Inputs
Formula used
The calculator first determines volumetric flow rate Q in m³/s.
Then it computes the nominal (apparent) wall shear rate for a circular capillary:
γ̇app = 4Q / (πR³) = 32Q / (πD³)V = Q / AwhereA = πR²
For non‑Newtonian flow approximated by a power‑law index n, a common correction is:
γ̇w = γ̇app · (3n+1)/(4n).
If n is unknown, you can use n = 1.
How to use this calculator
- Enter die diameter and optional die length.
- Select a flow input method matching your test data.
- Provide flow values with the correct units.
- Enter
nif you want corrected wall shear rate. - Press Calculate to view results above the form.
- Use Download CSV or Download PDF for reporting.
Example data table
| Die D (mm) | Die L (mm) | Q (cm³/s) | n | γ̇app (s⁻¹) | γ̇w (s⁻¹) |
|---|---|---|---|---|---|
| 1.00 | 20 | 1.00 | 1.00 | 10185.916 | 10185.916 |
| 1.50 | 30 | 0.60 | 0.55 | 1810.993 | 2460.537 |
| 2.00 | 40 | 1.20 | 0.75 | 3055.775 | 3565.071 |
Values are illustrative. Your results depend strongly on die diameter.
Technical article
1) Why wall shear rate matters
In capillary rheometry, viscosity and melt stability depend on the shear field at the die wall. Wall shear rate (s⁻¹) is the standard x‑axis for flow curves because it links directly to molecular alignment, shear thinning, and the onset of surface defects. Small die‑diameter errors amplify shear‑rate uncertainty due to the cubic dependence on diameter.
2) Apparent versus corrected shear rate
The nominal expression assumes Newtonian velocity profile. Many melts are non‑Newtonian, so the true wall shear rate is higher than the apparent value when the fluid is shear‑thinning. The Rabinowitsch correction scales the nominal rate by (3n+1)/(4n) for a power‑law approximation, improving consistency across materials and temperatures.
3) Choosing the right flow input
Laboratories record flow as volumetric rate, mass rate, or piston speed. This calculator supports all three to reduce transcription mistakes. Mass flow requires density, which can be temperature dependent. Piston‑based flow is useful when only displacement data is available, but it assumes negligible leakage and compressibility effects.
4) Die geometry and L/D context
Die aspect ratio (L/D) influences entrance effects, pressure drop distribution, and thermal development. While L/D does not enter the basic shear‑rate equation, it is a practical quality check for comparing runs. Typical capillary dies use L/D values from about 10 to 40, depending on the rheometer and material behavior.
5) Interpreting the mean velocity
Mean velocity V = Q/A helps evaluate residence time and potential heating. Higher velocity can increase viscous dissipation, shifting apparent viscosity. Pair V with barrel and die temperatures to detect run‑to‑run drift, especially during long test sequences or when changing piston speed rapidly.
6) Using n for practical corrections
If you already fit a power‑law region, use that flow behavior index n here to correct wall shear rate for the same region. For strongly shear‑thinning melts, n may be 0.2–0.6, giving noticeable correction. If n is unknown, setting n = 1 returns the nominal Newtonian wall shear rate.
7) Data hygiene and unit control
Unit conversions are a common source of error in rheology spreadsheets. This tool converts all inputs to SI units internally and reports results in s⁻¹ and m/s. When comparing datasets, keep die diameter and flow units consistent, and document density assumptions when converting from mass flow.
8) Reporting and traceability
For professional reporting, record the die dimensions, flow method, Q, n, and both apparent and corrected shear rates. The CSV and PDF exports provide a simple audit trail for notebooks, LIMS attachments, and batch comparisons. Add material grade, temperature, and pressure data alongside the exported results to complete the test record.
FAQs
1) What is wall shear rate in a capillary rheometer?
It is the shear rate at the die wall during capillary flow. It is used to plot viscosity curves and compare shear‑dependent behavior across materials, temperatures, and processing conditions.
2) Why does die diameter affect the result so strongly?
Wall shear rate scales with 1/D³. A small measurement error in diameter produces a much larger error in shear rate, so accurate die gauging is critical for reliable rheology.
3) When should I use the Rabinowitsch correction?
Use it when the fluid is non‑Newtonian and you can approximate behavior with a power‑law index n in the region of interest. It improves the estimate of true wall shear rate.
4) I only have mass flow rate. Can I still calculate shear rate?
Yes. Convert mass flow to volumetric flow using Q = ṁ/ρ. Use a density value appropriate for the test temperature to reduce error in the computed wall shear rate.
5) What does the mean velocity tell me?
Mean velocity indicates how fast material travels through the die. It helps assess residence time and potential viscous heating, which can change apparent viscosity during high‑rate tests.
6) If n is unknown, what should I enter?
Leave n blank to use n = 1. This returns the nominal Newtonian wall shear rate. You can later update n after fitting a flow curve from experimental data.
7) Does die length change wall shear rate?
Die length does not appear in the basic shear‑rate equation, but L/D provides context for flow development and entrance effects. Include L/D when comparing results across different dies.