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Steady-state 1D inviscid fluid flow | Pipe Flow Mass Conservation | ||||||||||||||
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Equation of State (EOS) | Darcy–Weisbach | ||||||||||||||
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| distance along the fluid flow streamline | ||||||||
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| elevation along the 1D flow trajectory | ||||||||
| fluid temperature | ||||||||
| fluid pressure | ||||||||
| fluid density | ||||||||
| fluid velocity vector | ||||||||
| superficial velocity of the pipe flow | ||||||||
| volumetric density of all contact forces exerted on fluid body | ||||||||
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| fluid mass flux | ||||||||
| mass flowrate | ||||||||
| standard gravity constant |
Substituting
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\frac{d p}{d l} =
-j_m \, \frac{d}{d l} \left( \frac{j_m}{\rho} \right) + \rho \, g \, \cos \theta - f \cdot \frac{ \rho \, u^2 \, }{2 d} |
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