Apply Rabinowitsch correction to pipe and capillary flow. Choose inputs, units, and export results fast. Get reliable wall shear data for design and testing.
Select a mode, enter values, and compute corrected wall shear rate for power-law fluids.
For laminar tube flow in capillary rheometry, the apparent shear rate assumes a Newtonian profile:
For a power-law fluid, Rabinowitsch correction gives the true wall shear rate:
With a power-law model, stress relates to shear rate as:
Sample inputs and corrected shear rates for illustration.
| n | R (mm) | Q (mL/s) | γ̇app (1/s) | Correction factor | γ̇w (1/s) |
|---|---|---|---|---|---|
| 0.6 | 2.0 | 0.80 | 127.3 | 1.125 | 143.2 |
| 0.9 | 1.5 | 0.50 | 188.6 | 1.028 | 193.9 |
| 1.2 | 1.0 | 0.20 | 254.6 | 0.958 | 244.0 |
Capillary and pipe tests often report an apparent shear rate based on Newtonian assumptions. Power law fluids do not have a parabolic velocity profile, so the wall shear rate is higher or lower than the apparent estimate. Rabinowitsch correction converts measured flow data into a wall shear rate that matches the real velocity gradient at the tube wall.
For a power law fluid, the correction factor is (3n+1)/(4n). If n = 1 (Newtonian), the factor becomes 1.000 and the apparent and true wall shear rates match. For shear-thinning fluids (n < 1), the factor is typically greater than 1.
Many polymer solutions and paints show n ≈ 0.3–0.9. Some concentrated suspensions can be near n ≈ 0.2, while weakly shear-thickening fluids may reach n ≈ 1.1–1.5. These ranges help you sanity-check inputs before exporting results.
The apparent shear rate scales as γ̇app ∝ Q/R³. Halving the radius increases γ̇app by a factor of 8 for the same flow rate. That sensitivity is why accurate radius measurement is critical, especially for small capillaries.
In laminar tube flow the wall shear stress follows τw = (ΔP·R)/(2L). As a quick check, doubling tube length while keeping ΔP fixed halves τw. This calculator uses that relation to pair stress with corrected shear rate.
With the power law model τ = K γ̇ⁿ, you can compare measured τw from pressure data against the stress predicted by K and corrected γ̇w. Large differences often indicate entrance losses, slip, or mixed regimes.
Keep flow laminar, stabilize temperature, and record steady readings. For polymer melts or high-viscosity fluids, a few degrees can change viscosity noticeably. Use multiple flow points and verify that n remains consistent across the shear-rate window.
The corrected shear rate helps translate lab measurements into processing conditions, such as extrusion or pumping. Use the exported CSV for spreadsheets and the PDF for lab notebooks. Report R, L, ΔP, Q, n, and the correction factor to make results reproducible.
It adjusts the Newtonian-based apparent shear rate into a true wall shear rate for non-Newtonian power law fluids, improving the accuracy of rheology and flow calculations.
When n = 1. That case behaves like a Newtonian fluid, so the apparent and wall shear rates are the same and no correction is needed.
No. The relationships used here assume fully developed laminar tube flow. If the flow is turbulent, both stress and shear-rate estimates require different correlations and experimental validation.
Use Pa·sⁿ. Then τ = K γ̇ⁿ yields stress in pascals when γ̇ is in 1/s, keeping the model consistent.
Because γ̇app = 4Q/(πR³). A small radius error is magnified by the cubic term, which can significantly shift the corrected wall shear rate and apparent viscosity.
Check for entrance pressure losses, wall slip, temperature drift, or incorrect n. Also confirm that ΔP reflects only the fully developed section length used in the stress equation.
Use the flow mode when you measure Q and ΔP across a known length. Use the τw mode when stress and K are known and you want to back-calculate flow rate and pressure drop.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.