function toggleShearInputs() {
var method = document.getElementById('shearCalcMethod').value;
document.getElementById('simpleInputs').style.display = 'none';
document.getElementById('concentricInputs').style.display = 'none';
document.getElementById('coneInputs').style.display = 'none';
if (method === 'simple') {
document.getElementById('simpleInputs').style.display = 'block';
} else if (method === 'concentric') {
document.getElementById('concentricInputs').style.display = 'block';
} else if (method === 'cone') {
document.getElementById('coneInputs').style.display = 'block';
}
// Hide results when changing methods
document.getElementById('shearResult').style.display = 'none';
document.getElementById('shearError').style.display = 'none';
}
function calculateShearRate() {
// Inputs
var rpmStr = document.getElementById('shearRpm').value;
var method = document.getElementById('shearCalcMethod').value;
var errorDiv = document.getElementById('shearError');
var resultDiv = document.getElementById('shearResult');
// Reset display
errorDiv.style.display = 'none';
resultDiv.style.display = 'none';
errorDiv.innerHTML = "";
// Basic Validation
if (!rpmStr || isNaN(rpmStr)) {
errorDiv.innerHTML = "Please enter a valid RPM value.";
errorDiv.style.display = 'block';
return;
}
var rpm = parseFloat(rpmStr);
// Convert RPM to Radians per second
// Formula: rad/s = RPM * (2 * PI) / 60
var omega = rpm * (2 * Math.PI) / 60;
var shearRate = 0;
try {
if (method === 'simple') {
var factorStr = document.getElementById('shearFactor').value;
if (!factorStr || isNaN(factorStr)) {
throw "Please enter a valid Shear Rate Constant.";
}
var factor = parseFloat(factorStr);
// Formula: Shear Rate = RPM * Factor (Usually manufacturers provide factor in units compatible with RPM)
// Note: Sometimes factor is for rad/s, but commonly SRC is defined as Shear Rate / RPM.
// We assume SRC = Shear Rate / RPM based on standard simple user inputs.
shearRate = rpm * factor;
} else if (method === 'concentric') {
var rbStr = document.getElementById('bobRadius').value;
var rcStr = document.getElementById('cupRadius').value;
if (!rbStr || !rcStr || isNaN(rbStr) || isNaN(rcStr)) {
throw "Please enter valid radii for Bob and Cup.";
}
var rb = parseFloat(rbStr); // Bob Radius
var rc = parseFloat(rcStr); // Cup Radius
if (rb >= rc) {
throw "Cup radius must be larger than Bob radius.";
}
if (rb <= 0 || rc <= 0) {
throw "Radii must be positive numbers.";
}
// Formula for Concentric Cylinders (at the bob surface)
// Shear Rate = (2 * omega * Rc^2) / (Rc^2 – Rb^2)
var rcSq = rc * rc;
var rbSq = rb * rb;
shearRate = (2 * omega * rcSq) / (rcSq – rbSq);
} else if (method === 'cone') {
var angleStr = document.getElementById('coneAngle').value;
if (!angleStr || isNaN(angleStr)) {
throw "Please enter a valid Cone Angle.";
}
var angleDeg = parseFloat(angleStr);
if (angleDeg = 90) {
throw "Cone angle must be between 0 and 90 degrees (typically < 4).";
}
// Formula for Cone and Plate
// Shear Rate = omega / tan(theta)
// Theta must be in radians
var angleRad = angleDeg * (Math.PI / 180);
shearRate = omega / Math.tan(angleRad);
}
// Display Results
document.getElementById('resRpm').innerText = rpm + " RPM";
document.getElementById('resRad').innerText = omega.toFixed(3) + " rad/s";
document.getElementById('resShear').innerText = shearRate.toFixed(2) + " s⁻¹";
resultDiv.style.display = 'block';
} catch (err) {
errorDiv.innerHTML = err;
errorDiv.style.display = 'block';
}
}
Understanding the Shear Rate from RPM Calculation
In rheology and fluid dynamics, converting Rotational Speed (RPM) to Shear Rate ($\dot{\gamma}$) is a fundamental step in analyzing fluid behavior. While RPM measures how fast a spindle or impeller rotates, the shear rate describes the velocity gradient the fluid experiences, which is critical for determining viscosity in non-Newtonian fluids.
Why Can't I Just Use RPM?
RPM is a machine setting, whereas shear rate is a material-experienced parameter. For Newtonian fluids (like water), viscosity is constant regardless of speed. However, for non-Newtonian fluids (like ketchup, polymers, or blood), viscosity changes depending on how hard you shear them. To compare viscosity data across different instruments, you must calculate the shear rate, which depends heavily on the geometry of your measuring system (spindle shape and container size).
Calculation Formulas by Geometry
This calculator utilizes the standard rheological equations for the most common geometries:
1. Concentric Cylinders (Couette)
This geometry consists of a rotating inner cylinder (bob) and a stationary outer cup. The shear rate is highest at the surface of the bob.
Many viscometers (e.g., Brookfield, Anton Paar) simplify these calculations by providing a Shear Rate Constant (SRC) or M-factor for specific spindles.
Formula: $\dot{\gamma} (s^{-1}) = RPM \times SRC$
How to Use This Calculator
Select Method: Choose "Manufacturer Factor" if you have a constant from your manual, or select your specific geometry (Cylinders or Cone).
Input RPM: Enter the rotational speed of your instrument.
Input Dimensions:
For Cylinders, enter the radius (not diameter) of the Bob and Cup in millimeters.
For Cone & Plate, enter the cone angle in degrees.
Calculate: Click the button to see the shear rate in reciprocal seconds ($s^{-1}$).
Example Calculation
If you are using a concentric cylinder setup with a Bob radius of 15mm, a Cup radius of 16mm, running at 60 RPM: