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In fluid dynamics, dynamic pressure (denoted by q or Q and sometimes called velocity pressure) is the quantity defined by: [1] = where (in SI units): q is the dynamic pressure in pascals (i.e., N/m 2, ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s.
The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached.
The last equation may be identified as the pressure coefficient, meaning that Newtonian theory predicts that the pressure coefficient in hypersonic flow is: = For very high speed flows, and vehicles with sharp surfaces, the Newtonian theory works very well.
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...
A solution of the potential equation directly determines only the velocity field. The pressure field is deduced from the velocity field through Bernoulli's equation. Comparison of a non-lifting flow pattern around an airfoil; and a lifting flow pattern consistent with the Kutta condition in which the flow leaves the trailing edge smoothly
The first equation is a pressureless governing equation for the velocity, while the second equation for the pressure is a functional of the velocity and is related to the pressure Poisson equation.
The choked velocity is a function of the upstream pressure but not the downstream. Although the velocity is constant, the mass flow rate is dependent on the density of the upstream gas, which is a function of the upstream pressure. Flow velocity reaches the speed of sound in the orifice, and it may be termed a sonic orifice.
This pressure is the stagnation pressure of the fluid, also known as the total pressure or (particularly in aviation) the pitot pressure. The measured stagnation pressure cannot itself be used to determine the fluid flow velocity (airspeed in aviation). However, Bernoulli's equation states: Stagnation pressure = static pressure + dynamic pressure