Shear rate is a fundamental concept in fluid mechanics and rheology. It describes the rate at which adjacent layers of fluid move with respect to each other. When you apply force to a fluid, different layers move at different velocities; the gradient of this velocity is the shear rate.
How to Calculate Shear Rate
The calculation method depends on the geometry of the system:
Parallel Plate Flow: This is the simplest form. If you have a fluid between two plates and one moves at velocity v while the other is stationary with a gap h, the formula is: γ̇ = v / h
Pipe Flow (Newtonian): For a Newtonian fluid flowing through a circular pipe, the shear rate at the pipe wall is calculated using the volumetric flow rate (Q) and the pipe radius (r): γ̇ = 4Q / (πr³)
Example Calculation
Suppose you have a pipe with a diameter of 0.02 meters (radius of 0.01m) and a flow rate of 0.001 m³/s. Using the pipe formula:
Radius (r) = 0.01 m
r³ = 0.000001
π * r³ ≈ 0.00000314159
4 * Q = 4 * 0.001 = 0.004
Shear Rate = 0.004 / 0.00000314159 ≈ 1,273.24 s⁻¹
Why It Matters
Measuring shear rate is critical for industries such as chemical processing, food manufacturing, and pharmaceuticals. Many fluids are "non-Newtonian," meaning their viscosity changes depending on the shear rate. For example, ketchup becomes thinner as it is sheared (pushed out of the bottle), a phenomenon known as shear-thinning.
function toggleInputs() {
var type = document.getElementById('calcType').value;
var pipeDiv = document.getElementById('pipeInputs');
var plateDiv = document.getElementById('plateInputs');
var resultDiv = document.getElementById('shearResult');
resultDiv.style.display = 'none';
if (type === 'pipe') {
pipeDiv.style.display = 'block';
plateDiv.style.display = 'none';
} else {
pipeDiv.style.display = 'none';
plateDiv.style.display = 'block';
}
}
function calculateShear() {
var type = document.getElementById('calcType').value;
var resultValue = document.getElementById('resultValue');
var resultDiv = document.getElementById('shearResult');
var shearRate = 0;
if (type === 'pipe') {
var Q = parseFloat(document.getElementById('flowRate').value);
var D = parseFloat(document.getElementById('pipeDiameter').value);
if (isNaN(Q) || isNaN(D) || D <= 0) {
alert('Please enter valid positive numbers for Flow Rate and Diameter.');
return;
}
var R = D / 2;
// Formula: gamma = (4 * Q) / (pi * R^3)
shearRate = (4 * Q) / (Math.PI * Math.pow(R, 3));
} else {
var V = parseFloat(document.getElementById('plateVelocity').value);
var H = parseFloat(document.getElementById('gapDistance').value);
if (isNaN(V) || isNaN(H) || H <= 0) {
alert('Please enter valid positive numbers for Velocity and Gap Distance.');
return;
}
// Formula: gamma = V / H
shearRate = V / H;
}
resultValue.innerText = shearRate.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 4
});
resultDiv.style.display = 'block';
}