# Pressure coefficient

Physical key figure
Surname Pressure coefficient,
pressure coefficient
Formula symbol ${\ displaystyle c _ {\ mathrm {p}}}$
dimension dimensionless
definition ${\ displaystyle c _ {\ mathrm {p}} = {\ frac {p-p _ {\ infty}} {{\ frac {1} {2}} \, \ rho \, c _ {\ infty} ^ {2} }}}$
 ${\ displaystyle p}$ pressure ${\ displaystyle p _ {\ infty}}$ Pressure of the inflow ${\ displaystyle \ rho}$ density ${\ displaystyle c}$ Flow velocity
scope of application viscous currents

The pressure coefficient , often also referred to as the pressure coefficient , is a dimensionless quantity from aerodynamics that is often used in the design and analysis of wings , but also in other areas of aerodynamics, e.g. B. with internal currents. ${\ displaystyle c _ {\ mathrm {p}}}$

He will u. a. used to describe or graph the pressure distribution on the wing of aircraft ; The pressure distribution means the pressure on all points on the entire surface of the wing.

In relation to a certain point, the pressure coefficient represents the ratio of static pressure to dynamic pressure .

The pressure coefficient at the end of a body that flows through (e.g. a valve ) is called the pressure loss coefficient .

## formula

The pressure coefficient is defined as follows:

${\ displaystyle c _ {\ mathrm {p}} = {\ frac {p-p _ {\ infty}} {{\ frac {1} {2}} \, \ rho \, c _ {\ infty} ^ {2} }}}$

Assuming an incompressible flow ( Ma  <0.3) also applies:

${\ displaystyle c _ {\ mathrm {p}} = 1- \ left ({\ frac {c} {c _ {\ infty}}} \ right) ^ {2}}$

Here are:

• ${\ displaystyle p}$ = the static pressure measured at a given point
• ${\ displaystyle p _ {\ infty}}$ = the static pressure in the inflow
• ${\ displaystyle \ rho}$= the density of the surrounding medium (e.g. air )
• ${\ displaystyle c}$= Amount of the local speed of the surrounding medium (e.g. air); instead of is often also used or for the velocity component in the x direction.${\ displaystyle c}$${\ displaystyle v}$${\ displaystyle w}$
• ${\ displaystyle c _ {\ infty}}$= the flow velocity of the surrounding medium (analogous are also and common)${\ displaystyle v _ {\ infty}}$${\ displaystyle w _ {\ infty}}$

## meaning

The denominator of the fraction represents the back pressure is (or dynamic pressure) of the free inflow, therefore, 1 is the highest value that the pressure coefficient can be reached in an incompressible flow around rigid body and without energy supply (in stagnation point ). ${\ displaystyle {\ frac {1} {2}} \, \ rho \, c _ {\ infty} ^ {2}}$

The sign of the derivation of the pressure according to the length of the run indicates whether the flow is accelerated or decelerated compared to the inflow: ${\ displaystyle {\ frac {\ mathrm {d} p} {\ mathrm {d} x}}}$

• negative signs mean pressure decrease (i.e. acceleration)
• positive signs indicate pressure increase (i.e. areas where the flow is decelerated or at friction-prone flow detaches ).

By relating the coefficient to the dynamic pressure, the distribution of the pressure coefficient around a body does not change if the speed, density or static pressure of the inflow change, because then all the individual values ​​of the coefficient distributed around the body change in the same or similar way . The distribution also applies to all geometrically similar bodies. The actual pressures can therefore be calculated for a large range of flight speeds and altitudes from the pressure distribution around a wing profile .

Strictly speaking, these relationships only apply in a smooth, incompressible flow, but can often be used as a sufficient approximation in the general case. They do not apply to: Positions behind collisions, in the boundary layer , in flows with detachments and in flows with a variable position of the transition point between laminar and turbulent boundary layer.