1. FLUID FLOW AND MEASUREMENT
Presented By
Dr A. S. ADEYINKA
MB,BS (Lagos)

2. OUTLINE Introduction Definition of Flow Types of Flow
Factors Affecting Flow
Clinical Applications
Conclusion
Clinical Applications, especially as it relates to ANAESTHESIA

3. INTRODUCTION
A fluid is a state of matter (or matter- in-transition) in which its molecules move freely and do not bear a constant relationship in space to other molecules
Thus it has the ability to take up the shape of its container

4. Introduction (Cont’d)
Fluids are
Liquid
e.g. blood, i.v. infusions
Gas
e.g. O2 , N2O
Vapour (transition from liquid to gas)
e.g. N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state)
Dry ice (solid CO2), iodine

5. DEFINITION OF FLOW
Flow is defined as the quantity of fluid (gas, liquid, vapour or sublimate) that passes a point per unit time
A simple equation to represent this is:
Flow (F) = Quantity (Q)
Time (t)
Flow is sometimes written as ∆Q (rate of change of a quantity)
∆ = pronounced “delta”

6. TYPES OF FLOW
There are two types of flow:
Laminar flow
Turbulent flow

7. Laminar Flow Smooth, steady and orderly flow of fluid in a tube
All the fluid molecules move in a straight line
Therefore they move in parallel layers or laminae with no disruption between the layers
Velocity of flow is greatest in the axial stream (centre of the tube). It becomes progressively slower as the layers move to the periphery
Axial stream velocity is twice the mean flow velocity
Velocity of the layer in contact with the wall is virtually zero

8. Laminar Flow
Diagrammatic representation of laminar flow

9. Turbulent Flow Fluid does not move in orderly manner
The fluid molecules become more disorganized
They form swirls and eddies as they move down the pressure gradient in haphazard manner
There is increased resistance to flow as the eddy currents interfere with each other
Therefore greater energy is required for a given flow rate, compared to when the flow is laminar

10. Turbulent Flow
Diagrammatic representation of turbulent flow

11. FACTORS AFFECTING FLOW

12. Variables That Affect Flow
Pressure: flow is directly proportional to the pressure difference across the tube
Q ∞ ∆P
Radius: flow is directly proportional to the fourth power of the radius (or diameter) of the tube
Q ∞ r4, or Q ∞ d4
Length: flow is inversely proportional to the length of the tube
Q ∞ 1/l
Viscosity: flow is inversely proportional to the viscosity of the fluid
Q ∞ 1/η

13. Hagen-Poiseuille Equation
This equation incorporates the variables that determine flow
Q = πΔPr4
8ηl
where π/8 is a constant derived theoretically
or Q = πΔPd4
128ηl
where π/128 is a constant

14. Pressure/Flow Relationship
The relationship between pressure and flow is linear within certain limits
As velocity increases, a critical point (or critical velocity) is reached where flow changes from laminar to turbulent
Beyond this point, flow is proportional to the square root of pressure gradient

16. Reynolds’ Number
This number is calculated from an equation that incorporates the factors that determine the critical point
Reynolds’ number = vρr or vρd
η η
v = velocity of fluid flow
ρ = density of fluid
r = radius of tube
d = diameter of tube
η = viscosity of fluid
Reynolds number does not have any associated unit
It is a dimensionless number

17. Reynolds’ Number (Cont’d)
if Reynolds’ number exceeds 2000, flow is likely to be turbulent
a Reynolds’ number of less than 2000 is usually associated with laminar flow

18. Viscosity
Viscosity (η) is the property of a fluid that causes it to resist flow
It is a measure of the frictional forces acting between the layers of fluid as it flows along the tube
η = force x velocity gradient
area
Unit of viscosity is pascal second (Pa s)
Velocity gradient is equal to the difference between velocities of different fluid molecules divided by the distance between molecules

19. Viscosity (Cont’d)
Viscosity of a liquid decreases with increased temperature, while viscosity of a gas increases with increased temperature
From Hagen-Poiseuille equation, the more viscous a fluid is the lesser the flow. This however applies to laminar flow and not turbulent flow, where flow is dependent on the density of the fluid

20. Density Density (ρ) is defined as mass per unit volume
Unit of density is kilogram per meter cube (kgm-3)
Density is an important factor of fluid in turbulent flow through a tube, in which flow is inversely proportional to square root of density

21. Tube and Orifice
In a tube, the length of the fluid pathway is greater than the diameter
In an orifice, the diameter of the fluid pathway is greater than the length
diameter
length
diameter
length

22. Tube and Orifice (Cont’d)
As the diameter of a tube increases, the Reynolds number increases. Eventually if the diameter of the tube increases enough, it will exceed the length of the tube. We then call this an orifice
Flow through a tube is laminar and hence dependent on viscosity (provided that the critical velocity is not exceeded)
If the flow is through an orifice it is turbulent and dependent on density

23. Tube and Orifice (Cont’d)
The flow rate of a fluid through an orifice is dependent upon:
the square root of the pressure difference across the orifice
the square of the diameter of the orifice
the density of the fluid (flow through an orifice inevitably involves some degree of turbulence)

24. MEASUREMENT OF FLOW

25. GAS FLOWMETERS There are two types
Variable orifice (fixed pressure change) flowmeters
e.g Rotameter, peak flowmeter
Variable pressure change (fixed orifice) flowmeters
e.g. Bourdon gauge, pneumotacograph

26. Rotameter Cone shaped tubes that contain a bobbin
The gas enters the bottom of the tube applying a force to the bobbin
The bobbin then moves up the tube until the force pushing it up is cancelled out by the gravitational force
At this point it remains at that level and there is a constant pressure across the bobbin

28. Rotameter (Cont’d)
At low flows, the bobbin is near the bottom of the tube and the gap between the bobbin and wall of the flowmeter acts like a tube (diameter < length)
Gas flow is laminar and hence the viscosity of the gas is important
As flow rate increases, the bobbin rises up the flowmeter and the gap increases until it eventually acts like an orifice (diameter > length)
At this point the density of the gas affects its flow

30. Rotameter (Cont’d)
Individual gases have different densities and viscosities and therefore the flow past the bobbin will vary for each individual gas
EACH ROTAMETER MUST BE CALIBRATED FOR A SPECIFIC GAS
The flow changes from being directly proportional to pressure to proportional to the square root of pressure and hence the graduations on the flowmeters are not uniform

31. Peak Flowmeter
This useful clinical instrument is capable of measuring flow rates up to 1000 L per min
Air flow causes a vane to rotate or a piston to move against the constant force of a light spring
This opens orifices which permit air to escape
The vane or piston rapidly attains a maximum position in response to the peak expiratory flow
It is held in this position by a ratchet
The reading is obtained from a mechanical pointer which is attached to the vane or piston

32. Peak Flowmeter (Cont’d)
Accurate results demand good technique
These devices must be held horizontally to minimize the effects of gravity on the position of the moving parts
The patient must be encouraged to exhale as rapidly as possible

33. Bourdon Gauge
Bourdon gauge is used to sense the pressure change across an orifice and is calibrated to the gas flow rate
It uses a coiled tube which uncoils as pressure increases
A system of cogs converts uncoiling of the coil into clockwise movement of the needle over a calibrated scale
These rugged meters are not affected by changes in position and are useful for metering the flow from gas cylinders at high ambient pressure

35. Pneumotachograph
Measures flow rate by sensing the pressure change across a small but laminar resistance
Uses differential manometer that senses the true lateral pressure exerted by the gas on each side of the resistance element and transduce them to a continuous electrical output
It is a sensitive instrument with a rapid response to changing gas flow
It is used widely for clinical measurement of gas flows in respiratory and anaesthetic practice
However, practical application requires frequent calibration and correction or compensation for differences in temperature, humidity, gas composition and pressure changes during mechanical ventilation.

37. Other Devices For Measuring Gas Flow
Measurements other than pressure change across an orifice have been used to measure flow. eg,
Hot wire flowmeters
Ultrasonic flowmeters

38. CLINICAL APPLICATIONS

39. Endotracheal Tube
Resistance to breathing is much greater when an endotracheal tube of small diameter is used
Flow is significantly reduced in proportion to the fourth power of the diameter
changing the tube from an 8mm to a 4mm may reduce flow by up to sixteen-fold
Therefore the work of breathing is significantly increased
Over time, a spontaneously breathing patient becomes exhausted and soon becomes hypercapnic due to reduced respiration

41. Breathing Systems
In anaesthetic breathing systems, the following can cause turbulent flow, making the work of breathing greater
a sudden change in diameter of tubing
irregularity of the wall
acute angles at connections
Unnecessary long circuits
Thus, breathing tubes should possess smooth internal surfaces, gradual bends and no constrictions
They should be of as large a diameter and as short a length as possible

42. Heliox Heliox is a mixture of 21% oxygen and 79% helium
Helium is an inert gas that is much less dense than nitrogen (79% of air)
Heliox much less dense than air
In patients with upper airway obstruction, flow is turbulent and dependent on the density of the gas passing through it
Therefore for a given patient effort, there will be a greater flow of heliox (density = 0.16) than air (density = 1.0) or oxygen alone (density = 1.3)
However, heliox contains 21% oxygen – it may be of lesser benefit in hypoxic patient

43. Humidification of Inspired Gas
Humidification, in addition to its other benefits, makes inspired gas less dense
This may be of benefit by reducing the work of breathing

44. Intravenous Fluid
For a given fluid, with the same pressure applied to it, flow is greater through a shorter, wider cannula
Thus they are preferred in resuscitation

45. Blood Vessels Flow is principally laminar
There is a possibility of turbulence at the junction of the vessels or where vessels are constricted by outside pressure
Here turbulence results in a bruit which is heard on auscultation

46. BERNOULLI PRINCIPLE

47. Bernoulli Principle (Cont’d)
As fluid passes through a constriction, there is an increase in velocity of the fluid
Beyond the constriction, velocity decreases to the initial value
At point A, the energy in the fluid is both potential and kinetic
At point B the amount of kinetic energy is much greater because of the increased velocity
As the total energy state must remain constant, potential energy is reduced at point B and this is reflected by a reduction in pressure

48. VENTURI TUBE (INJECTOR)
In the Venturi tube, the pressure is least at the site of maximum constriction
Subatmospheric pressure may be induced distal to the constriction by gradual opening of the tube beyond the constriction

49. Application of Injectors
Oxygen therapy – Venturi mask
Nebulizer
Portable suction apparatus
Oxygen tents
As a driving gas in a ventilator

50. These masks, also termed high air flow oxygen enrichment
(HAFOE) devices, provide a constant and predictable inspired
oxygen concentration irrespective of the patient's ventilatory
pattern. This is achieved by supplying the mask with oxygen and
air at a high total flow rate.

51. gradient. This results in water being drawn up
through the tube and broken into a fine spray as it comes in contact
with the high-speed gas jet

53. COANDA EFFECT
describes a phenomenon whereby gas flow through a tube with two Venturis tends to cling either to one side of the tube or to the other
used in anaesthetic ventilators (fluidic ventilators), as the application of a small pressure distal to the restriction may enable gas flow to be switched from one side to another

55. SUMMARY

56. References
Mushambi MC, Smith NG. Basic Physics for the Anaesthetist. In: Textbook of Anaesthesia 4th Edition:
Paul Clements, Carl Gwinnutt. Physics of Flow. In: Update in Anaesthesia 2008; 2: Available at:
Rushton ARA, Langton JA. Clinical Measurement. In: Textbook of Anaesthesia 4th Edition: