Calculate the wall shear rate of a Newtonian fluid flowing through a circular pipe based on volumetric flow rate and pipe geometry.
L/min
GPM (US)
m³/hr
m³/s
mm
inch
m
cm
Please enter valid positive numbers for Flow Rate and Diameter.
Wall Shear Rate (γ̇)
0 s⁻¹
Based on Newtonian laminar flow assumption.
How to Calculate Shear Rate from Flow Rate
Shear rate is a critical parameter in fluid dynamics and rheology, representing the rate at which adjacent fluid layers move past one another. In the context of pipe flow, calculating the shear rate is essential for determining pressure drop, sizing pumps for non-Newtonian fluids, and ensuring that shear-sensitive fluids (like blood or polymers) are not damaged during transport.
The Shear Rate Formula
For a Newtonian fluid flowing under laminar conditions inside a circular pipe, the wall shear rate (where the shear is highest) can be calculated using the following equation:
γ̇ = (32 · Q) / (π · D³)
Where:
γ̇ (Gamma dot): Shear Rate in reciprocal seconds (s⁻¹)
Q: Volumetric Flow Rate (e.g., m³/s)
D: Internal Pipe Diameter (e.g., m)
π: Pi (~3.14159)
Understanding the Variables
To use the formula correctly, unit consistency is vital. The standard SI derivation requires Flow Rate in cubic meters per second (m³/s) and Diameter in meters (m). Our calculator handles these conversions automatically for standard industrial units like Liters per minute (L/min), Gallons per minute (GPM), millimeters (mm), and inches.
Why Calculation Matters
1. Viscosity Determination: For non-Newtonian fluids, viscosity changes with shear rate. Knowing the shear rate inside your pipe allows you to look up the fluid's apparent viscosity on a rheogram.
2. Process Safety: High shear rates can degrade complex molecules or emulsified products. Calculating the shear rate helps engineers stay within safe operating limits.
3. Piping Design: The shear rate at the wall directly influences the friction factor and, consequently, the energy required to pump the fluid.
Calculation Example
Suppose you have water flowing through a 50 mm (0.05 m) pipe at a rate of 100 Liters per minute.