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0 1 2 Velocity

FIGURE 7 As fluid flows through a round tube, an infinite number of concentric lamina will be formed, with each lamina flowing slightly faster than that surrounding it. Velocity of the fluid is zero at the vessel wall and increases parabolically until a maximum velocity is achieved at the center. If the flow rate is increased, the laminar flow profile may break down, resulting in turbulent flow.

0 1 2 Velocity

FIGURE 7 As fluid flows through a round tube, an infinite number of concentric lamina will be formed, with each lamina flowing slightly faster than that surrounding it. Velocity of the fluid is zero at the vessel wall and increases parabolically until a maximum velocity is achieved at the center. If the flow rate is increased, the laminar flow profile may break down, resulting in turbulent flow.

at the same velocity, as shown in Fig. 7. In a round tube, an infinite number of concentric circular lamina are formed where all particles in a given lamina move at the same velocity. The fluid immediately adjacent to the walls wets the walls and does not move at all. Moving toward the center of the vessel each lamina goes slightly faster than the lamina that surrounds it. This arrangement causes the fluid in the center of the stream to move the fastest. An equilibrium will be achieved with a parabolic velocity profile across the vessel having a peak flow in the center equal to exactly twice the average velocity. It is often remarked that resistance to flow results from the friction between the fluid and the walls of the vessel. This is wrong, of course, as it was pointed out above that the lamina of fluid adjacent to the wall does not move. The friction results from the relative motion between each lamina. Viscosity refers to the force generated by the particles of the fluid that resists any relative motion between them. The greater the viscosity of a fluid, the more it resists such movement. The viscosity of blood is the source of the frictional losses as it resists movement between adjacent laminae.

Let us now consider laminar flow through a round tube such as a blood vessel. Blood moves through the blood vessels along pressure gradients in the cardiovascular system. Flow through a tube is proportional to the pressure difference across it, AP. That flow is impeded by the resistance (R) of the tube such that:

Resistance is determined in part by the viscosity of the fluid. The more viscous a fluid, the more resistance the fluid will encounter passing through a tube, making resistance proportional to viscosity:

Resistance is also affected by the length (L) of the tube through which the fluid flows. The longer the length, the more resistance the fluid will encounter so that resistance is proportional to the length:

Finally, resistance is affected by the radius of the tube. The larger the radius, the more easily fluid can pass through the vessel. Although one might think that resistance should be related to the cross-sectional area and thus follow r2, it actually is inversely proportional to the fourth power of the radius (r) of the tube.

In the late 18th century, a French physician named Poiseuille found that all these terms could be grouped together into one equation by including the appropriate constants. The following is known as Poiseuille's equation:

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