*Note: This calculation assumes a no-slip boundary condition and laminar flow.
How to Calculate Shear Rate
Shear rate (denoted by γ̇, or "gamma dot") is a measure of how fast a fluid flows relative to the distance over which that flow occurs. It quantifies the rate of deformation of a fluid element. Understanding shear rate is critical in fields ranging from chemical engineering and rheology to injection molding and physiology (blood flow).
Quick Definition: Shear rate represents the velocity gradient perpendicular to the direction of flow. The standard unit is reciprocal seconds (s⁻¹).
1. Simple Shear (Parallel Plates)
The most fundamental definition of shear rate comes from the Couette flow model, where a fluid is trapped between two parallel plates—one stationary and one moving.
Formula:
γ̇ = v / h
γ̇ = Shear Rate (s⁻¹)
v = Velocity of the moving plate (m/s)
h = Gap distance between plates (m)
2. Pipe Flow (Newtonian Fluid)
For fluids flowing through a circular pipe, the shear rate is not constant; it is zero at the center and maximum at the wall. This calculator estimates the Shear Rate at the Wall for a Newtonian fluid.
Formula:
γ̇ = 8v / D
γ̇ = Shear Rate at the wall (s⁻¹)
v = Average flow velocity (m/s)
D = Inside Diameter of the pipe (m)
Calculation Example
Imagine a coating process where a blade moves over a surface (Parallel Plate model):
Velocity (v): 0.5 m/s
Gap Height (h): 1 mm (which is 0.001 meters)
Step 1: Convert units to match. 1 mm = 0.001 m.
Step 2: Apply the formula: γ̇ = 0.5 / 0.001
Result: The Shear Rate is 500 s⁻¹.
Why is Shear Rate Important?
Shear rate determines the viscosity of non-Newtonian fluids.