In fluid dynamics, the pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field. 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. Definition The pressure coefficient is a parameter for studying both incompressible/compressible fluids such as water and air. The relationship between the dimensionless coefficient and the dimensional numbers is where: is the static pressure at the point at which pressure coefficient is being evaluated is the static pressure in the freestream (i.e. remote from any disturbance) is the stagnation 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 Incompressible flow Using Bernoulli's equation, the pressure coefficient can be further simplified for potential flows (inviscid, and steady): where is the flow speed at the point at which pressure coefficient is being evaluated, and is the Mach number: the flow speed is negligible in comparison with the speed of sound. For a case of an incompressible but viscous fluid, this represents the profile pressure coefficient, since it is associated with the pressure hydrodynamic forces rather than the viscous ones. This relationship is valid for the flow of incompressible fluids where variations in speed and pressure are sufficiently small that variations in fluid density can be neglected. 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 corresponds to the stagnation pressure and indicates a stagnation point. the most negative values of in a liquid flow can be summed to the cavitation number to give the cavitation margin. If this margin is positive, the flow is locally fully liquid, while if it is zero or negative the flow is cavitating or gas.