@wikipedia
Motivation
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The pipeline and wellbore flow simulations require a model of static fluid pressure variation as a function of of elevation
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Equation
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The static balance equation for fluid column is:
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\frac{dp}{dz}= \rho(p) \cdot g |
Approximations
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with Incompressible fluid | Ideal Gas | Full-range model |
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| p(z) = p_0 + \rho_0 \cdot g \cdot (z-z_0) |
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| p(z) = p_0 \cdot \exp \left[ - \frac{\rho_0 \, g}{p_0} \cdot (z-z_0) \right] |
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| \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] |
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| p_2 - p_1 = \rho_0 \cdot g \cdot (z_2-z_1) |
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| p_2 - p_1 = p_1 \cdot \left( \exp \left[ \frac{ \rho_0 \cdot g \cdot (z_2-z_1)} {p_0} \right] - 1 \right) |
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| p_2 - p_1 = \frac{ (1+c_0 \, p_1)}{c_0} \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) |
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| body | --uriencoded--\displaystyle \frac%7B\rho_0%7D%7Bp_0%7D = \frac%7BM%7D%7BR\, T%7D |
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See also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics
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