Physics:Total pressure

In physics, the term total pressure may indicate two different quantities, both having the dimensions of a pressure:

• In fluid dynamics, total pressure ([math]\displaystyle{ p_0 }[/math]) refers to the sum of static pressure p, dynamic pressure q, and gravitational head, as expressed by Bernoulli's principle:

[math]\displaystyle{ p_0 = p + q + \rho g z\, }[/math]

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:

[math]\displaystyle{ p_0 = p + q\, }[/math]

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: [math]\displaystyle{ q = 1/2 \rho v^2 }[/math]

• In a mixture of ideal gases, total pressure refers to the sum of each gas' partial pressure.