Pipeline simulation

1 inlet -> 1 outlet (Darcy ΔP over a pipe)

Governing equations

The exact equations the solver works for a pipeline — the same math shown in the app's "Theory" panel, not a black box.

$\Delta P$

pressure drop [Pa]

$f$

Darcy friction factor

$L$

pipe length [m]

$D$

internal diameter [m]

$\rho$

fluid density [kg/m³]

$v$

flow velocity [m/s]

$g$

gravitational acceleration

$\theta$

inclination angle — the second term is static head, which can dominate on a hill

$\mathrm{Re}$

Reynolds number

$\varepsilon/D$

relative roughness

$K$

consistency index [Pa·s^n] (opt-in rheology_model)

$n$

flow behavior index [-] — n=1 is Newtonian, n<1 shear-thinning, n>1 shear-thickening

$\mathrm{Re}_{MR}$

Metzner-Reed generalized Reynolds number for power-law pipe flow

$f_{Fanning}$

Fanning friction factor (the literature convention for these correlations — this codebase's own Darcy-Weisbach ΔP formula above uses f_{Darcy}=4f_{Fanning})

Parameters

diameter [m], length [m]; optional angle_deg, roughness [m], viscosity [Pa·s]. Also usable as a mode='pressure_driven' resistance element (no extra params needed — the same Darcy-Weisbach law is inverted implicitly by that mode's Newton solve). polymer_melt [bool, default False]: when the inlet carries a polymerization reactor's polymer_mwd, derive a real non-Newtonian apparent viscosity instead of the constant 'viscosity' param — optional eta_ref_pa_s + mw_ref_kg_mol [reference melt-viscosity datapoint], mw_scaling_exponent [default 3.4], n [Carreau power-law index, default 0.4], lambda_relax_s [default 1.0], eta_inf_pa_s [default 0], temperature_ref + activation_energy_j_mol [optional Arrhenius T-shift]. rheology_model [one of 'power_law'/'bingham'/'herschel_bulkley', opt-in, mutually exclusive with polymer_melt]: replaces the friction factor itself with the matching generalized (Metzner-Reed/Dodge-Metzner/Buckingham-Reiner) correlation for slurries/suspensions — consistency_index_k [Pa*s^n], flow_behavior_index_n [-, default 1.0], yield_stress_pa [Pa, bingham/herschel_bulkley], plastic_viscosity_pa_s [Pa*s, bingham]

Example flowsheets that use it