Rpm to Shear Rate Calculator

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RPM to Shear Rate Calculator

Calculated Results:

Shear Rate: 0 s⁻¹

Tip Speed: 0 m/s

function calculateShearRate() { var rpm = parseFloat(document.getElementById('rpmVal').value); var diameter = parseFloat(document.getElementById('diameterVal').value); var gap = parseFloat(document.getElementById('gapVal').value); if (isNaN(rpm) || isNaN(diameter) || isNaN(gap) || gap <= 0) { alert("Please enter valid positive numbers. Gap distance cannot be zero."); return; } // Formula Logic: // 1. Convert Diameter from mm to meters: D_m = diameter / 1000 // 2. Convert RPM to Revolutions per second: RPS = rpm / 60 // 3. Tip Speed (V) = PI * D_m * RPS // 4. Shear Rate (gamma) = V / Gap_m var dMeters = diameter / 1000; var gapMeters = gap / 1000; var rps = rpm / 60; var tipSpeed = Math.PI * dMeters * rps; var shearRate = tipSpeed / gapMeters; document.getElementById('shearRateResult').innerText = shearRate.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('tipSpeedResult').innerText = tipSpeed.toLocaleString(undefined, {minimumFractionDigits: 3, maximumFractionDigits: 3}); document.getElementById('resultDisplay').style.display = 'block'; }

Understanding RPM to Shear Rate Conversion

In fluid dynamics and rheology, the conversion of rotational speed (RPM) to shear rate is critical for understanding how substances behave under stress. Whether you are working with high-shear mixers, viscometers, or industrial homogenizers, the shear rate determines the level of mechanical energy applied to the fluid.

The Shear Rate Formula

For a standard rotor-stator or concentric cylinder system, the shear rate (γ) is calculated based on the velocity gradient between the moving part (rotor) and the stationary part (stator). The formula used in this calculator is:

γ = (v) / (g)

Where:

  • γ (Shear Rate): Measured in reciprocal seconds (s⁻¹).
  • v (Tip Speed): The linear velocity at the outer edge of the rotor (m/s). Calculated as: π × Diameter × (RPM / 60).
  • g (Gap Distance): The clearance between the rotor and the stator (meters).

Practical Example

Imagine you are operating a laboratory mixer with a 40mm diameter impeller spinning at 2000 RPM. The gap between the impeller tip and the vessel wall is 1mm.

  1. Calculate Tip Speed: π × 0.04m × (2000 / 60) ≈ 4.188 m/s.
  2. Calculate Shear Rate: 4.188 m/s / 0.001m = 4,188 s⁻¹.

Why is Shear Rate Important?

Shear rate is a fundamental parameter in several industries:

  • Pharmaceuticals: Ensuring active ingredients are properly dispersed in emulsions.
  • Food Science: Controlling the texture of sauces, mayonnaises, and dairy products.
  • Cosmetics: Achieving the desired "feel" and stability of lotions and creams.
  • Paint and Coatings: Influencing the flow properties (thixotropy) during application.

Common Shear Rate Ranges

Process Typical Shear Rate (s⁻¹)
Sedimentation 10⁻⁶ to 10⁻⁴
Pouring from a bottle 10¹ to 10²
Mixing and Stirring 10¹ to 10³
Spraying and Brushing 10³ to 10⁵
High Speed Homogenization 10⁵ to 10⁷

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