Static pressure

Static pressure in fluid dynamics

The concept of pressure is central to the study of fluids. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods.

The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. These two pressures are not pressures in the usual sense - they cannot be measured using a pressure sensor. To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure; the term static pressure is identical to the term pressure, and can be identified for every point in a fluid flow field. The static pressure can be measured in flowing fluid using a hole or tube which is perpendicular to the flow.

In Aerodynamics, L.J. Clancy writes: "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure."

Bernoulli's equation is foundational to the dynamics of incompressible fluids. In many fluid flow situations of interest, changes in elevation are insignificant and can be ignored. With this simplification, Bernoulli's equation for incompressible flows can be expressed as

${\displaystyle P+\frac{1}{2}\rho v^2=P_0,}$

where:

• ${\displaystyle P}$ is static pressure,
• ${\displaystyle \frac{1}{2}\rho v^2}$ is dynamic pressure, usually denoted by ${\displaystyle q}$,
• ${\displaystyle \rho }$ is the density of the fluid,
• ${\displaystyle v}$ is the flow velocity, and
• ${\displaystyle P_0}$ is total pressure which is constant along any streamline. It is also known as the stagnation pressure.

Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own static pressure ${\displaystyle P}$, dynamic pressure ${\displaystyle q}$, and total pressure ${\displaystyle P_0}$. Static pressure and dynamic pressure are likely to vary significantly throughout the fluid but total pressure is constant along each streamline. In irrotational flow, total pressure is the same on all streamlines and is therefore constant throughout the flow.

The simplified form of Bernoulli's equation can be summarised in the following memorable word equation:

static pressure + dynamic pressure = total pressure.

This simplified form of Bernoulli's equation is fundamental to an understanding of the design and operation of ships, low speed aircraft, and airspeed indicators for low speed aircraft – that is aircraft whose maximum speed will be less than about 30% of the speed of sound.

As a consequence of the widespread understanding of the term static pressure in relation to Bernoulli's equation, many authors in the field of fluid dynamics also use static pressure rather than pressure in applications not directly related to Bernoulli's equation.

The British Standards Institution, in its Standard Glossary of Aeronautical Terms, gives the following definition:

4412 Static pressure The pressure at a point on a body moving with the fluid.