Pressure Coefficient - Incompressible Flow

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 (i.e. remote from any disturbance)

is the freestream fluid density (Air at sea level 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 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. The only time the coefficient will exceed plus one is when advanced boundary layer control techniques, such as blowing, is used.