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Fluid Dynamics (Vocabulary ((Resistance = Ratio of the pressure drop…
Fluid Dynamics
Vocabulary
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Viscosity = Ratio of the shear stress to the shear rate of a fluid; measure of the resistance of a fluid to flow due to the attraction of molecules.
Conservation of Energy = Energy is always conserved -- energy is never lost, only converted between forms
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Resistance = Ratio of the pressure drop across a flow path per volumetric flow; measure of the impediment that must be overcome for flow to occur
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Work = Amount of energy transferred. The total energy expended,.
Bernoulli's Equation
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The equation states that presuming no energy conservation to heat, in a closed system, the energy is conserved.
Flow through narrowing = higher velocity, increase in KE. Since energy is conserved, increase in KE results in an decrease in PE
Flow conduit expands to original dimension = Velocity decelerates reducing KE, reduction of KE = increase in PE and pressure will return to origin.
Flow through Rigid Tube
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Laminar = flow through wide segments, parallel streamlines
Plug Flow = Entrance/ inlet effect, increase velocity to maintain flow
Parabolic Laminar = Flattened laminar flow, more parabolic shape
Turbulence = As high veolcity exits narrow diameter, major change in flow constraints, chaotic flow
Reynolds Number
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Re > 2,000 results in turbulence
An increase in fluid density, vessel diameter, & mean velocity all increase the likelihood of turbulence.
Capacitance
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Capacitance is proportional to the change in volume.
Capacitance is inversely related to the change in time.
Hydrostatic Pressure
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Hydrostatic Pressure is proportional to the density of the fluid, height of the fluid, and the gravity.
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Poiseuille's Law
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Poiseuille's can be created by rewriting the simplified law in terms of the volumetric flow (Q) and the substituting for the resistance, R.
Resistance Equation
Resistance is proportional to length, viscosity, and inversely related to the radius to the fourth power
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Hemodynamics
Parallel Resistance
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Placing 4 short segments in parallel, effective resistance now decreases by a factor of 4
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Pressure, Flow & Resistance in CV System
Arterial Vessel Sizes = varying vessel diameter controls effective resistance through arterial system. It is critical to control pressure decrease as well as regulate volumetric flow
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From Lt. heart toward periphery, resistance decreases in progression from the low resistance of aorta to relatively high resistance of the arterioles.
Resistance in the capillaries is very high, although generally lower than the resistance of the arterioles because of sheer number of capillaries.
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Venous System
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Venous pressure in extremities is 15 mmHg & typical right atrial pressure is between 2 - 8 mmHg. As a result, there are only about 10 mmHg dynamic pressure to drive venous return
Capacitance acts as a reservoir to supply volume under higher demand and venovasomotor tone regulates mean arterial pressure
Calf Muscle pump helps overcome the effect of gravity to aid with venous return for a patient in the standing position.
By muscle contraction, venous volume is ratcheted back toward the Rt. heart through a series of valves which open and close with muscle contraction.
Sub-Critical Disease
Energy losses under normal metabolic demand are small enough that the body can adequately compensate, & end organ is adequately perfused.
Perfusion requirements are met, the patient is asymptomatic for normal metabolic demand.
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Series Resistance
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4 shorter segments connected in series is simply four times the resistance of one short segment.
4 shorter segments connected in a series have the same effective resistance as one longer segment of the same diameter.
Blood Viscosity
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For small vessels, apparent viscosity also changes
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Rigid Flow Conduits
Arteries are elastic and not rigid conduits for flow. The driving pressure for blood flow is highly pulsatile (dynamic pressure is not steady)
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Capacitance of aorta allows energy to be stored in the walls of aorta, to provide energy to propel blood during diastole.
Run off from the capacitive aorta through the resistive arterioles and capillaries reduces the pulsatility, improving heart efficiency.
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Elastic Veins
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Reservoir serves as a means to store blood until it is needed due to blood loss or increased volumetric demand.
Transmural Pressure
A measure of the difference of the pressure inside the vessel (Intravascular pressure) relative to the pressure outside the vessel (Tissue pressure).
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Spectral Windows
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Loss of SW can be affected by many parameters such as proximity of sample volume to the vessel wall, a large sample volume of CW Doppler, over-gaining, spectral broadening
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Pressure Gradient
Normal Metabolic demand, the pressure drop depicted is related to 4 times the velocity v squared.
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An increase in demand by a factor of 4, with exercise, results in a factor of 4 increase in velocity.
Pressure gradient is related to 4 times the square of 4v. Increase in pressure gradient by a factor of 16 occurs.
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Critical stenosis
Energy lost to frictional and viscous effects becomes so severe that volume is not maintained though lesion
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