Pressure coefficient
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.
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:
Using Bernoulli's Equation, the pressure coefficient can be further simplified for potential flows (inviscid, and steady):
where u is the flow speed at the point at which pressure coefficient is being evaluated, and Ma is the Mach number: the flow speed is negligible in comparison with the sound speed. For a case of an incompressible but viscous fluid, this represents the profile pressure coefficient, since it is associated to the pressure hydrodynamic forces rather than to the viscous ones.
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