. So there will be no normal
forces. The opposite situation is when you
have a thin plate that is perpendicular to
the flow. So again we have a u going this
way, and now we only have normal forces or
pressure forces. If you look at a sphere for
example, and you look at flow pass the sphere.
So here we have a sphere and we have some
velocity of a fluid coming in. You will see
that we not only have normal forces that are
pressure. Up here we also have these tangential
forces, which are our friction drag. So as
you can see by looking at this the greater
the area of the forces that are acted on.
In other words the bigger the object the greater
the drag that is on this. So why would be
interested in drag. Well it has a great impact
on things such as acceleration, because it
is drag that causes the deceleration of a
drag car, or if you have parachute it is the
deceleration of this parachute. That makes
sure you hit the ground at a safe speed. So
lets take a look at the pressure drag. So
when we are look at the pressure drag. What
we are really look at are these forces that
are normal. So this drag is the integral of
the pressure times its position in another
words the angle that it hits at. So its orientation
times our differential area, and we define
a dimensionless coefficient of pressure drag
as this drag, and here we go d of p because
it is the pressure of drag over 1/2 times
rho times u^2 divided by the area. You can
see that this coefficient of drag depends
on area and velocity. If we rewrite this,
it is this integral times its pressure times
the cosine of theta, da divided by our 1/2,
rho, u^2,A and we let this equal our Cp, which
is our coefficient of pressure times the cosine
of theta, da, which is in the integral divided
by area, where our Cp equals p- some reference
pressure, divided by rho, u^2, divided by
2.This pressure coefficient is actually a
dimensionless form of the pressure. So you
might want to know. What about this reference
pressure? Well the level doesn't influence
the drag directly because what you are really
looking for is the net pressure force on the
body, and that is 0 if the pressure is constant
on the entire surface. So what happens if
the inertial forces are large. What that means
is that we have a large Re number. If that
is the case our pressure coefficient is independent
of the Re. However if we have viscous forces
that are large. Now our Re number cannot be
neglected, and the drag coefficient is proportional
to 1 over Re. What if the viscosity were 0.
Then you would have no pressure drag in a
steady flow at all. There would be large pressure
forces on the front portion, but you would
have the opposite and equally large forces
on the rear.
