🧴 Non-Newtonian Pipe Flow Calculator
Analyze pipe flow of power-law, Bingham plastic, and Herschel-Bulkley fluids. Outputs generalized Reynolds number, pressure drop, apparent viscosity, and velocity profile with plug core.
🔬 Flow Profile Schematic
📝 Configuration
Key Equations:
Power-law: τ = K γ̇ⁿ
Bingham: τ = τy + K γ̇
Herschel-Bulkley: τ = τy + K γ̇ⁿ
ReMR = ρV2−nDn / [K′ 8n−1]
f = 64/ReMR (laminar)
Power-law: τ = K γ̇ⁿ
Bingham: τ = τy + K γ̇
Herschel-Bulkley: τ = τy + K γ̇ⁿ
ReMR = ρV2−nDn / [K′ 8n−1]
f = 64/ReMR (laminar)
📊 Results
Configure inputs and click Calculate to view results.
📘 Calculation Methodology
Mathematical Model
Three rheological models are implemented. The Metzner-Reed generalized Reynolds number extends laminar friction factor f = 64/Re to non-Newtonian fluids. Turbulent flow uses the Dodge-Metzner or Blasius-type approximation.
Velocity Profile
Power-law fluids have a blunted parabolic profile. Bingham and Herschel-Bulkley fluids exhibit a rigid plug core where shear stress is below the yield stress, surrounded by a sheared annular region.
Assumptions
- Fully developed, steady, isothermal pipe flow.
- Time-independent non-Newtonian behavior.
- No wall slip.
- Turbulent regime uses Blasius-type correlation.
- Herschel-Bulkley plug radius is approximated from wall/yield stress ratio.