Parallel Plate Shear Rate Calculator

Calculator

Choose a motion model, enter values, then compute γ̇.

Motion model

Pick translation for linear motion, rotation for rheometers.

Plate gap, h

Small gaps increase shear rate strongly.

Relative velocity, v

Use plate-to-plate relative speed.

Angular speed, ω

rpm is common for lab instruments.

Plate radius, R

Shear rate grows linearly with radius.

Report shear rate as

Average uses effective radius 2R/3.

Optional Provide either viscosity or shear stress for additional outputs.

Dynamic viscosity, η

Used to estimate shear stress: τ = ηγ̇.

Shear stress, τ

If viscosity is blank, η = τ/γ̇ is computed.

Notes

Use consistent geometry for your experiment. Keep gap uniform and avoid plate slip. Report basis clearly for rotational plates.

Example data

Sample inputs and computed shear rate values.

Case	Model	Inputs	Shear rate, γ̇ (s^-1)
1	Translational	v = 0.05 m/s, h = 1 mm	50
2	Rotational (rim)	ω = 60 rpm, R = 25 mm, h = 1 mm	157.1
3	Rotational (average)	ω = 60 rpm, R = 25 mm, h = 1 mm	104.7

Values are rounded for readability. Your results depend on units and basis.

Formula used

Core relationships for shear rate in parallel plates.

Translational plates: γ̇ = v / h, where v is relative velocity and h is gap.
Rotational plates: γ̇(r) = ω r / h, where ω is angular speed and r is radius position.
Optional Newtonian relation: τ = η γ̇, linking shear stress τ and viscosity η.

How to use this calculator

A quick workflow for reliable results.

Select translational or rotational motion.
Enter the plate gap with the correct unit.
Provide velocity, or provide angular speed and radius.
For rotation, choose rim or area-weighted average.
Optionally enter viscosity or shear stress for extras.
Press Calculate to view results above the form.

Parallel plate shear rate: practical guide

Technical context, assumptions, and interpretation tips.

1) Why shear rate matters

Shear rate describes how quickly fluid layers slide past each other. In parallel plates, it links motion and gap, letting you compare tests, set mixing targets, and report rheology consistently. Many lab procedures specify a shear-rate window to reproduce structure changes and flow behavior.

2) What this calculator represents

This tool computes an idealized velocity gradient across a uniform gap. It assumes laminar flow, no wall slip, and a linear profile between plates. When these conditions hold, the computed value is a reliable control parameter for viscosity curves, yield studies, and time-dependent measurements.

3) Translational plates: v/h

For linear motion, the top plate moves at speed v relative to the bottom plate. The nominal shear rate is γ̇ = v/h. Example: v = 0.05 m/s and h = 1 mm gives 50 s⁻¹. Halving the gap doubles γ̇ instantly.

4) Rotational plates: ωr/h

For rotation, local shear rate depends on radius because tangential speed grows with distance from the center. The relation is γ̇(r) = ωr/h. At the rim, you get the highest value. This is common in parallel-plate rheometers and rotating fixtures.

5) Rim versus area-weighted average

Reporting the rim shear rate is conservative and easy to interpret, but it overstates the average condition experienced by most of the sample. A widely used area-weighted representative value uses an effective radius r = 2R/3. This calculator lets you choose either basis explicitly.

6) Units and data quality

Small unit mistakes dominate shear-rate results. Convert gaps carefully, especially micrometers to millimeters. Angular speed in rpm must be converted to rad/s internally. Measure the true gap under load, and keep plates parallel; a slight tilt can create a large local gradient variation.

7) Typical operating ranges

Many fluids are tested from about 0.1 s⁻¹ to 10,000 s⁻¹, depending on equipment and sample stability. Very high shear rates can cause heating, edge fracture, or inertial effects. Use the optional viscosity or stress fields to estimate Newtonian stress via τ = ηγ̇.

8) Interpreting results responsibly

If your material slips at the wall, the real shear rate inside the sample can be lower than the nominal value. Roughened plates, appropriate normal force, and repeat tests at different gaps help validate assumptions. Always report the geometry, gap, and whether you used rim or average shear rate.

FAQs

Short answers for common lab and design questions.

1) What is the difference between shear rate and shear stress?

Shear rate is a kinematic gradient (s⁻¹). Shear stress is a force per area (Pa). For Newtonian fluids, stress equals viscosity times shear rate: τ = ηγ̇.

2) When should I use translational versus rotational mode?

Use translational mode when plates slide linearly. Use rotational mode for rheometers or rotating fixtures where tangential speed depends on radius and you must specify a basis.

3) Why does rotational shear rate vary across the plate?

Tangential velocity increases with radius. Near the center, velocity is small, giving low shear rate. Near the rim, velocity is largest, giving the maximum shear rate.

4) What does “area-weighted average” mean here?

It reports a representative value for the whole disk using an effective radius 2R/3. This captures the fact that more area exists near the rim than near the center.

5) Can I compute viscosity from measured torque with this tool?

This calculator does not convert torque to stress. If you already have shear stress, enter it to estimate viscosity using η = τ/γ̇. Use instrument software for torque-to-stress conversion.

6) How do I reduce wall slip errors?

Increase surface roughness, use serrated plates, select an appropriate normal force, and repeat tests at multiple gaps. If measured behavior changes strongly with gap, slip may be present.

7) Is the computed shear rate always exact?

It is nominal and model-based. Non-uniform gaps, edge effects, inertia, heating, and non-Newtonian profiles can shift the true internal shear rate. Report assumptions and measurement conditions.