Reynolds number aorta

The flow rate of blood through the heart is approximately 4-5lmin for adults. The typical mean blood velocity through the aorta (which is the largest artery with a diameter of 2-3 cm), when pumped from the left heart, is approximately 25 cm s"i (mean) the maximum velocity is approximately 60 cm s h The Reynolds number for the maximum velocity is about 3000. In general, the blood flow through arteries and veins is laminar in nature. In capillaries, the typical blood velocity is 0.5-1 mm s , and the Reynolds number is on the order of 0.001. 

Li, J.K.-J. Laminar and turbulent flow in the mammalian aorta Reynolds number. J. Theor. Biol. 135 409 14,1988. 

Flow in the arterial circulation is predominantly laminar with the possible exception of the proximal aorta and main pulmonary artery. In steady flow, transition to turbulence occurs at Reynolds numbers (Nr) above approximately 2300... 

Mean and peak Reynolds numbers in human and dog are given in Table 56.2, which also includes mean, peak, and minimum velocities as well as the Womersley number. Mean Reynolds numbers in the entire systemic and pulmonary circulations are below 2300. Peak systolic Reynolds numbers exceed 2300 in the aorta and pulmonary artery, and some evidence of transition to turbulence has been reported. In dogs, distributed flow occurs at Reynolds numbers as low as 1000, with higher Womersley numbers increasing the transition Reynolds number [Nerem and Seed, 1972]. The values in Table 56.2 are typical for individuals at rest. During exercise, cardiac output and hence Reynolds numbers can increase severalfold. The Womersley number also affects the shape of the instantaneous velocity profiles as discussed below. 

ANS That would be a major effect. But you are not going to have that kind of ratio in a coronary artery because of the Reynolds number there as compared to the aorta. It s well known that in the aorta there is anything but a parabolic situation. Our own measurements in coronary arteries in a number of animals suggest it s reasonably close, i.e. a parabolic velocity profile is a reasonable approximation. 

Since the entrance length, in units of tube diameters, is proportional to the Reynolds number and the mean Reynolds number for flow in large tubes such as the aorta and trachea is of the order of 500 to 1000, the entrance length in these vessels can be as much as 20 to 30 diameters. In fact, there are few segments of these vessels even close to that length without a branch or curve that perturbs their flow. Consequently, flow in them can be expected to almost never be fuUy developed. In contrast, flow in the smallest bronchioles, arterioles, and capillaries may take place with Re < 1. As a result, their entrance length is 1 diameter, and flow in them will virtually always be nearly or fully developed. 

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