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at each geopotential altitude, where g is the standard acceleration of gravity, and R specific is the specific gas constant for dry air (287.0528J⋅kg −1 ⋅K −1). The solution is given by the barometric formula. Air density must be calculated in order to solve for the pressure, and is used in calculating dynamic pressure for moving vehicles.
Pressure as a function of the height above the sea level. There are two equations for computing pressure as a function of height. The first equation is applicable to the atmospheric layers in which the temperature is assumed to vary with altitude at a non null lapse rate of : = [,, ()] ′, The second equation is applicable to the atmospheric layers in which the temperature is assumed not to ...
The acceleration resulting from the pressure gradient is then, =. The effects of the pressure gradient are usually expressed in this way, in terms of an acceleration, instead of in terms of a force. We can express the acceleration more precisely, for a general pressure P {\displaystyle P} as, a → = − 1 ρ ∇ → P . {\displaystyle {\vec {a ...
(See graph.) Of course the real atmosphere does not have a temperature distribution with this exact shape. The temperature function is an approximation. Values for pressure and density are then calculated based on this temperature function, and the constant temperature gradients help to make some of the maths easier.
The geopotential thickness between pressure levels – difference of the 850 hPa and 1000 hPa geopotential heights for example – is proportional to mean virtual temperature in that layer. Geopotential height contours can be used to calculate the geostrophic wind , which is faster where the contours are more closely spaced and tangential to ...
g is the acceleration due to gravity, h is height from reference point 0, k is the Boltzmann constant, T is the temperature in kelvins. Therefore, instead of pressure being a linear function of height as one might expect from the more simple formula given in the "basic formula" section, it is more accurately represented as an exponential ...
If the static pressure of the system (the third term) increases, and if the pressure due to elevation (the middle term) is constant, then the dynamic pressure (the first term) must have decreased. In other words, if the speed of a fluid decreases and it is not due to an elevation difference, it must be due to an increase in the static pressure ...
Here the pressure P D is referred to as dynamic pressure due to the kinetic energy of the fluid experiencing relative flow velocity u. This is defined in similar form as the kinetic energy equation: P D = 1 2 ρ u 2 {\displaystyle P_{\rm {D}}={\frac {1}{2}}\rho u^{2}}