CHEMISTRY / PHYSICS
ANOTHER LOOK AT WEEK FOUR'S CLASS OUTLINE
Nature of Flow
that are capable of flowing. Fluids are either liquid, which has size but no
shape, or gases, which have neither shape nor size.
Definitions: Flow: Motion through a constraint which
is accompanied by a deformation of the fluid. Measured in cm2 /sec
- States of fluid
Density: Think of it as thickness of a fluid. Mass/volume
Viscosity: Think of it as stickiness of a fluid. It is
the internal friction of molecules of liquid or gas. Temp and being mixed with
other substances will affect viscosity.
Critical Flow Rate: This rate exists for a given tube diameter for a
given fluid at a given temp. If it exceeds this rate it goes from laminar to
turbulent flow. The critical flow rate varies directly as the diameter of the
tube. The narrower the tube, the less the flow rate necessary to convert a flow
from a laminar to a turbulent one. The wider the tube, the greater the volume of
fluid which may be discharged through it in a unit of time before a laminar flow
is converted to a turbulent one.
Rate of flow through orifices and tubes – Reynolds # is
determined for each particular fluid and is the product of the density of the
fluid, the linear velocity of the fluid, and the diameter of the tube, divided
by the viscosity of the fluid.
Density x velocity x diameter
Viscosity this number is dimensionless, as in it has no value. So this #
means that turbulent flow is likely to occur when the fluid density and linear
velocity are high, when the diameter is large, or when the viscosity is low. In
a long straight, rigid tube, turbulent flow is said to occur when Reynold’s #
exceeds approximately 2300, but this number can change under different
conditions. A tube can be defined as a pathway through which a fluid may
pass, the diameter of which is considerably less than the length. An orifice,
on the other hand, is an opening through which a fluid may pass, the diameter of
which is considerably greater than the length.
Laminar and turbulent flow – Laminar flow is streamlined
and consists of large # of concentrically arranged cylinders of fluid that are
flowing at different rates. Flow moves along in an orderly fashion in paths
parallel to the walls of the tube. Turbulent flow is not orderly flow. It
has many breakdowns of cylinders as the vortex changes. Paths of molecules are
haphazard and at angles to the walls of the tube. Flow is disorderly and at high
velocity. Transitional flow is when laminar flow converts to turbulent
flow and has a mixture of both. This usually occurs at branch points or
narrowing or partial obstruction or constricture of vessels.
Effects of friction and resistance- Resistance is the pressure
difference btw 2 ends of a tube – one end vs the other. Resistance to flow is
highest for the cylinders that come in contact with the outside wall of a
vessel. They have 0 velocity and theoretically are not moving. There is greater
velocity for the cylinders in the centers as they are moving faster. Unit of
measure is dynes/cm5. Friction is why pressure drops when you increase length.
Use as square root/flow.
Airway factors affecting flow – flow through an orifice will
affect flow rate. Any kinks or bends will slow flow. If there is nonuniformity
to the interior walls the flow rate will be decreased. Therefore it is important
to straighten things like an ETT. Also should use the largest diameter and
reduce the length as much as possible. Certain tubes used in the OR such as RAE
tubes don’t or aren’t able to be straight. These are curved tubes at the 1st
part. They can be nasal or oral. The special curve moves it out of the way of
the mouth or nose so that surgery can take place. But the problem is that this
curve now increases resistance, which decreases flow. Airway anatomy could
affect flow. If there were any tumors or reactive airway disease such as asthma,
bronchitis, COPD, these will all affect flow by increasing resistance. A status
asthmaticus pt can break this cycle by an inhalation induction since the agents
have a relaxing affect to smooth muscle. Tumors could make this worse though if
you have a ball and valve tumor and you relax them, the ball could fall in place
and now you have a mechanical obstruction and can’t oxygenate them.
Effects of speed and pressure If you increase pressure, flow
increases. Analogy to BP and CO. Where CO = MAP Resistance = MAP
SVR CO When you increase resistance then CO will decrease. Our anesthetic
agents will decrease SVR, BP and FLOW
Bernoulli’s theorem- pressure flowing through a tube will vary
according to cross-sectional diameter. If the tube narrows down and then
enlarges again the area with the least amount of pres is where the tube 1st
decreases its diameter and the area with the widest portion will have the
greatest pressure and flow will be the slowest.
Venturi system- works on Bernoulli’s theorem. Air in the narrowed
area will entrain pres from the outside and lower the pressure. It acts like a
vacuum and allows entrapment of air/fluid from the other side. Normally as fluid
flows through an area of constriction the velocity of the fluid through the
constricted area will be greatest. As the constriction widens back out and if it
does so gradually in a cone like manner at an angle not exceeding 15 degrees,
the velocity and pressure will return to near normal values. The pressure in the
middle section will be lower and could be subatmospheric. If you had the same
tube but the constriction changed abruptly the pressure on the other end will
remain lower than the front. If you put a port of entry at this constricted
area, it will entrain fluid or gas there. Since the pressure is lowest it can
entrain fluids or drugs. The ratio of aspirated fluid or drug is independent of
flow of the fluid. Even if you sped up flow you won’t change the amt of ratio
of drug. This is how nebulizers or atomizers work. If you push fluid or air
through the space the pres goes down since the velocity is faster and you have a
decrease in pressure on the lateral wall.
Viscosity and flow Viscosity is the internal friction of molecules
of liquid or gas. Friction comes from two places. One portion is caused by the
contact of the molecules of the fluid with the surface of the tube; the other is
due to internal friction, that is, friction of the molecules within the fluid.
When a fluid moves through a tube of uniform diameter the velocity of the
molecules is not uniform throughout its mass. If the molecules could be
visualized, those adjacent to and in immediate contact with the wall, a single
layer, would appear to be at complete rest. The next layer moves, but
sluggishly. The next moves more rapidly. As the center of the tube is
approached, the molecules in each layer move with greater velocity, the
molecules in the center moving the fastest. The forward advance of a row of
molecules extending along the diameter of the tube would be represented by a
Poiseuille’s Law- the volume of a fluid discharged through a tube
varies with the length of the tube, the diameter of the tube; the decline in
pressure as the fluid is propelled along the tube and the viscosity of the
fluid. The volume(q) discharged through a uniform diameter tube is equal to pie
r4 divided by eight times the coefficient of viscosity (n) multiplied by the
pressure difference (delta p) from one end of the tube to the other divided by
the length of the tube (L) Equation looks like:
Q= pie r4 x delta p
8 n L
Need to know principle as it r/t effect on flow. The radius would have the
largest effect while the length of tube inversely affects rate of fluid and is
proportional to the radius. If you double the radius or increase length as in IV
catheters or ETT, the tube must be uniform in size, large diameter and have
laminar flow to optimize flow. The viscosity coefficient is inversely r/t flow
and is directly proportional to change in pressure. Resistance is Change if
Pressure/Flow If you double the radius you decrease resistance to flow by
16fold. If you decreased the radius by half you would increase resistance by 16.
The discharge or output volume through the orifice is inversely proportional to
length and inversely proportional to radius.
Pascal’s Law – used for any liquid in a confined pathway. For any
confined liquid any applied pressure is treated undiminished to all parts of
liquid. "water pipes" – open valve you get instant flow since liquid
Effects of length and radius on volume – the longer the tube the
more resistance to flow. Radius is as above.
Effects of density and viscosity on flow - Viscosity is independent
of density of the fluid. Density will help us determine how fluid flows through
an orifice. The rate of efflux of a fluid is dependent on the density. The
influence of viscosity on flow is negligible. Once flow becomes turbulent the
density of fluid will then determine flow. The temp of a fluid will affect its
flow rate. Liquids become less viscous as temp increases while the viscosity of
gases will increase with the temp. The rate of discharge of a fluid is
proportional to its coefficient of viscosity.
Volume flowmeters Modern flowmeters are called Thorpe Tubes. They
work on the principle that flow past a resistance is proportional to pressure.
The flow of gas flows around the plug or ball. The least amt of pres on flow
tube is at top of the ball. Each is a graduated cylinder which is gas specific.
Nitrous is graduated in a different way from O2. Gas enters through the bottom
and leaves through the top, elevating an indicator ball that moves up and down
the tapered tube. The ball floats at the point of equilibrium where the downward
force of gravity on the ball is equal to the upward force of the gas flow. The
rate of flow is dependent on a change in pres across the constriction of the
tube and circumference around the indicator ball and the physical
characteristics of the gas. At low flow rates flow is laminar. At high flow
rates the flow becomes turbulent and there will be a resulting decrease in
density which will increase the actual flow rate but the meter will read lower
than the actual flow so caution must be realized at higher flow rates.
Physics of the circulatory system – Circulation time is the amt of
time for a substance to go through the liver at least one time. The circulator
system sends blood to the vessel rich groups first (VRG) – brain, heart,
liver, kidneys then on the muscle and fat. You must factor this in with IV
anesthetics. Thiopental or propafol can be given and then you must wait 3 min.
If the pt has a low CO, it could take longer for circulation to get through the
liver. If they finally fell asleep at 4min but you had already redosed them,
then you could have overdosed them. This is especially true for older pts.
Younger ones could be already waking up after 4 min! Beta blockers will slow the
HR, which will slow the uptake of all drugs since circulation time will be
Cardiac output – CO = HR x SV The fick formula will tell us O2
consumption. Must figure out CI, which is CO/BSA. Ejection fraction is SV/End
diastolic vol x 100. Normal is 60-75%. If you have a high EF but tight aortic
stenosis, the volume of blood ejecting will be smaller but the speed of ejection
SVR = MAP-CVP x 80
Normal CO is 4-8, Normal CI is 2-4, and Normal SV is 60-130cc. O2
consumption is 200-300ml/min. This is important to know since the
anesthesia machine is what is providing the body’s necessary O2 to
maintain bodily function. The machine is a closed circuit and this would
be the closed circuit method of anesthesia.
Cardiac shunts will have and affect on O2 delivery. A right to left
shunt allows unoxygenated blood to flow to the left side of the heart thus
it bypasses the lungs. Not only will it slow down the available O2
delivery, in anesthesia it will slow down the induction time. A left to
right shunt will not really change the speed of induction since you assume
the tissue of systemic flow is normal. Theoretically would cause less need
for anesthesia since they have a higher CO and thus have less need to
increase perfusion as a compensatory mechanism.
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