Reynold’s number (NR) is a dimensionless number that can predict whether turbulent or laminar flow exists in a tube under given conditions. NR is calculated by dividing inertial forces by viscous forces and is represented by Equation 17.12, where ρ is the fluid density, D is the tube diameter, v is the mean velocity, and η is the viscosity. Laminar flow is typically observed when NR is 2000 or less, turbulent flow when NR is 3000 or greater, and transitional flow when NR is between 2000 and 3000. Equation 17.12 reveals that turbulence is more likely to occur with high fluid densities, small tube diameters, high flow velocities, and low fluid viscosities. Additionally, turbulence can be caused by abrupt variations in tube dimensions or irregularities in the tube walls.

As blood flows through a vessel, it exerts a parallel force on the vessel wall known as shear stress (τ). Shear stress is directly proportional to the flow rate and viscosity of the fluid, as shown in Equation 17.13.

Turbulence within the cardiovascular system can be detected through a stethoscope during a physical examination, as it is usually accompanied by audible vibrations. When turbulence occurs in the heart, it produces a sound called a murmur, while in a vessel, it produces a sound called a bruit. Functional cardiac murmurs, which are murmurs not caused by structural abnormalities, are frequently detectable in severe anemia. This is due to the reduced viscosity of blood in anemia and the high flow velocities associated with the high cardiac output often found in anemic patients. Turbulent flow is more likely to lead to the development of blood clots or thrombi compared to laminar flow. In the surgical treatment of valvular heart disease using artificial valves, a concern is the potential occurrence of thrombi in association with the prosthetic valve. These thrombi can become dislodged and obstruct crucial blood vessels. Therefore, it is important to design such valves in a way that prevents turbulence and to include anticoagulants as part of therapy.
Whether turbulent or laminar flow exists in a tube under given conditions may be predicted on the basis of a dimensionless number called Reynold’s number (NR). This number represents the ratio of inertial to viscous forces. For a fluid flowing through a cylindrical tube,
Equation 17.12 where ρ= fluid density, D = tube diameter, v = mean velocity, and η= viscosity. When NR is 2000 or less, the flow is usually laminar; when NR is 3000 or greater, the flow is turbulent; and when NR is between 2000 and 3000, the flow is transitional between laminar and turbulent.
Eq. 17.12 indicates that high fluid densities, small tube diameters, high flow velocities, and low fluid viscosities predispose to turbulence. In addition to these factors, abrupt variations in tube dimensions or irregularities in the tube walls may produce turbulence.
Shear Stress on the Vessel Wall
As blood flows through a vessel, it exerts a force on the vessel wall parallel to the wall. This force is called a shear stress (τ). Shear stress is directly proportional to the flow rate and viscosity of the fluid:
Equation 17.13
Turbulenceisusuallyaccompaniedbyaudiblevibrations.Turbulentflowwithinthecardiovascularsystemmaybedetectedthroughastethoscopeduringphysicalexamination.Whentheturbulenceoccursintheheart,theresultantsoundistermedamurmur; whenitoccursinavessel,thesoundistermedabruit. Insevereanemia,functionalcardiacmurmurs(murmursnotcausedbystructuralabnormalities)arefrequentlydetectable.Thephysicalbasesforsuchmurmursresidesare(1)thereducedviscosityofbloodinanemiaand (2)thehighflowvelocitiesassociatedwiththehighcardiacoutputthatusuallyprevailsinanemicpatients.Bloodclots,orthrombi,aremorelikelytodevelopinturbulentflowthaninlaminarflow.Aproblemwiththeuseofartificialvalvesinthesurgicaltreatmentofvalvularheartdiseaseisthatthrombimayoccurinassociationwiththeprostheticvalve.Thethrombimaybedislodgedandoccludeacrucialbloodvessel.Itisimportanttodesignsuchvalvestoavertturbulenceandtoincludeanticoagulantsasapartoftherapy.