The elementary principles of liquid dynamics are described by the equations of Bernoulli and Poiseuille. Bernoulli's equation deals with nonviscous liquids under steady streamline flow. Pressures in such flows are related to gravity and/or acceleration. Changes in elevation affect the gravitational potential energy of the liquid and the velocity of flow determines the kinetic energy. The sum of these three factors represented in the Bernoulli equation remains constant, but the variables are interconvertible. In contrast, the Poiseuille equation describes the pressures related to viscous resistance only, and the energy of flow is dissipated as heat. A combination of the two equations describes the flow in tubes more realistically than either equation alone. In "open" systems gravity hinders uphill flow and causes downhill flow, in which the liquid acts as a falling body. In contrast, in "closed" systems, like the circulation, gravity does not hinder uphill flow nor does it cause downhill flow, because gravity acts equally on the ascending and descending limbs of the circuit. Furthermore, in closed systems, the liquid cannot "fall" by gravity from higher levels of gravitational potential to lower levels of potential. Flow, up or down, must be induced by some source of energy against the resistance of the circuit. In the case of the circulation, the pumping action of the heart supplies the needed energy gradients. Flow in collapsible tubes, like veins, obeys the same basic laws of liquid dynamics except that transmural pressures near zero or below zero reduce markedly the cross-sectional area of the tube, which increases the viscous resistance to flow.(ABSTRACT TRUNCATED AT 250 WORDS)

The flow of blood through the cardiovascular system depends on basic principles of liquid flow in tubes elucidated by Bernoulli and Poiseuille. The elementary equations are described involving pressures related to velocity, acceleration/deceleration, gravity, and viscous resistance to flow (Bernoulli-Poiseuille equation). The roles of vascular diameter and number of branches are emphasized. In the closed vascular system, the importance of gravity is deemphasized, and the occurrence of turbulence in large vessels is pointed out.

Controversy exists over the principles involved in determining blood flow to the head of a giraffe, specifically over the role of gravity pressure (pgh) in the collapsible jugular vein in facilitating uphill flow in arteries. This study investigated the pressures within vertically oriented models containing both rigid and collapsible tubes. An inverted U tube was constructed (height = 103 cm) of thick rubber tubing in the ascending limb and collapsible dialysis tubing in the descending limb. Water flow was induced by a variable speed pump maintained at the reservoir level such that the descending limb was partially collapsed. Pressure measurements were made at various levels within the U tube by two methods: 1) with the transducer at same level as the tip of the water-filled catheter and 2) with the transducer at the reservoir level. During flow, the pressure at any point was nearly atmospheric along the length of the descending limb. Such methods of obtaining pressure indicated that the pressure gradient within the partially collapsed descending limb was the sum of viscous flow pressure (P1-P2 of Poiseuille) and gravitational pressure (pgh). To study the facilitatory effect of a siphon, the descending limb was compared with a horizontally placed limb (length = 100 cm), and the flow was kept constant. Calculations of hydraulic "work" (pressure x flow) indicated that with a partially collapsed descending limb, work of the pump was reduced by 15% compared with uphill flow to the elevated horizontal position. It is concluded that the siphon mechanism operates in a partially collapsed descending limb of a siphon loop.

No abstract

No abstract