# 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

In order to determine the shear stress applied onto your cells cultured under flow, please indicate the following values:

• Flow parameters (flow rate, pressure or shear stress)
• Fluid properties (viscosity and density)
• Tubing dimensions (optional) – important to calculate the hydraulic resistance of your system
• Channel geometry and dimensions inside your microfluidic chip – important for both the hydraulic resistance and the shear stress

You can use our calculator:

• To extract the value of the shear stress applied in your system when working with a fixed flow rate or a fixed pressure
• To determine which flow rate or pressure to apply in order to deliver a specific shear stress

Flow parameters

Fluid Properties

Tubing Resistance

Microfluidic chip: Channel geometry and dimensions