A thorough knowledge of fluid dynamics allows a physician to understand the cardiovascular system, both when functioning normally and in certain disease states. In addition to Bernoulli’s principle, a thorough understanding of the processes of fluid flow is essential.  This is particularly true when attempting to understand the physiology of the cardiovascular system. 

    The continuity equation relates the volume flow rate (Q) to the cross sectional area of a blood vessel (A) and the velocity with which blood flows through it (v).  It allows the physiologist to predict flow velocity and, through application of Bernoulli’s principle, the pressures in different areas of the circulatory system. 

Q = A*v

Cross sectional areas and diameters of various blood vessels are provided in Table 1. 

Vessel Total Cross Sectional Area in cm2 Diameter of Individual Vessel in cm
 Aorta 2.5 1.8
 Arteries 20 
 Arterioles 40 
 Capillaries 2500 0.0008
 Venules 250 
 Small Veins 80 
 Vena Cava 8 3.2

                                                                                Table 1

    The variations in pressure in different parts of the circulation place strains on the walls of the blood vessels.  This strain, known as wall tension, is a function of both the pressure of the fluid in the vessel and its radius.  Wall tension is given by LaPlace’s principle, which states that the tension on the wall of a vessel is proportional to both its radius and its local blood pressure.

T = P*r

    The flow of blood in the circulatory system can be compared to the flow of electrons in an electrical circuit.  Ohm’s law can therefore be applied analogously to a circulatory system using a pressure difference for voltage difference, blood flow for current, and vascular resistance for electrical resistance, yielding very useful clinical measurements.

Ohm’s Law for Circuits

Ohm’s Law for Fluid Flow

    Kirchoff’s rules can also be applied to circulatory circuits to make deductions about blood flow. Figure 1 outlines one such partial circuit (fetal circulation), in which the ductus arteriosus is used to shunt blood from the pulmonary artery to the aorta, bypassing the lungs.

                                Figure 1

    The total performance of the heart can be assessed by measuring the volume of blood it pumps per unit time (cardiac output) and the volume of blood it pumps per beat (stroke volume): 
CO = SV * HR

Question #0005

Which of the following graphs depicts the relationship between the radius of a blood vessel and the tension in its wall?

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