Quick From Eq1 below:
The static pressure is P.
The dynamic pressure is ρv2/2.
The stagnation pressure is the sum of static and dynamic pressures, as given by Eq2 below.
The Bernoulli equation states that the sum of the flow, kinetic, and potential energies of a fluid particle along a streamline is constant. Therefore, the kinetic and potential energies of the fluid can be converted to flow energy (and vice versa) during flow, causing the pressure to change. This phenomenon can be made more visible by multiplying the Bernoulli equation by the densityρ:
(Eq1)
P + ρ
v2
2
+ ρgz = constant
Each term in this equation has pressure units, and thus each term represents some kind of pressure:
• P is the static pressure (it does not incorporate any dynamic effects); it represents the actual thermodynamic pressure of the fluid. This is the same as the pressure used in thermodynamics property tables.
• ρv2/2 is the dynamic pressure; it represents the pressure rise when the fluid in motion is brought to a stop isentropically.
• ρgz is the hydrostatic pressure, which is not pressure in a real sense since its value depends on the reference level selected; it accounts for the elevation effects, i.e., of fluid weight on pressure.
The sum of the static, dynamic, and hydrostatic pressures is called the total pressure. Therefore, the Bernoulli equation states that the total pressure along a streamline is constant.
The sum of the static and dynamic pressures is called the stagnation pressure, and it is expressed as:
(Eq2)
Pstag = P + ρ
v2
2
The stagnation pressure represents the pressure at a point where the fluid is brought to a complete stop isentropically. The static, dynamic, and stagnation pressures are shown in the following figure:
When static and stagnation pressures are measured at a specified location, the fluid velocity at that location can be calculated from:
Eq3 is useful in the measurement of flow velocity when a combination of a static pressure tap and a Pitot tube is used, as illustrated above. In situations in which the static and stagnation pressure of a flowing liquid are greater than atmospheric pressure, a vertical transparent tube called a piezometer tube (or simply a piezometer) can be attached to the pressure tap and to the Pitot tube, as shown above. The liquid rises in the piezometer tube to a column height (head) that is proportional to the pressure being measured. If the pressures to be measured are below atmospheric, or if measuring pressures in gases, piezometer tubes do not work. However, the static pressure tap and Pitot tube can still be used, but they must be connected to some other kind of pressure measurement device such as a U-tube manometer or a pressure transducer. Sometimes it is convenient to integrate static pressure holes on a Pitot probe. The result is a Pitot-static probe, as shown. A Pitot-static probe connected to a pressure transducer or a manometer measures the dynamic pressure (and thus fluid velocity) directly.
When the static pressure is measured by drilling a hole in the tube wall, care must be exercised to ensure that the opening of the hole is flush with the wall surface, with no extrusions before or after the hole as shown. Otherwise the reading will incorporate some dynamic effects, and thus it will be in error.
When a stationary body is immersed in a flowing stream, the fluid is brought to a stop at the nose of the body (the stagnation point). The flow streamline that extends from far upstream to the stagnation point is called the stagnation streamline as shown. For a two-dimensional flow in the xy-plane, the stagnation point is actually a line parallel the z-axis, and the stagnation streamline is actually a surface that separates fluid that flows over the body from fluid that flows under the body. In an incompressible flow, the fluid decelerates nearly isentropically from its free-stream value to zero at the stagnation point, and the pressure at the stagnation point is thus the stagnation pressure.