Calculator Inputs
Plotly Graph
The graph compares generalized Reynolds number and apparent viscosity against velocity, using the entered rheological properties.
Formula Used
For a power law fluid in circular pipe flow, the Metzner and Reed generalized Reynolds number is:
Re_g = [ρ · V^(2-n) · D^n] / [K · 8^(n-1) · ((3n+1)/(4n))^n]Supporting equations used on this page:
γ_w = ((3n+1)/(4n)) · (8V/D) μ_app = K · γ_w^(n-1) f_laminar = 16 / Re_g ΔP = 4f(L/D)(ρV²/2)These equations estimate non Newtonian flow behavior, apparent viscosity, laminar friction factor, and a first pass pressure drop for engineering screening.
How to Use This Calculator
- Enter the fluid density and choose the matching density unit.
- Provide average pipe velocity and internal pipe diameter.
- Enter the power law consistency index K and behavior index n.
- Optionally refine loss estimates with pipe length and roughness.
- Press Calculate to show results above the form.
- Review Reynolds value, viscosity, shear rate, flow regime, and losses.
- Use the graph for sensitivity trends across a velocity range.
- Export the result summary to CSV or PDF when needed.
Example Data Table
| Case | Density (kg/m³) | Velocity (m/s) | Diameter (m) | K (Pa·sⁿ) | n | Generalized Re |
|---|---|---|---|---|---|---|
| Polymer Slurry | 1050 | 1.80 | 0.050 | 0.65 | 0.72 | 167.11 |
| Food Paste | 1120 | 0.95 | 0.040 | 1.90 | 0.48 | 19.54 |
| Drilling Mud | 1250 | 2.20 | 0.075 | 0.85 | 0.63 | 321.87 |
FAQs
1. What does the generalized Reynolds number show?
It compares inertial effects with non Newtonian viscous resistance in pipe flow. It helps classify flow behavior when the fluid does not follow constant Newtonian viscosity.
2. When should I use this calculator?
Use it for power law fluids such as slurries, food products, polymer solutions, inks, coatings, and drilling fluids flowing through circular pipes.
3. What is the flow behavior index n?
The value n describes shear response. Values below one indicate shear thinning, one behaves Newtonian, and values above one indicate shear thickening behavior.
4. What is the consistency index K?
K is the rheological parameter that scales apparent viscosity for a power law fluid. Larger K values usually indicate greater resistance to flow.
5. Is the pressure drop result exact?
No. It is a practical screening estimate based on the laminar style friction factor relation. Detailed design may need experimental rheology and turbulent non Newtonian correlations.
6. Why does apparent viscosity change with velocity?
Velocity changes wall shear rate. In non Newtonian fluids, viscosity depends on shear rate, so the apparent viscosity changes as the operating point shifts.
7. Can I use roughness for turbulent design here?
Roughness is reported as relative roughness for reference. This page does not apply a full turbulent non Newtonian rough pipe correlation to friction losses.
8. Which units work best?
SI units are easiest for checking results, but the calculator converts several common density, velocity, diameter, and consistency inputs automatically.