๐งด Non-Newtonian Pipe Flow
Analyze pipe flow of power-law, Bingham plastic, and Herschel-Bulkley fluids. Compute Metzner-Reed Re, pressure drop, and velocity profile.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Fluid Mechanics
๐ Solver Telemetry
โ ACTIVE
๐๏ธ Views
141
โก Solves
113
๐พ Downloads
508
๐ฆ Fortran Code
4.5 KB
๐
Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ก
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๐ฌ Flow Profile Schematic
๐ Configuration
Key Equations:
Power-law: ฯ = K ฮณฬโฟ
Bingham: ฯ = ฯy + K ฮณฬ
Herschel-Bulkley: ฯ = ฯy + K ฮณฬโฟ
ReMR = ฯV2โnDn / [Kโฒ 8nโ1]
f = 64/ReMR (laminar)
Power-law: ฯ = K ฮณฬโฟ
Bingham: ฯ = ฯy + K ฮณฬ
Herschel-Bulkley: ฯ = ฯy + K ฮณฬโฟ
ReMR = ฯV2โnDn / [Kโฒ 8nโ1]
f = 64/ReMR (laminar)
๐ Results
Configure inputs and click Calculate to view results.
๐ 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.