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 = vρror vρd η η

v = velocity of fluid flowρ = density of fluidr = radius of tubed = diameter of tubeη = 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

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

diameter

diameter

length

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