In physics, the term total pressure may indicate two different quantities, both having the dimensions of a pressure:
* In fluid dynamics, total pressure refers to the sum of static pressure p, dynamic pressure q, and gravitational head, as expressed by Bernoulli's principle for incompressible flow: where ρ is the density of the fluid, g is the local acceleration due to gravity, and z is the height above a datum. If the variation in height above the datum is zero, or so small it can be ignored, the above equation reduces to the following simplified form: Because this is the static pressure that occurs in locations where the fluid flow is entirely stopped (stagnated), this case is also called the stagnation pressure. A fluid can lose total pressure through energy dissipation. An example is the friction between the fluid and a pipe inner surface. The dynamic pressure is calculated using the density and velocity of the fluid:
* In a mixture of ideal gases, total pressure refers to the sum of each gas' partial pressure. For compressible flow the isentropic relations can be used (also valid for incompressible flow): At standard conditions the scientific community usually takes as the threshold to compressibility. Flows with a higher Mach number cannot approximate the total pressure using the incompressible formula given above. At non-standard conditions the flow may be considered compressible at lower Mach numbers. An example would be a flow through a long insulated pipe where wall friction is not neglected. Then the flow's temperature increases farther down the pipe and must be considered compressible after some length. The higher the pressure and temperature are, the less good the incompressible formula becomes. At standard conditions and low Mach numbers it is very good and widely used.
