Biofluid Mechanics
In a flow distribution network that progresses from a large tube to many small tubes (e.g. a blood vessel network), the frequency, density, and dynamic viscosity are (usually) the same throughout the network, but the tube radii change. Therefore the Womersley number is large in large vessels and small in small vessels. As the vessel diameter decreases with each division the Womersley number soon becomes quite small. The Womersley numbers tend to 1 at the level of the terminal arteries. In the arterioles, capillaries, and venules the Womersley numbers are less than one. In these regions the inertia force becomes less important and the flow is determined by the balance of viscous stresses and the pressure gradient. This is called microcirculation.
Some typical values for the Womersley number in the cardiovascular system for a canine at a heart rate of 2Hz are:
- Ascending Aorta -- 13.2
- Descending Aorta -- 11.5
- Abdominal Aorta -- 8
- Femoral Artery -- 3.5
- Carotid Artery -- 4.4
- Arterioles --.04
- Capillaries -- 0.005
- Venules -- 0.035
- Inferior Vena Cava -- 8.8
- Main Pulmonary Artery -- 15
It has been argued that universal biological scaling laws (power-law relationships that describe variation of quantities such as metabolic rate, lifespan, length, etc., with body mass) are a consequence of the need for energy minimization, the fractal nature of vascular networks, and the crossover from high to low Womersley number flow as one progresses from large to small vessels.
Read more about this topic: Womersley Number
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