In a narrow section (B) of a tube, the linear velocity (v) and therefore the dynamic component of pressure (ρv2/2) are greater than in the wide sections (A and C) of the same tube. If the total energy is virtually constant throughout the tube (i.e., if the energy loss due to viscosity is negligible), the lateral pressure in the narrow section is lower than the lateral pressure in the wide sections of the tube (see the heights of the column of fluid above compartments A, B, and C, each of which reflects pressure).

The energy loss from viscosity is negligible (i.e., this fluid is an "ideal fluid"). The effect of velocity on the dynamic component (Pdyn) can be estimated as follows:

Equation 17.2 where ρ is the density of the fluid (grams per cubic centimeters) and v is velocity (centimeters per second). Assume that the fluid has a density of 1 g/cm3. In section A in Fig. 17.2, the lateral pressure is 100 mm Hg; note that 1 mm Hg equals 1330 dynes/cm2. According to Eq. 17.2, Pdyn = 5000 dynes/cm2, or 3.8 mm Hg. In the narrow section B of the tube, where the velocity is twice as high, Pdyn = 20,000 dynes/cm2, or 15 mm Hg. Thus the lateral pressure in section B is 15 mm Hg lower than the total pressure, whereas the lateral pressures in sections A and C are only 3.8 mm Hg lower. In most arterial locations, the dynamic component is a negligible fraction of the total pressure. However, at sites of an arterial constriction or obstruction, the high flow velocity is associated with large kinetic energy, and the dynamic pressure component may therefore increase significantly. Hence, the pressure would be reduced, and perfusion of distal segments would be correspondingly decreased. This example helps explain how pressure changes in a vessel that is narrowed by atherosclerosis or spasm of the blood vessel.

Laminar and Turbulent Flow: A, When flow is laminar, all elements of the fluid move in streamlines that are parallel to the axis of the tube; the fluid does not move in a radial or circumferential direction. The layer of fluid in contact with the wall is motionless; the fluid that moves along the central axis of the tube has the maximal velocity. B, In turbulent flow, the elements of the fluid move irregularly in axial, radial, and circumferential directions. Vortices frequently develop.

In narrowed sections of a tube, the dynamic component increases significantly because the flow velocity is associated with large kinetic energy. This occurs due to the wall effect. The dynamic component is a negligible fraction of the total pressure in most arterial locations. However, at sites of arterial constriction or obstruction, the high flow velocity is associated with large kinetic energy, leading to a significant increase in the dynamic pressure component. This results in a reduced pressure and decreased perfusion of distal segments. This example helps in understanding how pressure changes in a vessel narrowed by atherosclerosis or spasm of the blood vessel.

The flow of fluids through cylindrical tubes is governed by Poiseuille's law. Poiseuille, a French physiologist, derived this law empirically in the 1840s. Although he primarily focused on the physical determinants of blood flow, he conducted his measurements using simpler liquids in glass capillary tubes. Poiseuille's observations were so precise and important that they have been designated Poiseuille's law.

Poiseuille's law applies to the steady (nonpulsatile) laminar flow of newtonian fluids through rigid cylindrical tubes. A newtonian fluid is one whose viscosity remains constant, and laminar flow refers to the motion in which the fluid moves as a series of individual layers, with each layer moving at a velocity different from that of its neighboring layers.
˜v2/2 = 3.8 mm Hg 15 mm Hg 3.8 mm Hg •Fig. 17.2 Inanarrowsection(B)ofatube,thelinearvelocity(v)andhencethedynamiccomponentofpressure(ρv2/2)aregreaterthaninthewidesections(AandC),ofthesametube.Ifthetotalenergyisvirtuallyconstantthroughoutthetube(i.e.,iftheenergylossbecauseofviscosityisnegligible),thelateralpressureinthenarrowsectionislowerthanthelateralpressureinthewidesectionsofthetube(seetheheightsofthecolumnoffluidabovecompartmentsA,B,andCeach,whichreflectpressure).
the energy loss from viscosity is negligible (i.e., this fluid is an “ideal fluid”). The effect of velocity on the dynamic component (Pdyn) can be estimated as follows:
Equation 17.2 where ρ is the density of the fluid (grams per cubic centimeters) and v is velocity (centimeters per second). Assume that the fluid has a density of 1 g/cm3. In section A in
Fig. 17.2 , the lateral pressure is 100 mm Hg; note that 1 mm Hg equals 1330 dynes/cm2. According to
Eq. 17.2, P dyn = 5000 dynes/cm2, or 3.8 mm Hg. In the narrow section B of the tube, where the velocity is twice as high, Pdyn = 20,000 dynes/ cm2, or 15 mm Hg. Thus the lateral pressure in section B is 15 mm Hg lower than the total pressure, whereas the lateral pressures in sections A and C are only 3.8 mm Hg lower. In most arterial locations, the dynamic component is a negligible fraction of the total pressure. However, at sites of an arterial constriction or obstruction, the high flow velocity is associated with large kinetic energy, and the dynamic pressure component may therefore increase significantly. Hence, the pressure would be reduced, and perfusion of distal segments would be correspondingly decreased. This example helps explain how pressure changes in a vessel that is narrowed by atherosclerosis or spasm of the blood vessel •Fig. 17.3 Laminar and Turbulent Flow. A, Whenflowislaminar,allelementsofthefluidmoveinstreamlinesthatareparalleltotheaxisofthetube;thefluiddoesnotmoveinaradialorcircumferentialdirection.Thelayeroffluidincontactwiththewallismotionless;thefluidthatmovesalongthecentralaxisofthetubehasthemaximalvelocity.B, Inturbulentflow,theelementsofthefluidmoveirregularlyinaxial,radial,andcircumferentialdirections.Vorticesfrequentlydevelop.
wall: that is, in narrowed sections of a tube, the dynamic component increases significantly because the flow velocity is associated with large kinetic energy.
The most fundamental law that governs the flow of fluids through cylindrical tubes was derived empirically by the French physiologist Jean Léonard Marie Poiseuille in the 1840s. He was interested primarily in the physical determinants of blood flow, but he replaced blood with simpler liquids in his measurements of flow through glass capillary tubes. His work was so precise and important that his observations have been designated Poiseuille’s law.
Poiseuille’s law applies to the steady (i.e., nonpulsatile) laminar flow of newtonian fluids through rigid cylindrical tubes. A newtonian fluid is one whose viscosity remains constant, and laminar flow is the type of motion in which the fluid moves as a series of individual layers, with each layer moving at a velocity different from that of its neighboring layers (