1. Nature of Flow

1. States of fluid- Substances that are capable of flowing. Fluids are either liquid, which has size but no shape, or gases, which have neither shape nor size.
2. Definitions: Flow: Motion through a constraint which is accompanied by a deformation of the fluid. Measured in cm2 /sec

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.

3. 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.

4. 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.
5. 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.
6. 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 1^st 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.
7. 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

 

8. 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 1^st decreases its diameter and the area with the widest portion will have the greatest pressure and flow will be the slowest.



9. 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.
10. 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 parabolic curve.
11. 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 isn’t compressible.

12. Effects of length and radius on volume – the longer the tube the more resistance to flow. Radius is as above.
13. 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.
14. 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.
15. 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 slower.
16. 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 is less.

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