where (using SI units):
dynamic pressure in pascals (i.e., kg⋅m−1⋅s−2), fluid mass density (e.g. in kg/m3, in SI units), flow speed in m/s.
It can be thought of as the fluid's kinetic energy per unit volume.
For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by
where and are the total and static pressures, respectively.
Dynamic pressure is the kinetic energy per unit volume of a fluid. Dynamic pressure is one of the terms of Bernoulli's equation, which can be derived from the conservation of energy for a fluid in motion.
At a stagnation point the dynamic pressure is equal to the difference between the stagnation pressure and the static pressure, so the dynamic pressure in a flow field can be measured at a stagnation point.
Another important aspect of dynamic pressure is that, as dimensional analysis shows, the aerodynamic stress (i.e. stress within a structure subject to aerodynamic forces) experienced by an aircraft travelling at speed is proportional to the air density and square of , i.e. proportional to . Therefore, by looking at the variation of during flight, it is possible to determine how the stress will vary and in particular when it will reach its maximum value. The point of maximum aerodynamic load is often referred to as max q and it is a critical parameter in many applications, such as launch vehicles.
The dynamic pressure, along with the static pressure and the pressure due to elevation, is used in Bernoulli's principle as an energy balance on a closed system. The three terms are used to define the state of a closed system of an incompressible, constant-density fluid.
When the dynamic pressure is divided by the product of fluid density and acceleration due to gravity, g, the result is called velocity head, which is used in head equations like the one used for pressure head and hydraulic head. In a venturi flow meter, the differential pressure head can be used to calculate the differential velocity head, which are equivalent in the adjacent picture. An alternative to velocity head is dynamic head.
Many authors define dynamic pressure only for incompressible flows. (For compressible flows, these authors use the concept of impact pressure.) However, the definition of dynamic pressure can be extended to include compressible flows.
and also , dynamic pressure can be rewritten as:
gas (static) pressure (expressed in pascals, in the SI system) mass density (in kg/m3) is always the product between number density and the gas average molecular mass Mach number (non-dimensional), ratio of specific heats (non-dimensional; 1.4 for air at sea-level conditions), flow speed in m/s, speed of sound in m/s
- Pressure head
- Hydraulic head
- Total dynamic head
- Drag, lift and pitching moment coefficients
- Derivations of Bernoulli equation
- L. J. Clancy (1975), Aerodynamics, Pitman Publishing Limited, London. ISBN 0-273-01120-0
- Houghton, E.L. and Carpenter, P.W. (1993), Aerodynamics for Engineering Students, Butterworth and Heinemann, Oxford UK. ISBN 0-340-54847-9
- Liepmann, Hans Wolfgang; Roshko, Anatol (1993), Elements of Gas Dynamics, Courier Dover Publications, ISBN 0-486-41963-0 CS1 maint: discouraged parameter (link)
- Clancy, L.J., Aerodynamics, Section 3.5
- Clancy, L.J., Aerodynamics, Section 3.12 and 3.13
- "the dynamic pressure is equal to half rho vee squared only in incompressible flow."
Houghton, E.L. and Carpenter, P.W. (1993), Aerodynamics for Engineering Students, Section 2.3.1
- Clancy, L.J., Aerodynamics, Section 10.2
- Liepmann & Roshko, Elements of Gas Dynamics, p. 55.
- Definition of dynamic pressure on Eric Weisstein's World of Science