Turbulent flow

   The tendency for turbulent flow increases in direct proportion to the velocity of blood flow, in direct proportion to the diameter of the blood vessel, and inversely proportional to the viscosity of the blood divided by its density in accordance with the following equation:

Re = (v·d)/(h/r)

in which Re is Reynolds’ number and is the measure of the tendency for turbulence to occur, v is the velocity of blood flow (in centimeters/sec), h is the viscosity (in poises), and r is the density. The viscosity of the blood is normally about 1/30 poise, and the density is only slightly greater than 1. When Reynolds’ number rises above 200 to 400, turbulent flow will occur at some branches of vessels, but will die out along the smooth portions of the vessels. However, when Reynolds’ number rises above approximately 2000, turbulence will usually occur even in a straight, smooth vessel. Reynolds’ number for flow in the vascular system even normally rises to 200 to 400 in large arteries; as a result, there is almost always some turbulence of flow at the branches of the vessels. In some proximal portions of the aorta and pulmonary artery, Reynolds’ number can rise to several thousand during the rapid phase of ejection by the ventricles; this causes considerable turbulence in the proximal aorta and pulmonary artery where many conditions are appropriate for turbulence:  (1) high velocity of blood flow, (2) pulsatile nature of the flow, (3) sudden change in vessel diameter, and (4) large vessel diameter.
   However, in small vessels, Reynolds’ number is almost never high enough to cause turbulence.

ex AC Guyton, Textbook of Medical Physiology, ed 7, Saunders, 1986, p 210.