Fundamentals of Haemodynamics - Computational Hemodynamics: Theory, Modelling and Applications - page 80

Fig. 4.10 a Turbulent and laminar velocity power-law empirical velocity profile defined by
Eq. 4.15. b Exponent n as a function of the Reynolds number defined by Eq. 4.16

Fig. 4.11 Fluid particle layers moving in a laminar and turbulent flow. The diffusion (or mixing)
of the fluid particles in a laminar flow is limited between adjacent layers because of the ordered
flow structure. For turbulent flow, there is intense mixing and fluid particles throughout mix which
creates a more even velocity distribution

4.6.3 Poiseulle's Law

The amount of blood that flows through the vessels depends on the difference in
pressure at the two ends P 1 and P 2 , the radius r and the length L of the pipe, and
the viscosity µ of the blood. Poiseuille's Law relates these parameters under steady
laminar flow condition, for a Newtonian fluid in a rigid pipe. If turbulence is pres-
ent, then the predicted flow rate does not comply since in general this value is
smaller than in laminar flows.
In many instances of the circulatory system, the vessels are rarely straight and
rigid to allow a parabolic profile. The aorta is a large curved vessel which exhibits
a Re number of around 1300 and an entrance length of 200 cm, much longer than
the entire aorta. This means that the flow profile can never reach a fully developed