Pressure coefficient
Encyclopedia
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.
where:
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.
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
. The only time the coefficient will exceed plus one is when advanced boundary layer control techniques, such as blowing, is used.
(the dynamic pressure) 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. (It is always true in isentropic
flow but the presence of shock wave
s can cause the flow to depart from isentropic.) As a result, pressure coefficients can be greater than one in compressible flow.
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.
The coefficient of lift for an airfoil 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
is the trailing edge
When the lower surface
is higher (more negative) on the distribution it counts as a negative area as this will be producing down force rather than lift.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
. The pressure coefficient is used in aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
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
Wind tunnel
A wind tunnel is a research tool used in aerodynamic research to study the effects of air moving past solid objects.-Theory of operation:Wind tunnels were first proposed as a means of studying vehicles in free flight...
or water tunnel
Water tunnel (hydrodynamic)
A water tunnel is an experimental facility used for testing the hydrodynamic behavior of submerged bodies in flowing water. It is very similar to a recirculating wind tunnel but with water as the working fluid, and related phenomena are investigated, such as measuring the forces on scale models of...
, 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 very useful 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 iswhere:
-
is the pressure at the point at which pressure coefficient is being evaluated -
is the pressure in the freestreamFreestreamThe freestream is the air far upstream of an aerodynamic body, that is, before the body has a chance to deflect, slow down or compress the air. Freestream conditions are usually denoted with a \infty symbol, e.g. V_\infty, meaning the freestream velocity...
(i.e. remote from any disturbance) -
is the freestream fluid densityDensityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
(Air at sea levelSea levelMean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...
and 15 °C is 1.225
) -
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
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
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 pressureStagnation pressureIn fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...
and the point is a stagnation pointStagnation pointIn fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object...
. -
of minus one is significant in the design of glidersGlider (sailplane)A glider or sailplane is a type of glider aircraft used in the sport of gliding. Some gliders, known as motor gliders are used for gliding and soaring as well, but have engines which can, in some cases, be used for take-off or for extending a flight...
because this indicates a perfect location for a "Total energy" port for supply of signal pressure to the VariometerVariometerThe term variometer also refers to a type of variable transformer or an instrument for measuring the magnitude and direction of a Magnetic field....
, 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
Stagnation pressure
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...
. The only time the coefficient will exceed plus one is when advanced boundary layer control techniques, such as blowing, is used.
Compressible flow
In the flow of compressible fluids such as air, and particularly the high-speed flow of compressible fluids, (the dynamic pressure) is no longer an accurate measure of the difference between stagnation pressureStagnation pressure
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...
and static pressure
Static pressure
In fluid mechanics the term static pressure has several uses:* In the design and operation of aircraft, static pressure is the air pressure in the aircraft’s static pressure system....
. Also, the familiar relationship that stagnation pressure
Stagnation pressure
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...
is equal to total pressure does not always hold true. (It is always true in isentropic
Isentropic process
In thermodynamics, an isentropic process or isoentropic process is one in which for purposes of engineering analysis and calculation, one may assume that the process takes place from initiation to completion without an increase or decrease in the entropy of the system, i.e., the entropy of the...
flow but the presence of shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
s can cause the flow to depart from isentropic.) 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 attackAngle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...
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 an airfoil 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 is the trailing edgeWhen the lower surface
is higher (more negative) on the distribution it counts as a negative area as this will be producing down force rather than lift.See also
- Lift coefficientLift coefficientThe lift coefficient is a dimensionless coefficient that relates the lift generated by a lifting body, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body...
- Drag coefficientDrag coefficientIn fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...
- Pitching moment coefficient