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\frac{d p}{d l} =
-j_m \,cdot \frac{d}{d l} \left( \frac{j_m}{\rho} \right) + \rho \, g \, \cos \theta - f \cdot \frac{ \rho \, }{2 d} \cdot \left( \frac{j_m}{\rho} \right)^2 |
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\frac{d p}{d l} =
j^2_m \cdot \frac{1}{\rho^2} \frac{d \rho}{dl} + \rho \, g \, \cos \theta - \frac{j_m^2}{2 d} \cdot \frac{f}{\rho} |
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\frac{d p}{d l} =
j^2_m \cdot \frac{1}{\rho^2} \frac{d \rho}{dp} \cdot \frac{d p}{dl} + \rho \, g \, \cos \theta - \frac{j_m^2}{2 d} \cdot \frac{f}{\rho} |
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\frac{d p}{d l} =
j^2_m \cdot \frac{1}{\rho} \cdot c \cdot \frac{d p}{dl} + \rho \, g \, \cos \theta - \frac{j_m^2}{2 d} \, cdot \frac{f}{\rho} |
and finally
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\left( 1 - j_m^2 \cdot \frac{c}{\rho} \right ) \frac{dp}{dl} = \rho \, g \, \ |
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cos \theta - \frac{j_m^2 }{2 d} \cdot \frac{f |
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Alternative forms
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1j_m =\left[ \rho -j_m^2 \, c \right] \cdot \frac{ |
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\rho_0 \cdot q_0}{ A} ...
d p}{dl} =
\rho^2 \, g \, \cos \theta - \frac{j_m^2 }{2d} \cdot f(\rho) |
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| \left[ \frac{1}{c} - \frac{j_m^2}{\rho} \right] \cdot \frac{d \rho}{dl} =
\rho^2 \, g \, \cos \theta - \frac{j_m^2 }{2d} \cdot f(\rho) |
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See Also
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Petroleum Industry / Upstream / Pipe Flow Simulation / Water Pipe Flow @model / Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model
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