Shear Rate Calculator

Formula Used

Shear rate (γ̇) describes how quickly adjacent fluid layers move relative to each other. It is commonly expressed in s⁻¹.

• Parallel plates (Couette): γ̇ = V / h, where V is plate speed and h is gap.
• Circular pipe (laminar, Newtonian): γ̇_w = 32Q / (πD³) or γ̇_w = 8V̄ / D.
• Cone-and-plate: γ̇ = Ω / tan(θ), where Ω is angular speed and θ is cone angle.

How to Use This Calculator

1. Select a method that matches your setup (plates, pipe, or cone-and-plate).
2. Enter the required values and choose units for each input.
3. Click Calculate to display shear rate above the form.
4. Review the listed steps to confirm unit conversions and formula.
5. Use Download CSV or Download PDF for records.

Example Data Table

Examples are illustrative and depend on method assumptions.

Shear Rate Guide

1) Why shear rate matters in fluid systems

Shear rate (γ̇) measures how quickly velocity changes across a fluid layer. It directly influences viscosity for many real materials, including polymer melts, inks, slurries, blood, and food products. In equipment design, γ̇ helps predict mixing intensity, heat generation, and potential shear damage to sensitive suspensions.

2) Definition and core relationship

In simple shear, γ̇ is the velocity gradient normal to flow. For parallel motion, γ̇ ≈ ΔV/Δy, expressed in s⁻¹. Higher values indicate stronger deformation per second. When fluids behave as Newtonian, shear stress links linearly to γ̇ via τ = μγ̇, where μ is dynamic viscosity.

3) Parallel plates: Couette-style estimation

For a fluid confined between two plates, the calculator uses γ̇ = V/h. This is widely used for coatings, tribology gaps, and lubrication films. Example: V = 0.25 m/s with h = 2 mm gives 125 s⁻¹. Reducing the gap tenfold increases γ̇ by ten.

4) Circular pipe: wall shear rate from flow

For laminar Newtonian flow in a round tube, the velocity profile is parabolic and the wall shear rate becomes γ̇_w = 32Q/(πD³). With Q = 2 mL/s and D = 4 mm, γ̇_w ≈ 127.32 s⁻¹. Small diameter changes strongly affect γ̇ because D is cubed.

5) Circular pipe: wall shear rate from average velocity

If you know average velocity instead of volumetric flow, the equivalent relation is γ̇_w = 8V̄/D. For V̄ = 0.30 m/s and D = 10 mm, γ̇_w = 240 s⁻¹. This mode is useful when velocity comes from a pump curve or flow sensor.

6) Cone-and-plate: rotational rheometry

In cone-and-plate geometry, shear rate is nearly uniform, making it ideal for viscosity curves. The calculator applies γ̇ = Ω/tan(θ). For 120 rpm and θ = 2°, Ω ≈ 12.566 rad/s and γ̇ ≈ 718.37 s⁻¹. Smaller angles increase γ̇ for the same speed.

7) Typical ranges and unit handling

Industrial shear rates span orders of magnitude: gentle stirring may be 1–10 s⁻¹, many process pipes operate around 100–10,000 s⁻¹, and thin-film coating or high-speed mixing can exceed 100,000 s⁻¹. This calculator converts common length, velocity, flow, and angle units to keep inputs consistent.

8) Interpreting results and key assumptions

Reported values are estimates based on idealized models. Pipe formulas assume laminar flow, a circular tube, and Newtonian behavior. Plates assume a uniform gap and negligible slip. Cone-and-plate assumes small angles and correct alignment. Use the export feature to document inputs, method, and steps in reports.

FAQs

1) What unit is shear rate reported in?

Shear rate is reported in inverse seconds, s⁻¹. It represents deformation rate per second and is independent of fluid density.

2) Which pipe formula should I choose: Q or V̄?

Use the Q option when a flow meter provides volumetric flow. Use the V̄ option when you know average velocity from a pump curve, sensor, or simulation. Both are equivalent for laminar Newtonian flow.

3) Does this work for turbulent pipe flow?

The included pipe relations are for laminar Newtonian flow. Turbulent wall shear rate depends on friction factors and velocity profiles, so results may underestimate or misrepresent turbulent conditions.

4) Can shear rate be negative?

Shear rate magnitude is typically reported as a positive value. Direction matters for vector analysis, but rheology and process design usually use |γ̇| to describe intensity.

5) Why does diameter affect pipe shear so strongly?

When using flow rate, the wall shear rate scales with 1/D³. Small diameter reductions dramatically increase shear, which can change pressure drop, heating, and material response.

6) Why is cone-and-plate popular for viscosity curves?

Cone-and-plate provides nearly uniform shear rate across the sample. That uniformity improves repeatability when measuring non-Newtonian fluids across controlled shear conditions.

7) What should I export in my lab report?

Export the method, inputs with units, computed shear rate, and the step list. This documents assumptions and makes your calculation traceable for reviews or audits.