# Shear Stress Calculator

The shear stress corresponds to the dragging force generated by the friction of a moving fluid onto a surface. Thus, cells exposed to a fluid flow endure this shear stress, known to affect their phenotype, morphology and their maturation.

You can use our Shear Stress Calculator to determine your experimental parameters. Define the flow rate or the pressure to be applied in your system, the dimension of microfluidic chip and tubing length in order to apply the correct shear stress for your cell culture under flow conditions.

Of note, the dimension of your chip (width) as well as the tubing connected to it (inner diameters and length) determine the overall hydraulic resistance of your system.

## Cylindrical channel

For a circular cross-section of diameter d

Shear stress is:

τ = 4ηQ / r³π

Where Q is the flow rate, η the dynamic viscosity and r the radial distance from the centerline of the channel (r=d/2)

## Rectangular channel

In rectangular channels, the flow velocity profile and subsequent shear stress are more complex. Wall shear stress is not constant and varies across the top, bottom, and side walls of the channel. However, the geometry can be simplified by considering two infinite parallel plates instead of closed channels.

Under this assumption, the shear stress follows the equation:

τ = 6ηQ / h²w

Where Q is the flow rate, η the dynamic viscosity, h the channel height and w the channel width

# Shear stress calculator

### Flow parameters

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*The shear stress is often measured in dyne per cm² (dyn/cm²) or in Pascal (Pa). Of note, 1 Pa = 10 dyn/cm²