Parameters
Vessel Type
Vessel Radius R
12.5 mm
0.5 μm (capillary) — 12 mm (aorta)
Vessel Length L
20.0 cm
Pressure Drop ΔP
1333 Pa
10 mmHg = 1333 Pa
Blood Viscosity μ
3.5 mPa·s
Temperature & hematocrit dependent
Hematocrit Hct
45 %
Stenosis
0 %
Radius reduction (0% = normal, 90% = severe)
Heart Rate HR
72 bpm
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Flow Rate Q [ml/min]
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Mean Velocity [cm/s]
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Wall Shear Stress τ_w [Pa]
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Reynolds Number Re
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Womersley Number Wo
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WSS Risk Assessment
Velocity Profile (Cross-section)
Flow Rate vs Radius (R⁴ dependence)
Stenosis % vs Wall Shear Stress
Governing Equations
Hagen-Poiseuille (steady laminar pipe flow):
$$Q = \frac{\pi R^4 \Delta P}{8 \mu L}$$Wall shear stress: $\tau_w = \dfrac{4\mu Q}{\pi R^3} = \dfrac{R\,\Delta P}{2L}$
Velocity profile: $u(r) = \dfrac{\Delta P}{4\mu L}(R^2 - r^2)$
Womersley number: $Wo = R\sqrt{\omega/\nu}$ ($\omega = 2\pi \cdot HR/60$)
Biomedical Engineering Applications: Vascular stent design (WSS optimization) / LVAD & artificial heart CFD pre-analysis / Aneurysm simulation hand-calculation verification / Microfluidic bioreactor design. Re < 2300 is the laminar flow condition (Poiseuille equation validity range).