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Pipeline Flow Pressure Model is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.

Outputs

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Inputs

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LaTeX Math Inline body T_s	Intake temperature	LaTeX Math Inline body T(l)	Along-pipe temperature profile
LaTeX Math Inline body p_s	Intake pressure	LaTeX Math Inline body \rho(T, p)	Fluid density
LaTeX Math Inline body q_s	Intake flowrate	LaTeX Math Inline body \mu(T, p)	Fluid viscosity
LaTeX Math Inline body z(l)	Pipeline trajectory TVDss	LaTeX Math Inline body A	Pipe cross-section area
LaTeX Math Inline body \theta (l)	Pipeline trajectory inclination, LaTeX Math Inline body --uriencoded--\displaystyle \cos \theta (l) = \frac%7Bdz%7D%7Bdl%7D	LaTeX Math Inline body \epsilon	Inner pipe wall roughness

Assumptions

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Equations

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\bigg( 1 -  \frac{c(p) \, \rho_s^2 \, q_s^2}{A^2}   \bigg )  \frac{dp}{dl} = \rho \, g \, \frac{dz}{dl}  - \frac{\rho_s^2 \, q_s^2 }{2 A^2 d} \frac{f({\rm Re}, \, \epsilon)}{\rho}

q(l) = \frac{\rho_s \cdot q_0}{\rho}

u(l) = \frac{\rho_s \cdot q_s}{\rho \cdot A}

p(l=0) = p_s

q(l=0) = q_s

\rho(T_s, p_s) = \rho_s

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