Vascular Wall Shear Stress Calculator

Cardiovascular biomechanics & hemodynamics: Determine endothelial Wall Shear Stress ($WSS$), blood flow Reynolds number, and Womersley pulsatility parameter across arterial geometries.

Vessel Geometry & Volumetric Flow

Arterial Lumen Diameter D (mm): Internal diameter (e.g. Carotid ~6mm, Aorta ~25mm)

Blood Flow Rate Q (mL/min): Mean volumetric blood flow

Blood Rheology & Heart Rate

Dynamic Viscosity μ (cP / mPa·s): Whole blood ~3.5 cP at 37°C

Blood Density ρ (kg/m³): Normal blood density ~1060 kg/m³

Heart Rate (bpm): Used for Womersley pulsatile frequency

Poiseuille Wall Shear Stress (WSS)

For laminar blood flow through a cylindrical vessel:
$$\tau_w = \frac{4 \mu Q}{\pi R^3} = \frac{32 \mu Q}{\pi D^3}$$ Pulsatile inertia is governed by the Womersley number $\alpha = R \sqrt{\frac{\omega \rho}{\mu}}$ where $\omega = 2\pi f$.

Endothelial Wall Shear Stress

Wall Shear Stress (Pa)

Wall Shear Stress (dyn/cm²)

Flow Kinematics & Dimensionless Numbers

Reynolds Number (Re)

Laminar if Re < 2000

Womersley Number (α)

Unsteady inertial parameter

Endothelial Mechanobiology

Mean Blood Flow Velocity (v̄): --

Velocity Profile Shape: --

Atherosclerosis Vulnerability: --

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