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@wikipedia
(1) |
\frac{dp}{dz}= \rho(p) \cdot g |
Approximations
Incompressible fluids
(2) |
p(z) = p_0 + \rho \cdot g \cdot (z-z_0) |
Ideal gases
(3) |
p(z) = p_0 \cdot \exp \left[ - \frac{M \, g}{R \, T} \cdot (z-z_0) \right] |
Also known as Hydrostatic Boltzmann pressure distribution
Full-range model
(4) |
\frac{1+ c_0 \, p(z)}{1 + c_0 \, p_0} = \exp \left[ \frac{ с_0 \cdot \rho_0 \cdot g \cdot (z-z_0)}{1+c_0 \, p_0} \right] |
The pressure drop between two points is going to be:
(5) |
p_2 - p_1 = \frac{ (1+p_0 \, p_1) \cdot \left( \exp \left[ \frac{ с_0 \cdot \rho_0 \cdot g \cdot (z_2-z_1)}{1+c_0 \, p_0} \right] - 1 \right) }{c_0} |
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics
[ Fluid Dynamics ]