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Pressure profilePressure gradient profile


LaTeX Math Block
anchorPPconst
alignmentleft
p(l) = p_s + \rho_s \, g \, \Delta z(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s \, l



LaTeX Math Block
anchorgradP
alignmentleft
\frac{dp}{dl} = \rho_s \, g \cos \theta(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s


Mass FluxMass Flowrate


LaTeX Math Block
anchorMassFlux
alignmentleft
j_m = \rho_s \cdot \sqrt{\frac{2 \, d}{f_s \, l }} \cdot \sqrt{g \, \Delta z(l) + (p_s - p)/ \rho_s}



LaTeX Math Block
anchorMassFlowrate
alignmentleft
\dot m = j_m \cdot A = \rho_s \cdot A \cdot \sqrt{\frac{2 \, d}{f_s \, l }} \cdot \sqrt{g \, \Delta z(l) + (p_s - p)/ \rho_s}


 Volumetric Flowrate

Fluid velocity


LaTeX Math Block
anchorPPconst
alignmentleft
q_s = \dot m / \rho_s = A \cdot \sqrt{\frac{2 \, d }{ f_s \, l }} \cdot \sqrt{  g \, \Delta z(l) + (p_s - p)/ \rho_s }



LaTeX Math Block
anchorPPconst
alignmentleft
u_s = q_s / A = \sqrt{\frac{2 \, d }{ f_s \, l }} \cdot \sqrt{  g \, \Delta z(l) + (p_s - p)/ \rho_s }


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