Fluid flow and measurement

 Introduction

Definition of Flow
 Types of Flow

Factors Affecting Flow
 Clinical Applications
 Conclusion

 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

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

 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)

 There are two types of flow:

 Laminar flow

 Turbulent 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

Diagrammatic representation of laminar 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

Diagrammatic representation of turbulent 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

 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

 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

 if Reynolds’ number exceeds 2000, flow is likely to be
turbulent

 a Reynolds’ number of less than 2000 is usually
associated with laminar flow

 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)

 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

 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

 In a tube, the length of the fluid pathway is greater than
the diameter
diameter

length

 In an orifice, the diameter of the fluid pathway is
greater than the length
diameter

length

 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

 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)

 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

 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

 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

 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

 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

 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.

 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

 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

 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

 Humidification, in addition to its other benefits, makes
inspired gas less dense

 This may be of benefit by reducing the work of
breathing

 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


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

 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

 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

 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

Fluid flow and measurement

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