The pressure coefficient is a dimensionless number which describes the
relative pressures throughout a flow field in fluid dynamics. The pressure
coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid
flow field has its own unique pressure coefficient, .
In many situations in aerodynamics and hydrodynamics, the pressure coefficient
at a point near a body is independent of body size. Consequently an engineering
model can be tested in a wind tunnel or water tunnel, pressure coefficients can
be determined at critical locations around the model, and these pressure
coefficients can be used with confidence to predict the fluid pressure at those
critical locations around a full-size aircraft or boat.
Incompressible flow The pressure coefficient is a parameter
for studying the flow of incompressible fluids such as water, and also the
low-speed flow of compressible fluids such as air. The relationship between
the dimensionless coefficient and the dimensional numbers is
where: is the pressure at the point at which
pressure coefficient is being evaluated is the pressure in the freestream
is the freestream fluid density is the freestream velocity of the fluid,
or the velocity of the body through the fluid
Using Bernoulli's Equation, the pressure coefficient can be further simplified
for incompressible, lossless, and steady flow:
where V is the velocity of the fluid at the point at which pressure coefficient
is being evaluated. This relationship is also valid for the
flow of compressible fluids where variations in speed and pressure are
sufficiently small that variations in fluid density can be ignored. This is a
reasonable assumption when the Mach Number is less than about 0.3.
of zero indicates the pressure is the same as the free stream pressure.
of one indicates the pressure is stagnation pressure and the point is a
stagnation point. of minus one is significant in the
design of gliders because this indicates a perfect location for a "Total energy"
port for supply of signal pressure to the Variometer, a special Vertical Speed
Indicator which reacts to vertical movements of the atmosphere but does not
react to vertical maneuvering of the glider.
In the fluid flow field around a body there will be points having positive
pressure coefficients up to one, and negative pressure coefficients including
coefficients less than minus one, but nowhere will the coefficient exceed plus
one because the highest pressure that can be achieved is the stagnation
pressure. Compressible flow
In the flow of compressible fluids such as air, and particularly the high-speed
flow of compressible fluids, is no longer an accurate measure of the
difference between stagnation pressure and static pressure. Also, the familiar
relationship that stagnation pressure is equal to total pressure does not always
hold true. As a result, pressure coefficients can be greater than one in
compressible flow. greater than one indicates the
freestream flow is compressible. Pressure distribution
An airfoil at a given angle of attack will have what is called a pressure
distribution. This pressure distribution is simply the pressure at all points
around an airfoil. Typically, graphs of these distributions are drawn so that
negative numbers are higher on the graph, as the for the upper surface of
the airfoil will usually be farther below zero and will hence be the top
line on the graph. and relationship
The coefficient of lift for a two-dimensional airfoil section with
strictly horizontal surfaces can be calculated from the coefficient of
pressure distribution by integration, or calculating the area between the lines
on the distribution. This expression is not suitable for direct numeric
integration using the panel method of lift approximation, as it does not take
into account the direction of pressure-induced lift.
where: is pressure coefficient on the lower
surface is pressure coefficient on the upper
surface is the leading edge location
is the trailing edge location When the lower surface is higher on the
distribution it counts as a negative area as this will be producing down
force rather than lift. See also
Lift coefficient Drag coefficient
Pitching moment coefficient References
Clancy, L.J. Aerodynamics, Pitman Publishing Limited, London. ISBN
0-273-01120-0 Abbott, I.H. and Von Doenhoff, A.E.
Theory of Wing Sections, Dover Publications, Inc. New York, Standard
Book No. 486-60586-8 Anderson, John D Fundamentals of
Aerodynamic 3rd Edition, McGraw-Hill. ISBN 0-07-237335-0