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== Pressure ==
Three types of pressure are used in the physics of flying. This section introduces the concepts, which will be used subsequently in later sections.
Gliding is a kind of low speed flying, so we shall ignore compressiblility effects where applicable: a note will be made when this happens.
Pressure is a potential. It measures the ability of some gas to do useful mechanical work. Compressed gas can be used to move a piston and start an engine, for example, because that gas is at high pressure. Thus, a gas at some pressure also has some energy associated with it. Understanding this part will show that some definitions are not invented in random.
=== Definitions ===
==== Static pressure ====
The static pressure, denoted as \(p\), is a thermodynamic property of the air. By the ideal gas Equation of State, the static pressure can be determined if the density and temperature is known.
==== Dynamic pressure ====
The dynamic pressure is a quantity (i.e. not a thermodynamic property) that describes the energy due to the motion of a fluid. If a body of mass \(m\) is moving at speed \(V\), then the kinetic energy it has is found to be:
\[E_K = \frac{1}{2} m V^2 \]
This can be shown by considering the work input to accelerate the body from rest to the speed \(V\).
We need something similar to describe the kinetic energy of a moving fluid, and we need this to have the dimensions of pressure. It is found that the following quantity is suitable:
\[p_D = \frac{1}{2} \rho V^2 \]
where \(p_D\) is defined as the '''dynamic pressure'''. It is the kinetic energy of one unit volume of fluid moving at the speed \(V\).
==== Total pressure ====
The '''total pressure''', also known as the '''stagnation pressure''', is a sum of the static and dynamic pressures. \[ p_0=== How p+p_D \] It is the pressure that the fluid will reach if it is '''stagnated''', i.e. brought to a rest from motion. If you stick an object into water flow (try this with a finger, be sure not to measure use hot water), you will observe the water level increase a bit in front of that object, which is a consequence of stagnating the water increasing its pressure ===, reflected in depth. There is an extra requirement that the stagnation happens in an isentropic manner, but this is usually true when we consider air at low speeds. In fact, the stagnation of air is usually treated as isentropic unless we know it is not (for example, if we know a shock wave is present). Not being isentropic means mechanical energy is dissipated in the process, if you spill water on the ground and let itself come to a rest, you will not observe the level rise, for example.
=== Pressure coefficient ===
=== How to measure pressure ===
== Atmosphere ==
