changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Jun 13, 2020
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j_m = j_m[p(l)] \rightarrow p = p(l)
\frac{dp}{dl} = {\rho_s \, g \cos \theta(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_srm Numerical} \ {\rm Derivative}
j_m = \sqrt{ 2 \cdot \frac { g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho} } { \left( \frac{1}{\rho^2} - \frac{1}{\rho_0^2} \right) + \left( \frac{1}{\rho^2} + \frac{1}{\rho_0^2} \right) \cdot \frac{f \, \cdot \, l}{ 2 \, d} } }
\dot m = j_m \cdot A = A \cdot \sqrt{ 2 \cdot \frac { g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho} } { \left( \frac{1}{\rho^2} - \frac{1}{\rho_0^2} \right) + \left( \frac{1}{\rho^2} + \frac{1}{\rho_0^2} \right) \cdot \frac{f \, \cdot \, l}{ 2 \, d} } }
Volumetric Flowrate
Intake Fluid velocity
q_s = \dot m / \rho_s = \frac{A}{\rho_s} \cdot \sqrt{ 2 \cdot \frac { g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho} } { \left( \frac{1}{\rho^2} - \frac{1}{\rho_0^2} \right) + \left( \frac{1}{\rho^2} + \frac{1}{\rho_0^2} \right) \cdot \frac{f \, \cdot \, l}{ 2 \, d} } }
u_s = j_m/ \rho_s =q_s / A \frac{1}{\rho_s} \cdot \sqrt{ 2 \cdot \frac { g \, \Delta z + \int_p^{p_0} \frac{dp}{\rho} } { \left( \frac{1}{\rho^2} - \frac{1}{\rho_0^2} \right) + \left( \frac{1}{\rho^2} + \frac{1}{\rho_0^2} \right) \cdot \frac{f \, \cdot \, l}{ 2 \, d} } }
