Please enter valid positive numbers for both fields. Viscosity cannot be zero.
Calculated Shear Rate
0
s⁻¹ (reciprocal seconds)
Normalized Output:
Shear Stress: Pa
Viscosity: Pa·s
function calculateShearRate() {
// Get input elements
var stressInput = document.getElementById('shearStress');
var viscosityInput = document.getElementById('viscosity');
var stressUnit = document.getElementById('stressUnit');
var viscosityUnit = document.getElementById('viscosityUnit');
var resultBox = document.getElementById('resultBox');
var errorMsg = document.getElementById('errorMsg');
var finalRateDisplay = document.getElementById('finalRate');
var displayStress = document.getElementById('displayStress');
var displayViscosity = document.getElementById('displayViscosity');
// Parse values
var stressVal = parseFloat(stressInput.value);
var viscVal = parseFloat(viscosityInput.value);
// Validation
if (isNaN(stressVal) || isNaN(viscVal) || viscVal === 0) {
errorMsg.style.display = 'block';
resultBox.style.display = 'none';
if (viscVal === 0) {
errorMsg.innerHTML = "Viscosity cannot be zero (division by zero).";
} else {
errorMsg.innerHTML = "Please enter valid numeric values.";
}
return;
}
errorMsg.style.display = 'none';
// Convert Stress to Pascals (Pa)
var stressPa = stressVal;
if (stressUnit.value === 'dyn_cm2') {
// 1 dyne/cm² = 0.1 Pa
stressPa = stressVal * 0.1;
}
// Convert Viscosity to Pascal-seconds (Pa·s)
var viscPas = viscVal;
if (viscosityUnit.value === 'cP') {
// 1 cP = 0.001 Pa·s
viscPas = viscVal * 0.001;
} else if (viscosityUnit.value === 'P') {
// 1 Poise = 0.1 Pa·s
viscPas = viscVal * 0.1;
}
// Calculate Shear Rate
// Formula: Shear Rate = Shear Stress / Viscosity
var shearRate = stressPa / viscPas;
// Display Results
resultBox.style.display = 'block';
// Format logic: if number is very small or very large, use scientific notation
if (shearRate > 10000 || (shearRate 0)) {
finalRateDisplay.innerHTML = shearRate.toExponential(4);
} else {
finalRateDisplay.innerHTML = shearRate.toFixed(4);
}
displayStress.innerHTML = stressPa.toFixed(4);
displayViscosity.innerHTML = viscPas.toFixed(4);
}
How to Calculate Shear Rate from Viscosity
Understanding fluid dynamics often requires determining the shear rate acting upon a fluid. Whether you are designing piping systems, formulating paints, or analyzing blood flow, the relationship between shear stress, viscosity, and shear rate is fundamental. This guide explains how to calculate shear rate specifically when the viscosity and shear stress are known.
The Fundamental Formula
For Newtonian fluids, the relationship between shear stress and shear rate is linear and is defined by Newton's Law of Viscosity. The formula is:
τ = μ × γ̇
Where:
τ (Tau): Shear Stress (measured in Pascals, Pa)
μ (Mu) or η (Eta): Dynamic Viscosity (measured in Pascal-seconds, Pa·s)
γ̇ (Gamma dot): Shear Rate (measured in reciprocal seconds, s⁻¹)
To calculate the Shear Rate, we rearrange the formula:
Let's look at a practical example involving a hydraulic fluid.
Scenario:
You have a fluid flowing between two plates. The shear stress exerted on the fluid is calculated to be 50 Pascals (Pa). The dynamic viscosity of the fluid is known to be 100 Centipoise (cP).
Step 1: Standardize Units
Calculations must be done in consistent SI units. The standard unit for viscosity in these equations is Pascal-seconds (Pa·s).
Given Viscosity: 100 cP
Conversion Factor: 1 cP = 0.001 Pa·s
Converted Viscosity: 100 × 0.001 = 0.1 Pa·s
Step 2: Apply the Formula
Now, divide the shear stress by the converted viscosity:
It is critical to note that the calculator above uses the definition for Newtonian fluids.
Fluid Type
Behavior
Examples
Newtonian
Viscosity remains constant regardless of shear rate. The calculation $\dot{\gamma} = \tau / \mu$ is valid across all rates.
Water, Oil, Air, Honey
Non-Newtonian
Viscosity changes as shear rate changes (Shear-thinning or Shear-thickening). The calculation is only valid for a specific point in time.
Ketchup, Blood, Paint, Cornstarch solution
If you are working with a Non-Newtonian fluid, the viscosity value you enter into the calculator must be the apparent viscosity at that specific stress level.
Common Unit Conversions
Rheology often uses a mix of CGS and SI units. Here is a quick reference for converting inputs before calculating:
Viscosity: 1000 cP = 1 Pa·s = 10 Poise.
Shear Stress: 1 Pa = 10 dyne/cm².
Why is Shear Rate Important?
Calculating shear rate is vital for engineering applications:
Piping Design: High shear rates near pipe walls can cause degradation of sensitive fluids (like polymers or food products).
Coating Processes: When applying paint or coating, the shear rate is extremely high. Knowing the rate helps ensure the viscosity is low enough for a smooth finish (shear thinning).
Quality Control: Ensuring a product has the correct consistency requires measuring viscosity at the specific shear rates the product will experience during use (e.g., rubbing lotion on skin).