อัปเดต 2026-09-07

Non-Newtonian pipe flow

power-law / Bingham / Herschel-Bulkley

Pipe friction pressure drop for power-law, Bingham-plastic and Herschel-Bulkley fluids — a validated TypeScript mirror of the backend's non_newtonian.py, pinned to it by a parity fixture.

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Rheology-specific shear-stress model feeds a model-specific generalized Reynolds number (Metzner–Reed for power-law with the Rabinowitsch–Mooney wall-shear correction, generalized Re for Herschel-Bulkley, Bingham Re for Bingham); laminar Bingham flow uses the exact Buckingham-Reiner friction factor, turbulent flow uses Dodge–Metzner on Re_MR. All pressure drop uses the Fanning (not Darcy) friction relation.

สมการ

Rheology models

τ = K γ ˙^{n} (power-law), τ = τ_{y} + μ_{p} γ ˙ (Bingham), τ = τ_{y} + K γ ˙^{n} (Herschel-Bulkley)

τ = wall shear stress, γ̇ = shear rate, K = consistency index, n = flow-behaviour index, τ_y = yield stress, μ_p = plastic viscosity

Metzner-Reed Reynolds number

R e_{M R} = \frac{ρ V ^{2 - n} D ^{n}}{K ^{'} 8 ^{n - 1}}, K^{'} = K (\frac{3 n + 1}{4 n})^{n}

K' = Rabinowitsch–Mooney generalized consistency; reduces to Newtonian Re at n=1

Fanning pressure drop

Δ P = 2 f ρ V^{2} \frac{L}{D}

f = Fanning friction factor (16/Re_MR laminar, Dodge–Metzner turbulent, or exact Buckingham-Reiner for Bingham); NOT the Darcy ¼-scale form

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