Laminar Flow Turbulent Flow Hagen Poiseuille law Reynolds number Venturi Effect Bernoulli Principle Coanda Effect

1. PHYSICS OF FLOW
DR EKWELIBE E.O

2. OUTLINE
INTRODUCTION TO FLOW
BASIC DEFINITIONS OF PHYSICAL QUANTITIES
TYPES OF FLOW
HAGEN- POISEUILLE’S LAW
REYNOLDS NUMBER
CLINICAL APPLICATIONS OF FLOW
BERNOULLI PRINCIPLE AND VENTURI EFFECT
CONDA EFFECT
CONCLUSION
REFERENCES

3. INTRODUCTION TO FLOW
• GASES, LIQUIDS AND VAPOUR DIFFER CONSIDERABLY IN THEIR PHYSICAL
PROPERTIES, THEY DISPLAY SIMILAR BEHAVIOR UNDER FLOW CONDITIONS,
AND CAN BOTH BE DESCRIBED AS BEING FLUID.
• FLOW IS PRODUCED, IN BOTH GASES AND LIQUIDS, BY THE APPLICATION OF A
PRESSURE GRADIENT.
• FLOW IS DEFINED AS THE QUANTITY OF FLUID (GAS, LIQUID OR VAPOR) THAT
PASSES A POINT PER UNIT TIME. A SIMPLE EQUATION TO REPRESENT THIS IS:
• FLOW = QUANTITY (Q) L/MIN.
TIME (T)
• FLOW IS SOMETIMES WRITTEN AS ∆Q (RATE OF CHANGE OF A QUANTITY,
MASS OR VOLUME).

4. • FLOW THROUGH A TUBE IS DIRECTLY PROPORTIONAL TO
THE PRESSURE DROP ACROSS THE TUBE AND INVERSELY
PROPORTIONAL TO RESISTANCE.
FLOW ∝ PRESSURE DROP
RESISTANCE
• RESISTANCE IS DIRECTLY PROPORTIONAL TO LENGTH AND
INVERSELY PROPORTIONAL TO RADIUS TO THE FOURTH
POWER.
RESISTANCE ∝ LENGTH
RADIUS4

5. BASIC DEFINITIONS OF PHYSICAL
QUANTITES
• THE FUNDAMENTAL QUANTITIES IN PHYSICS ARE MASS, LENGTH AND
TIME.
• MASS (M) IS DEFINED AS THE AMOUNT OF MATTER IN A BODY. THE
UNIT OF MASS IS THE KILOGRAM (KG).
• LENGTH (L) IS DEFINED AS THE DISTANCE BETWEEN TWO POINTS. THE
SI UNIT IS THE METER (M), WHICH IS DEFINED AS THE DISTANCE
OCCUPIED BY A SPECIFIED NUMBER OF WAVELENGTHS OF LIGHT.
• TIME (T) IS MEASURED IN SECONDS. THE REFERENCE STANDARD FOR
TIME IS BASED ON THE FREQUENCY OF RESONATION OF THE CESIUM
ATOM.

6. Several units of measurement may be derived from these basic definitions
such as;
Volume has units of m3.
Density is defined as mass per unit volume: ρ= M kg/m
V
Velocity is defined as the distance travelled per unit time Ŋ= dm/s
t
Acceleration is defined as the rate of change of velocity A=V
T
Pressure is defined as force per unit area P= f pascal
a

7. • FORCE IS THAT WHICH IS REQUIRED TO GIVE A MASS ACCELERATION. THE SI
UNIT OF FORCE IS THE NEWTON (N). ONE NEWTON IS THE FORCE REQUIRED
TO GIVE A MASS OF 1 KG AN ACCELERATION OF 1MS.
• WEIGHT IS THE FORCE OF THE EARTH’S ATTRACTION FOR A BODY. SI UNIT IS IN
KG
• MOMENTUM IS DEFINED AS MASS MULTIPLIED BY VELOCITY:
MOMENTUM=M × V
• WORK IS UNDERTAKEN WHEN A FORCE MOVES AN OBJECT: WORK=FORCE ×
DISTANCE = F × L ( JOULES, J)
• VISCOSITY (Η) IS THE CONSTANT OF PROPORTIONALITY RELATING THE
STRESS (Τ) BETWEEN LAYERS OF FLOWING FLUID (OR BETWEEN THE FLUID
AND THE VESSEL WALL), AND THE VELOCITY GRADIENT ACROSS THE
VESSEL, DV/DR.

9. TYPES OF FLOW
THERE ARE TWO DIFFERENT TYPES OF FLOW ;
• LAMINAR
• TURBULENT
A NUMBER OF DIFFERENT PHYSICAL CHARACTERISTICS DETERMINE WHETHER
A FLUID OBEYS THE PRINCIPLES OF ONE OR THE OTHER, THEY ARE AS
FOLLOWS:
• SIZE OF TUBE OR ORIFICE
• LENGTH
• DIAMETER (OR RADIUS)
• PRESSURE IN THE TUBE
• VISCOSITY OF MEDICATION ADMINISTERED
• DENSITY OF GAS ADMINISTERED

10. LAMINAR FLOW
In laminar flow the molecules of the fluid can be imagined to be moving
in numerous ‘layers’ or laminae as shown below. Molecules are moving in
straight lines but they are not all uniform in their velocity. If the mean
velocity of the flow is v, then the molecules at the center of the tube are
moving at approximately 2v (twice the mean), while the molecules at the
side of the tube are almost stationary.

11. HAGEN POISEUILLE LAW
• THIS LAW STATES THAT THE FLUID FLOW RATE (Q) THROUGH A STRAIGHT TUBE
OF UNIFORM BORE IS PROPORTIONAL TO THE PRESSURE GRADIENT (ΔP) AND
THE FOURTH POWER OF THE RADIUS (R), AND IS RELATED INVERSELY TO THE
VISCOSITY OF THE GAS (Ŋ), AND THE LENGTH (L) OF THE TUBE.
• THE HAGEN–POISEUILLE FORMULA APPLIES ONLY TO NEWTONIAN FLUIDS AND
TO LAMINAR FLOW.
• IN NON-NEWTONIAN FLUIDS SUCH AS BLOOD, INCREASE IN VELOCITY
OF FLOW MAY ALTER VISCOSITY BECAUSE OF VARIATION IN THE
DISPERSION OF CELLS WITHIN PLASMA.

12. FACTORS AFFECTING LAMINAR
FLOW
VDL
• LAMINAR FLOW IS VISCOSITY DEPENDENT,
• DENSITY INDEPENDENT,
• HIGHLY DEPENDENT ON DIAMETER
• LENGTH OF TUBE

13. TURBULENT FLOW
Turbulent flow occurs in constricted passages and is governed by a different law.
Turbulent flow is chaotic and less efficient molecules swirl in vortices. It is found in a
orifice, irregular or wide tubes with corners, where there is a constriction or
narrowing or with fast flow rates.

14. FACTORS AFFECTING TURBULENT
OF FLOW
PRED2
• PRESSURE DIFFERENCE DRIVING THE FLOW
• DIAMETER OF THE VESSEL
• DENSITY (Ρ) OF THE FLUID

15. REYNOLDS NUMBER
• REYNOLDS NUMBER IS A DIMENSIONLESS NUMBER WHICH IS PREDICTIVE
OF WHETHER FLOW IS LAMINAR OR TURBULENT.
• WHERE V REPRESENTS THE MEAN VELOCITY OF THE GAS, R REPRESENTS THE AIRWAY RADIUS,
Ρ REPRESENTS THE GAS DENSITY, AND Ŋ IS THE VISCOSITY OF THE GAS. THE REYNOLDS
NUMBER IS THE RATIO OF INERTIAL FORCES (DENSITY DEPENDENT, VISCOSITY INDEPENDENT)
TO VISCOUS FORCES (VISCOSITY DEPENDENT, DENSITY INDEPENDENT).
• WHEN RAYNAULDS NUMBER IS
• <2000 FLOW IS LAMINAR
• 2000 TO 4000 TRANSITIONAL
• >4000 FLOW IS TURBULENT

16. CLINICAL APPLICATION OF FLOW
• FLUID RESUSCITATION
• CHOICE OF APPROPRIATE SIZE OF ETT
• OXYGEN DELIVERY SYSTEMS; VENTURI EFFECT, BERNOULLI
PRINCIPLE, COANDA EFFECT.
• REDUCING WORK OF BREATHING IN AIRWAY OBSTRUCTION
• UNDERSTANDING FLOWMETERS

17. FLUID RESUSITATION
• FLOW = THE QUANTITY OF FLUID (GAS, LIQUID OR VAPOR) THAT PASSES A
POINT PER UNIT TIME.
• FLOW = QUANTITY (Q)
TIME (T) .
• GAUGE IS ABBREVIATION FOR STANDARD WIRE GAUGE
• A SHORTER CANNULA ALLOWS GREATER FLOW THAN A LONGER CANNULA OF
EQUIVALENT BORE. FOR EXAMPLE, A 16-GAUGE CANNULA WILL ALLOW
GREATER FLOW (I.E. FASTER RESUSCITATION) THAN A (SMALLER) 18-GAUGE
CANNULA.
• LIKEWISE, A 14-GAUGE PERIPHERAL IV CANNULA WILL ALLOW GREATER FLOW
THAN AN EQUIVALENT CALIBER CENTRAL LINE, WHICH IS, BY NECESSITY,
SIGNIFICANTLY LONGER. FROM A PRACTICAL PERSPECTIVE, A 16 GAUGE
CANNULA IS THE SMALLEST SIZE WHICH ALLOWS RAPID ADMINISTRATION OF
BLOOD.

19. FLOW IN ENDOTRACHEAL TUBES
• ETT MAINTAINS AIRWAY PATENCY, PERMITS OXYGENATION AND VENTILATION,
ALLOWS FOR SUCTIONING OF SECRETIONS, LOWERS THE RISK OF ASPIRATION
OF GASTRIC CONTENTS OR OROPHARYNGEAL SECRETIONS, AND FACILITATES
THE USE OF INHALATION ANESTHETICS.
• THE SIZE OF AN ETT SIGNIFIES THE INNER DIAMETER OF ITS LUMEN IN
MILLIMETERS. AVAILABLE SIZES RANGE FROM 2.0 TO 12.0 MM IN 0.5 MM
INCREMENTS

20. THE LARGER THE DIAMETER OF ETT THE BETTER THE FLOW RATE ;
ETT USED IN EVERY PATIENT SHOULD BE THE LARGEST DIAMETER WHICH WILL
OPTIMIZE FLOW WITHOUT CAUSING TRAUMA TO THE AIRWAY AND
SURROUNDING STRUCTURES.
KINKING BENDS, OR CHANGES IN CROSS SECTIONAL AREA OF THE ETT WILL
CHANGE THE FLOW FROM LAMINAR TO TURBULENT.
(RECALL PRED2)

21. FLOW IN OXYGEN DELIVERY
SYSTEMS
• THERE ARE 2 MAJOR CLASSIFICATIONS OF OXYGEN
DELIVERY SYSTEMS ;
• LOW FLOW SYSTEM
• HIGH FLOW SYSTEM

22. LOW FLOW OXYGEN DELIVERY
SYSTEM
• LOW FLOW NASAL CANNULA
; THE RATE OF FLOW IN THIS
SYSTEM IS ABOUT 2 TO 4
LITRES PER MINUTE OF 22
TO 60% OXYGEN.
• OXYGEN FACE MASK; THE
RATE OF FLOW IN THIS
SYSTEM IS ABOUT 6 TO 10
LITRES PER MINUTE WITH 35
TO 60% OXYGEN.

23. HIGH FLOW OXYGEN DELIVERY
SYSTEM

24. • NON REBREATHING FACE MASK WITH RESERVOIR; THE RATE
OF FLOW IN THIS SYSTEM IS ABOUT 10 TO 15 LITRES PER
MINUTE OF 22 TO 95% OXYGEN.

27. THE BERNOULLI PRINCIPLE
• “BERNOULLI'S EQUATION STATES THAT FOR AN INCOMPRESSIBLE,
INVISCID FLUID THE TOTAL MECHANICAL ENERGY OF THE FLUID IS
CONSTANT” . THE PRINCIPLE WAS FORMULATED BY DANIEL
BERNOULLI IN 1778
• AN INCREASE IN THE VELOCITY OF A FLUID THAT IS ACCOMPANIED BY A
DECREASE OF PRESSURE.
• HE DEMONSTRATED THAT, IN MOST CASES, THE PRESSURE IN A LIQUID
OR GAS DECREASES AS THE LIQUID OR GAS MOVES FASTER THIS IS
CALLED THE BERNOULLI'S PRINCIPLE .

28. FOR BERNOULLI EQUATION TO APPLY; VI2DS
• THE FLUID VELOCITY AT A POINT CANNOT CHANGE WITH
TIME,
• THE FLOW MUST BE INCOMPRESSIBLE, INVISCID
• EVEN THOUGH PRESSURE VARIES,
• THE DENSITY MUST REMAIN CONSTANT ALONG A
STREAMLINE;
• THE FLOW MUST BE STEADY,
• FRICTION BY VISCOUS FORCES HAS TO BE NEGLIGIBLE

29. VENTURI EFFECT
A VENTURI IS A TUBE WITH A SECTION OF SMALLER DIAMETER THAN EITHER
THE UPSTREAM OR THE DOWNSTREAM PARTS OF THE TUBE.
• THE VENTURI EFFECT IS THE REDUCTION IN FLUID PRESSURE THAT
RESULTS WHEN A FLUID FLOWS THROUGH A CONSTRICTED SECTION (OR
CHOKE) OF A TUBE.
• THE VENTURI EFFECT IS NAMED AFTER ITS DISCOVERER, GIOVANNI
BATTISTA VENTURI IN 1797.
• THE PRINCIPLES GOVERNING THE BEHAVIOR OF FLUID FLOW THROUGH A
VENTURI WERE FORMULATED BY DANIEL BERNOULLI IN 1778

30. In a venturi, in order that the fluid flow be continuous, its velocity
must
increase through its narrowed throat (v2>v1 ). After the
constriction, velocity decreases back to the initial value and the
pressure rises again, total energy state must remain constant.
At point A, the energy in the fluid consists of
potential (pressure) and kinetic (velocity),
but at point B the amount of kinetic energy
has increased because of the increased veloci
As the total energy state must remain constan
pressure is reduced at point B.

31. CLINICAL USES OF BERNOULLIS
PRINCIPLE
• VENTURI MASK; DRAWS IN ROOM AIR TO PROVIDE AIR/ OXYGEN
PNEUMATIC POWER. ACTING AS AN INJECTOR BY MULTIPLYING THE AMOUNT
OF AIR FLOWING THROUGH THE VENTURI TOWARDS THE PATIENT’S LUNGS
• PREVENTS AN INCREASE IN APPARATUS DEAD SPACE WHICH ALWAYS
ACCOMPANIES THE USE OF LOW-FLOW OXYGEN DEVICES.
• NEBULIZERS
• DRIVING MECHANISM OF VENTILATORS
• SCAVENGING EQUIPMENT
• HUMIDIFYING GAS

32. COANDA EFFECT
THE COANDA EFFECT DESCRIBES A PHENOMENON WHEREBY
WHEN GAS FLOWS THROUGH A TUBE AND ENTERS A Y-
JUNCTION, GAS TENDS TO CLING EITHER TO ONE SIDE OF
THE TUBE OR TO THE OTHER.
IT WAS DISCOVERED IN THE 1935 BY A ROMANIAN NAMED
HENRI-MARIE COANDA, WHO BUILT THIS FIRST FLYING
SAUCER USING THIS PRINCIPLE.
THIS IS BECAUSE A Y-JUNCTION USUALLY IMPLIES A
REDUCTION IN DOWNSTREAM TUBE DIAMETER, AND THUS
AN INCREASE VELOCITY AND REDUCED PRESSURE ADJACENT
TO THE WALL.

33. CLINICAL USES OF COANDA
EFFECT
• THE PRINCIPLE HAS BEEN USED IN ANESTHETIC
VENTILATORS (TERMED FLUIDIC VENTILATORS), AS THE
APPLICATION OF A SMALL PRESSURE DISTAL TO THE
RESTRICTION MAY ENABLE GAS FLOW TO BE SWITCHED
(USING AN EXTERNAL CROSS FLOW OF GAS) FROM ONE SIDE
TO ANOTHER .

34. HELIOX
• HELIOX IS A MIXTURE OF HELIUM AND OXYGEN GASES. STANDARD HELIOX
CYLINDERS CONTAIN 80:20 (HE:O RATIO) HELIOX, THOUGH HELIOX IS ALSO
AVAILABLE IN 70:30 AND 60:40 MIXTURES.
• THE BEHAVIOR OF A FLUID IN FLOW IS RELATED TO DENSITY AND VISCOSITY.
THE DENSITY OF HELIUM IS 0.179 G/L, WHICH IS 70% TO 80% LESS THAN THE
DENSITY OF OXYGEN WHICH OS 1.429 G/L OR AIR 1.293 G/L.
• VISCOSITY IS AN INTERNAL PROPERTY OF A GAS, WHICH CAUSES RESISTANCE
TO FLOW. A FLUID WITH HIGH VISCOSITY STRONGLY RESISTS FLOW.

35. • Decreasing the density (ρ) will increase the flow.
• As flow velocity decreases and/or airway resistance increases, there is a critical
level at which the flow pattern changes from the laminar to turbulent.
• In patients with increased airway resistance, heliox administration will reduce the
resistance to flow by carrying oxygen through the resistance, which will lead to
decreased work of breathing.

36. FLOWMETERS
• FLOWMETERS ARE USED TO MEASURE THE FLOW OF LIQUIDS AND GASES IN PIPES AND
SHEATHED LINES.
• THIS DEVICE USES AN ADJUSTABLE NEEDLE VALVE TO DELIVER THE DESIRED FLOW IN ML
OR LITERS PER MINUTE TO THE PATIENT CIRCUIT.
• PRINCIPLE IS THAT A FLOAT IS INSTALLED IN A VERTICAL TUBE WHOSE DIAMETER
GRADUALLY WIDENS TOWARDS THE TOP.
• IN A VARIABLE ORIFICE FLOWMETER, GAS FLOW AT LOW FLOW RATES IS
PREDOMINANTLY LAMINAR.
• FLOW DEPENDS ON VISCOSITY. AT HIGHER FLOW RATES, BECAUSE THE FLOWMETER
BEHAVES AS AN ORIFICE, TURBULENT FLOW DOMINATES AND DENSITY IS MORE
IMPORTANT THAN VISCOSITY.
• FLOWMETERS ARE INDIVIDUALLY CALIBRATED FOR A SPECIFIC GAS, E.G., OXYGEN OR
NITROUS OXIDE.

38. • FLOW IS THE QUANTITY OF FLUID PER UNIT TIME. LAMINAR
FLOW IS LINEAR AND ORDERLY , FOUND USUALLY IN
TUBULAR STRUCTURES WHERE THE LENGTH IS GREATER
THAN THE DIAMETER. IT IS GOVERNED BY THE H.
POUSIELLE EQUATION ;
• TURBULENT FLOW IS NOT ORDERLY , FOUND IN ORIFICES,
AND CONSTRICTIONS WHERE THE DIAMETER IS GREATER
THAN THE LENGTH.
• RAYNAULDS NUMBER IS A DIMENSIONLESS NUMBER WHICH
IS PREDICTIVE OF WHETHER FLOW IS LAMINAR OR
TURBULENT.
When REYNOLDS NUMBER is
• <2000 flow is Laminar
• 2000 to 4000 TRANSITIONAL
• >4000 flow is Turbulent
CONCLUSIO
N

39. • UNDERSTANDING PHYSICS OF FLOW IS IMPORTANT IN
ANESTHESIA TO ENSURE EFFECTIVE DELIVERY OF FLUID
(GAS, LIQUID OR VAPOR) TO THE PATIENT DURING THE
PRACTICE OF ANESTHESIA.

40. PRACTICE QUESTIONS
• WHY ARE THE SCALES ON ROTAMETERS (FLOW METERS) NON UNIFORM
AS THE FLOW INCREASES?
FLOW METER HAS A VERTICAL TUBE DIAMETER WHICH GRADUALLY
INCREASES AS FLOW INCREASES THEREBY TURNING A TUBE INTO AN ORIFICE
; LAMINAR TO TURBULENT FLOW.
• WHY ARE THERE DIFFERENT ROTAMETERS FOR DIFFERENT GASES?
THE DIFFERENT GASES VARY IN DENSITY AND VELOCITY THEREFORE
DIFFERENT ROTAMETERS ARE CALIBRATED FOR DIFFERENT GASES.
• UNDER WHAT CIRCUMSTANCES IS THE GAS IN HELIOX USEFUL.
UPPER AIRWAY THE FLOW IS TURBULENT , IN UPPER AIRWAY OBSTRUCTION,
HELIOX, A MIXTURE OF HELIUM AND OXYGEN (UP TO 79% HELIUM),
REPLACES NITROGEN IN AIR WITH LESS-DENSE HELIUM. THIS DECREASES THE
TURBULENCE OF GAS FLOW THROUGH THE HIGH-RESISTANCE GLOTTIS,
ALLOWING FOR INCREASED OXYGEN DELIVERY TO THE LUNGS.

41. • WILL THERE BE MUCH DIFFERENCE IN VENTILATING THROUGH A SIZE 4
ENDOTRACHEAL TUBE COMPARED TO A SIZE 8
INCREASE IN DIAMETER OF A TUBE WILL INCREASE THE RATE OF FLUID
FLOW THROUGH THE TUBE, THE SMALLER THE DIAMETER OF THE TUBE
THE HIGHER THE PRESSURE GRADIENT ; VENTILATING THROUGH A 8MM
ETT WILL BE MORE EFFICIENT THAN A 4MM ETT
• HOW MUCH MORE FLUID CAN BE ADMINISTERED THROUGH A 14G
CANNULA THAN A 22G CANNULA?
14 GUAGE CANNULA CAN ALLOW UP TO 250MLS OF FLUID PER MINUTE
WHILE 22 GUAGE CANNULA CAN ALLOW UP TO 36ML/MIN.

43. REFRENCES
• MAGEE ET AL SMITH AND AITKENHEADS TEXTBOOK OF ANESTHESIA SIXTH
EDITION CH.236; PAGE 243, BASIC PHYSICS FOR ANESTHETISTS
• CLEMENTS ET AL UPDATE IN ANAESTHESIA VOLUME 24 NUMBER 2, CH.
141,PHYSICS OF FLOW .
• BATCHELOR, G. K. (2000) [1967]. AN INTRODUCTION TO FLUID DYNAMICS.
CAMBRIDGE MATHEMATICAL LIBRARY SERIES, CAMBRIDGE UNIVERSITY
PRESS. ISBN 978-0-521-66396-0.
• MARCUCCI ET AL AVOIDING COMMON ANESTHESIA ERRORS 2ND EDITION ,
ANESTHESIOLOGY CORE REVIEW PART 1 BASIC EXAM, MACGRAW HILL
• SMITH ET AL FUNDAMENTALS OF ANESTHESIA 3RD EDITION
• RAYMER ET AL UNDERSTANDING ANESTHESIA A LEARNER’S HANDBOOK 1ST
EDITION PAGE 22

44. • WWW.EMNOTE.ORG/EMNOTES/IV-CANNULA-AND-FLOW-RATES
• HTTPS://ACCESSANESTHESIOLOGY.MHMEDICAL.COM/CONTENT.ASPX
?BOOKID=974&SECTIONID=61588730
• HANDBOOK OF SUPPORTIVE AND PALLIATIVE RADIATION ONCOLOGY
2017, PAGES 101-118