Chapter 12: Fluid Dynamics
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12
d)
e) All are appropriate
5.
Which of the following two fluid systems performed more
work?
SystemA: 10 liters pumped out in 10 minutes
System B: 11 liters pumped out in 40 minutes
6.
In a lossless closed system, if the velocity of flow doubles the
kinetic energy _________ .
7.
A change of 5 ml per mmHg is a measure of what flow
parameter?
8.
A change of 5 ml per second is a measure of what flow
parameter?
9.
Which system has a higher capacitance?
SystemA: can receive 10 liters in 1 minute
System B: can receive 2 liters in 10 minutes
10. If energy can be lost to heat, fluid at a distal point (later in
the flow path) will have ________ energy than/as the fluid
at a proximal point, for a closed system.
a) less
b) more
c) the same
3. Derivation of Equations
3.1 Introduction
Before developing the fluid dynamic equations, there are three
important points that will facilitate a better and more intuitive
understanding.
1) The starting points for some of the equations are found in the
answer section of the flow analogy. Make certain to review the
analogy exercises and explanations.
2) The fundamental fluid dynamic equation, Poiseuille’s law, was
originally determined empirically (from observation and ex-
perimentation rather than theory and mathematical rigor). Most
treatments of hemodynamics begin by simply stating Poiseuille’s
equation and thenmanipulating the equation to derive the resistance
equation, the simplified law of hemodynamics, and the volumetric
flow equation. In this text, we will do exactly the opposite. Using
observation, reasoning and mathematical relationships, we will de-
velop the resistance equation, the simplified law of hemodynamics,
and the volumetric flow equation. From these three equations we
will express Poiseuille’s law.
The standard approachmore clearly reflects how the equations were
discovered, but the approach taken here will help develop a more
intuitive understanding of the equations.
3) The development of the equations will be based on intuitive un-
derstanding and will not be mathematically rigorous. There is value
in mathematical rigor when proving the validity of mathematical
expression, but this is not our goal.These equations have been long
since validated and require no proof. Our goal is to understand how
the equations can be applied and what each tells us about the flow
of blood with varying hemodynamic situations.
KEY CONCEPT
3.2 The Resistance Equation
The conceptual foundation for the resistance equation was found by
answering questions 10, 11 and 12 of the flow analogy. For the sake
of clarity, similar scenarios will be repeated here to help develop the
mathematical relationships between the physical parameters which
determine the resistance to flow.
Scenario 1: (Varying Length)
Assume there are two pipelines through which the same volumetric
flow of 10 liters/min is required. Which of these two pipelines, as
illustrated in
Figure 4
, would require more energy, hence offering
greater resistance?
Fig. 4
Effect of length on resistance
Clearly the longer flow conduit will requiremore energy to transport
the same volumetric flow. By definition,energy per volumetric flow
is the resistance. Therefore as the length of the conduit increases
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