Flow and Flowmeter

Dr.Mohammad Abdeljawad
Anesthesia Specialist
AL-Bashir Hospital

Fluid Flow
Definition of flow (F)
Flow is defined as the quantity of a fluid, i.e. a gas or a liquid,
passing a point in unit time.
Therefore, the flow is the rate of the change of quantity which
has a symbol (Q}. It is pronounced "Q dot” The small dot above
the letter Q indicates the rate of change of quantity to
differentiate the flow from the quantity (Q).

Flow of Fluids may occur through:
A) A tube of a constant diameter.
B)A tube of a variable (non-uniform) diameter.
C) An orifice.

A) Flow of Fluids through a tube of a constant diameter.
In order to drive a fluid through a tube, a pressure difference (~ P)
must be present across both ends of - tube i.e., Pl-P2.
LAMINAR FLOW
In laminar flow (Fig. 2.1) a fluid moves in a steady manner and there
are no eddies or turbulence

Characteristics:
• It occurs when a flow passes through a smooth uniform tube
• The fluid moves in a steady regular manner and there are no
eddies. The fluid passes as if it is in concentric layers which are
parallel to the sides of the tube.
 The flow is greatest in the central axial layer (twice the
mean flow) and decreases gradually towards the periphery
where it reaches zero in the layer touching the sides of the tube
i.e., parabolic velocity profile.
• The flow is silent.
• It occurs when the flow moves with a velocity below
a critical velocity.

The graph in Fig. 2.2 shows the result if various flows are passed
through a tube and the resulting pressure drop across the ends is
recorded. There is a Unear relationship so that flow is directly
proportional to pressure under conditions of laminar flow.
The ratio of pressure to flow is a constant known as the resistance R of
the apparatus or tube concerned.

•The flow of fluids varies directly with the pressure
difference (~ P) i.e., the relationship between the flow and the
pressure is linear (figure 5-52) and the resistance (R) is
constant.
• The resistance is lower than that for the same turbulent
flow.

Figure 2.3 shows how resistance can be measured. A known
constant flow Q is passed through the apparatus concerned and
the difference in pressure Pi—P2 between the ends of the
apparatus is measured.
By dividing pressure difference by the flow the resistance of the
apparatus is obtained and, provided that flow is laminar, the
resistance is independent of the flow. A technique such as this may
be used to measure resistance with either gas or liquid flow

The resistance (R) is affected by:
1-Radius of the tube (r): the resistance is inversely proportionate to
the power of 4 of the radius i.e., R a 1/r4
Halving the diameter reduces the flow to onesixteenth of its original value
if the pressure drop along the tube remains the same.
In other words, the flow is proportional to the fourth power of the
diameter.
Consequently, a slight reduction of the diameter of an
endotracheal tube can have an appreciable effect on resistance and
therefore on flow
Factors affecting the laminar flow:

2- Length of the tube (l):the resistance is directly proportionate
to the length i.e., R a l
If the length of the tube is halved, the flow will double,

3-Viscosity of fluid (q): the resistance is directly proportionate to
the viscosity i.e., R a I]
Viscosity is a measure of the frictional forces acting between the
layers of the fluid as it flows along the tube
the viscosity of the fluid affects resistance to laminar flow in such
a way that the higher the viscosity the slower is the flow.

The effects described may be
summarized as follows:

All these factors are incorporated in an equation which can be
derived theoretically and is known as the Hagen-Poiseuille equation:
Hagen-Poiseuille equation:
Laminar flow obeys Hagen-Poiseuille formula and depends on the
viscositv.

clinical Applications:
•To increase the rate of transfusion of fluids :
Through an intravenous line, it is more important to increase the
radius of the cannula inserted rather than increase the pressure, as
flow is porportional to pressure i.e., an increase in the presure
increases the flow by the same ratio, but flow is proportional to the
power of 4 of the radius i.e., an increase in the radius produces an
increase in the flow by 16 times (if r = 2 so, 24 = 16).
•Resistance to breathing is much greater when a tracheal
tube of a small diameter is used as in pediatrics
-To determine.the peripheral vascular resistance
As Q =deltaP/R or P= QxR –
this relationship can be applied to the circulation as
Main blood pressure (P) = Cardiac output (Q) x resistance (R)

TURBULENT FLOW
laminar flow may change to turbulent flow if a constriction is
reached which results in the fluid velocity increasing.
In turbulent flow, fluid no longer flows in a smooth fashion but
swirls in eddies and the resistance is higher than for the same
laminar flow.

Characteristics:
• It occurs when a flow passes through a smooth uniform tube with a
constriction, an orifice, a sharp bend, or some other irregularity.
• The fluid moves in an irregular manner and there are eddies (figure
5-51). The fluid passes in a haphazard manner and the lines of the flow
are!'. parallel to the sides of the tube. There is no marke.: difference
between the velocity in the center and the periphery i.e., flat flow
profile.

• The flow is noisy i.e., it creates sounds e.g., carotid
bruit and cardiac murmurs.
• It occurs when the flow moves with a velocitv above a
critical velocity.
• The resistance is higher than that for the same laminar
flow.
.The variation of fluid velocity across the tube is different
in turbulent flow from that which occurs in laminar flow.

• The flow in not directly proportional to the pressure difference
(~ P), but AP is proportional to the square of the flow i.e., the
relationship between the flow and the pressure is not linear
(figure 5-52) and the resistance is not constant.
in order to double the flow, the pressure must be increased by a
factor of four.

Factors affecting the turbulent flow:
Q a r4

i.e., turbulent flow does not obey Hagen-Poiseuille formula
and depends on the density.
Density represented by the Greek letter rho
(p) and is equal to mass divided by volume (kgm~3).

ONSET OF TURBULENT FLOW
turbulent flow may occur if there is a sharp increase in the flow through
a tube, but there are several other factors influencing the type of flow,
such as the viscosity and density of the fluid and the diameter of the
tube.
These factors may all be combined to give an index known
as Reynolds number, which is calculated as follows:

Empirical measurements with cylindrical tubes show that,
. if Reynolds number exceeds about 4000, then turbulent
flow is likely to be present.
. If Reynolds number is below 2000, the flow is likely to be
laminar.
. If Reynolds number is between 2000 -4000, the flow is
likely to be
N.B.: Critical velocity occurs when the Reynold number is >
2000

1- During bronchial asthma, broncho-constriction occurs; therefore, the
velocity of flow is increased above the critical velocity and the flow
becomes turbulent where the resistance is very high. When helium is
used (it has very low density) with oxygen, the density of the inhaled
flow is decreased; therefore, the Reynolds number falls below 2000 and
the flow returns back to the laminar flow with a low resistance
2- Flow of air in the respiratory tract is a mix between laminar
and turbulent flow.
• In the wider parts as the nose, nasopharynx, and trachea, the flow
is more laminar.
• In the branches of the bronchial tree, the flow is more turbulent.
• In the lower respiratory tract as the surface area is large, the
velocity is low so the flow is more laminar again. Any pathology as
spasm or infection increases the turbulent flow

3- During anesthesia, reduction of the resistance to flow can be
achieved by avoiding the angle piece connector and making the internal
surface of the breathing circuit smooth.

B) Flow of Fluids through a Tube of a Variable Diameter
‘when a fluid passes through a constriction in a tube, the velocity of
the fluid increases and the pressure exerted on the wall of the tube
falls. This is named after its discoverer Bernoulli.
Bernoulli Effect
EXPLANITION
~there are two types of energy when a fluid passes through a tube:
1-Potential energy: associated with the pressure exerted by the
fluid on the wall of the tube.
2- Kinetic energy: associated with the velocity of the flowing fluid
Both potential and kinetic energies are constant.

When a fluid passes through a constriction in a tube,
the velocity of the fluid increases, which - associated with an
increase in the kinetic energy. As the total energy is constant;
therefore, an increase the kinetic energy is accompanied by a fall in
the potential energy which is associated with a decrease the pressure
exerted on the wall of the tube.
The pressure exerted on the wall at the site of the constrict! may
fall greatly to be sub-atmospheric.

Venturi Arrangement:
When a cross-sectional area of a tube gradually decreases towards a
constriction then gradually incre again, this is called a Venturi tube
(figure 5-53).

The fluid passing through a Venturi shows the following changes:
• At first the velocity increases gradually as the fluid passes through
the gradually decreasing crosssectional area of the tube, and at the
site of the constriction, sub-atmospheric pressure occurs (Bernoulli
effect).
• Then when the fluid passes through the gradually increasing
cross-sectional area of the tube, its velocti decreases and the
pressure increases gradually again until it reaches its original value

Clinical Application:
.
3- Venturi facemask for oxygen therapy.
The sum of the driven gas (100%oxygen) and the entrained exceeds
the peak inspiratory flow rate; therefore, a constant oxygen
percentage is delivered to the pt.
2- Jet ventilation e.g., Sander's injector during bronchoscopy.

4- Nebulizers: the driven gas passes through the central tube, and the
liquid (an inhaled drug entrained via the side tube where it is broken up
into small droplets by a disc or an anvil. Gas-driven (pneumatic or jet)
nebulizer is used for humidification of inspired air.

ENTRAINMENT RATIO
The entrainment ratio is defined as the ratio of entrained flow to
driving flow.
Thus, a 9 to 1 entrainment ratio indicates that there are 9 litre min-1
being entrained by a driving gas of 1 litre min'1.
In clinical practice, entrainment ratios may not be constant and
obstruction at the outlet of the Venturi can result in a fall in the
entrainment ratio.
This gave rise to problems in ventilators worked by injectors in which
oxygen was used to entrain air or nitrous oxide. In such cases, back
pressure altered the flow and so the resulting oxygen concentration.

THE COANDA EFFECT
Based on the Bernoulli and Venturi effects, when a gas passes through a
constriction, a sub-atmospheric pressure is produced.
If there are no holes at the site of constriction, the sub-atmospheric
pressure will –hold the stream along the wall of the wide tube.
If a narrow tube is connected to a Y-connection of a wider i.e., a tube
with two Venturis, the flow which is held to the wall will tend to cling to
one side of the y - ccnnection (i.e., the flow does not divide evenly
between the two sides, but flows through only one of the 'Y'). This is
called the Coanda effect

Coanda effect explains:
• the uneven distribution of gas flow to alveoli when there is a
slight narrowing of the bronchiole before it divides, resulting in
alveolar collapse.
• the uneven distribution of coronary blood when there is a slight
narrowing of the coronary artery before it branches, resulting in
myocardial ischemia.

-· a small tube is inserted perpendicularly at the exit of a narrow tube
and little pressure is applied, asimple valve switch mechanism is
produced where the flow can be directed from one exit tube to the
(without any mechanical parts).
- This device is called fluid logic and can be used in gas-driven
ventilators (called fluidic ventilators).

flow of Fluid through an Orifice
In an orifice, the diameter of fluid (Dl) pathway exceeds the length
(Ll), but in the tube, the length (L2) exceeds the diameter (D2)
(figure 5-55).The flow through an orifice is turbulent.

Factors affecting flow of the fluid through an Orifice :
-1- The square root of the pressure difference across the orifice i.e.,
- 2- The square of the diameter ot the orifice i.e., •
-3- The density of the fluid i.e., Q a 1/ density
In the bobbin flowmeter "Rotameter®",
 at low flow rates, the narrow annular space between the bobbin and the
wall mimics a tube. At high flow rates, the width of the annulus is large in
relation to the height of the bobbin and the annular space forms an
orifice.
Thus at low rates, the viscosity of gas determines the ;poisition of the
bobbin (as it is laminar flow), whereas at higher rates the effect of the
density of the gas becomes more important (as it is turbulent flow).

Flowmeter
·Flowmeters on anesthesia machines are
classified into:
1- “variable orifice (constant or fixed pressure drop) flowmeters
(Rotameter): They are the conventional ones used.
2- Electronic flowmeters: They are available now in the recent
anesthetic machines. In these new machines, there must be a back-up
conventional (Thorpe) auxiliary oxygen flowmeter which is used in of in
case failure of the electronic type
Other models of anesthesia machines have the conventional
flowmeters but measurement of the gas flow is done electronically
along the Thorpe tube or there are digital/ graphic displays of the flow

Flowmeter in addition to delivering a controlled flow of oxygen,
nitrous oxide, or air, they also reduce the pressure of these gases form
4.1 bar (in the pipelines) to 1 bar, which is delivered to patients
variable orifice (constant or fixed pressure drop) flowmeters
(Rotameter)
Flowmeter Assemblies.- The flowmeter assembly consists
of the flow control valves and the flowmeters, and its purposes are
precise control and measurement of gas flow traveling to the common
gas outlet.

“
The valves themselves represent an important anatomic landmark
within the anesthesia workstation because they separate the
intermediate-pressure section from the low-pressure section.
.The operator regulates flow entering the lowpressure ircuit by
adjusting the flow control valves
.After leaving the flowmeters, the mixture of gases travels through a
common manifold and may be directed through an anesthetic
vaporizer if selected. The total fresh gas flow and the anesthetic vapor
then travel toward the common gas outlet.

Flow Control Valves.
The flow control valve assembly consists of a flow control knob,
a tapered needle valve, a valve seat, and a pair of valve stops.
The inlet pressure to the assembly is determined by the pressure
characteristics of the intermediate-pressure segment of the
respective machine
secondary pressure regulators are often used before the flow control
valves to provide stable input pressure despite fluctuations in hospital
pipeline supply pressure.
The location of the needle valve in the valve seat changes to
establish different orifices when the flow control valve is adjusted
Gas flow increases when the flow control valve is turned
counterclockwise, and it decreases when the valve is turned clockwise.

Saeftey Feature:
- Control knobs have the same color code as the gas
cylinders (figure 6-20).
- The oxygen knob is usually fluted, larger and protrudes further
than the other knobs

Flow Tubes.
Atapered glass or plastic tube (Thorpe tube), which is narrow at the
bottom and wide at the apex like ·an inverted cone, is present
vertically where a light metal alloy bobbin (its trade name is
Rotameter®)or ball present inside the tube
The quantity of flow is indicated on a scale associated with the flow tube.
Referred to as variable orifice area flow tubes or Thorpe tubes,
these glass tubes are narrowest at the bottom and widen vertically

An indicator float is housed within the tube that is free to move
vertically
Opening the flow control valve allows gas to travel through the
space between the float and the flow tube.
This space is known as the annular space, and it varies in size
depending on the position of the indicator in the tube

The indicator float hovers freely in an equilibrium position in the tube
where the upward force resulting from gas flow equals the downward
force on the float resulting from gravity at a given flow rate.
These flowmeters are commonly referred to as constant-pressure
flowmeters because the decrease in pressure across the float remains
constant for all positions in the tube.

When the flow increases, the bobbin or the ball rises in the wider
parts of the tube against the gravity and the annular orifice around it
increases;
therefore, the flow resistance decreases and the clearance around the
bobbin or the ball increases.
So, the effect of the gravity (weight of the bobbin or the ball) is
balanced by the increased flow and so the pressure across the bobbin
(or the ball) stays constant although the flow increases .

the reverse occurs when the flow decreases as the bobbin or the ball
falls in the narrower parts of the tube and the annular orifice around
it decreases;
therefore, the flow resistance increases and the clearance around the
bobbin or the ball decreases and so the pressure across the bobbin (or
the ball) stays constant despite the flow decreases i.e.,
there is a variable orifice and fixed pressure drop around the bobbin
(or the ball)

 At low flow rates, the narrow annular space between the bobbin (or
the ball) and the wall mimics a tube and the flow becomes laminar.
At high flow rates, the width of the annulus is large relative to the
_higet of the bobbin (or the ball), the annular space forms an orifice and
the flow becomes turbulent.
 at low rates, the viscosity of gas determines the position of the
bobbin (as it is laminar flow),
whereas at higher rates the effect of density of the gas becomes more
important (as it is turbulent flow).

Recently electronic flowmeters have been available on the
computer screen

Flows can be displayed numerically or sometimes graphically in the
form of a virtual, digitalized flowmeter.
Numerous types flow sensor technologies can be applied, such as hot-
wire anemometers, a differential pressure transducer method, or
mass flow sensors.
Electronic Flow Sensors.
An example of an electronic mass flow sensor :
A device relies on the principle of specific heat to measure gas flow.
As gas streams through a heated chamber of known volume, a specific
amount of electricity is required to maintain the chamber temperature.
The amount of energy required to maintain the temperature is
proportional to the flow of the gas and the gas’s specific heat.

Factors Affecting the Performance of the
Rotameter:
1- The viscosty and density :
Because the flow in this flowmeter is a mixture of laminar (at low flow
rates) and turbulent (at high flow rates) flow,
so both the viscosity (in laminar) and density (in turbulen of the gas is
important.
Therefore, each rotameter has to be calibrated for a specific gas i.e.,
different gases can not be used in the same flowmeter except after
recalibration or change of the scale written on the tapered tube.
Although temperature and barometric pressure can influence gas
density and viscosity, under normal clinical circumstances flow
tube accuracy is not significantly affected by mild changes in
temperature or pressure

2- Sticking The bobbin may touch the wall of the tapered tube
and stick to it. To avoid this:
The flowmeter tube must be kept vertical to reduce the friction
between the bobbin and the tube
As electrostatic charges (which increase sticking) may build up
on the bobbin and the wall of the tube it rubs against the wall of
the tube; therefore, to conduct away the electrostatic charges: -
Some tubes are coated from inside by a conductive transparent
material (as gold or tin" stannous oxid").
A conductive strip is present from inside the tube.
The plastic cover of the rotameter is sprayed with an antistatic
spray such as Croxtine.

Small slots are placed round the top of the bobbin causing it to
rotate centrally in the gas flow and a dois present in the body of the
bobbin indicating its rotation (the dot is not used to indicate the
level frorr which readings are made).
The ball is used as sticking is less.
Dust is prevented by incorporating a dust filter in the needle
valve at the bottom of the tube becaus dust on the bobbin may
cause sticking or even alteration in size of the annulus which causes
inaccuracies

It is within+ 2-2.5%. To increase the accuracy:
Accuracy:
 Avoid sticking, as above
Readings are made from the upper surface of the bobbin (more
accurate as there is a well defined surface for reading) or the central
equator (the middle) of the ball (less accurate).

 In recent anesthetic machines where very low flows are needed in
closed circuits, two flowmeters, on for the low and one for high
flows, are made in series and are still controlled by one valve
(figure 6-16).

• Attachment of a vaporizer or a ventilator e.g., Manley, after the
flowmeter produces back pressurwhich increases the resistance in
front of the flowmeter.
This in turn increases the pressure at the outlet ~the flowmeter.
This increased pressure affects in turn the calibration of the
flowmeter, due to affection the viscosity and density of the gases,
which affect the accuracy as there may be as much as 10% more
gas flow than that indicated on the flowmeter.
Some flowmeters are now pressurized and calibrated to wor at a
high pressure of several bars, which minimizes the effect of the
relatively smaller pressure change the outlet.

To increase the safety:
safety:
The position of the flowmeters
When there are flowmeters in series e.g., one for 02 and the other for
N20, and a break in the junction between two flowmeters occurs e.g.,
in air flowmeter, the concentration of the gas mixture obtained from e
flowmeters may be changed and become hypoxic as follows:
- the 02 flowmeter is located at first and the N20 flowmeter is located
after the air flowmeter, the 02 may w out of the break in the system as
in (A) and a hypoxic gas mixture is obtained

To solve this problem: -
The sequence of arrangement of the flowmeters is reversed,
where the 02 flowmeter is located after the air flowmeter as in
(B).This is the standard in North America.
- Because the standard in most other countries is placement of
the 02 flowmeter at first;
therefore, a channel is present at the outlet of the 02 flowmeter
to deliver it separately away from the N20 (C). This is the standard
in the United Kingdom. A

A leak in the oxygen flow tube may result in creation of a hypoxic
mixture even when oxygen is located in the downstream position (Fig.
29-10).
 Oxygen escapes through the leak, and nitrous oxide continues to
flow toward the common outlet, particularly at high ratios of
nitrous oxide to oxygen flow.

 Oxygen/nitrous oxide ratio:
In the modern anesthetic machines, there is a link between the
oxygen flow controller and nitrous oxide controller to ensure
administration of at least 25% 02 when the N20 flowmeter is turned
on alone.
When the N20 flowmeter is turned on alone, the 02 flowmeter is
turned on _obligatorily to at least 25% of the total gas mixture;
therefore, hypoxia is avoided.
This is achieved by one - the following methods:
A-mechanical method: where a chain link is present between
the 02 and NzO flowmeter control knobs

Datex-Ohmeda Link-25 Proportion-Limiting Control
System
The system is based on a mechanical integration of the nitrous oxide
and oxygen flow control valves and a difference in the taper of
the needles of the oxygen and nitrous oxide flow control valves.
It allows independent adjustment of either valve, yet it automatically
intercedes to maintain a minimum oxygen concentration with a
maximum nitrous oxide– oxygen flow ratio of 3:1.
The Link-25 automatically increases oxygen flow when then nitrous
oxide flow is increased to more than a certain point relative to
oxygen flow to prevent delivery of a hypoxic mixture

b- A Pneumatic method: where a pneumatic mixing valve is present.
The North American Dr‫ن‬ger sensitive oxygen ratio controller system
(SORC)
is a pneumaticmechanical, oxygen–nitrous oxide interlock system
designed to maintain a ratio of no less than 25% oxygen to 75% nitrous
oxide flow into the breathing circuit by limiting the nitrous oxide flow
when necessary.
The SORC is located between the flow control valves and the
electronic flow sensors.
The SORC consists of an oxygen chamber with a diaphragm, a
nitrous oxide chamber with a diaphragm, and a nitrous oxide
proportioning valve

All interconnected by a mobile horizontal shaft. Pneumatic
input into the device comes from the oxygen and nitrous oxide flow
control valves

As oxygen flows out of the SORC, it encounters a resistor that
creates backpressure
This backpressure is transmitted to the oxygen chamber
diaphragm, which causes the diaphragm to move to the right,
thereby opening the nitrous oxide proportioning valve.
As the oxygen flow is increased, so too is the backpressure and
the rightward motion of the shaft.
If the nitrous oxide flow is now turned on, it will also flow into the
SORC, through the proportioning valve, and past its resistor to create
backpressure that will press on the diaphragm in its respective
chamber.
The counterbalance between the two gas flows (backpressures)
determines the positioning of the nitrous oxide proportioning valve

If the oxygen is turned down too low (<25% of the nitrous oxide
flow), the shaft will move to the left and thus limit the nitrous
oxide flow.
If the operator tries to turn up the nitrous oxide too high
relative to the oxygen flow, the SORC will limit the nitrous
oxide flow regardless of how far the flow control valve is opened.
If the oxygen flow is decreased to less than 200 mL/minute, the
proportioning valve will close completely

c- An electronic method.
• Minimum oxygen flow: Some recent flowmeters allow minimum
oxygen flow of 150 mL/min O_ when the anesthesia machine is turned
on even when the oxygen flow valve is turned off.
This safety feature helps ensure that some oxygen enters the breathing
circuit even if the operator forgets to turn or the oxygen flow.

• The Quantiflex mixer flowmeter (figure 6-19)
eliminates the possibility of reducing the oxygen supplinadvertently
because:
-One dial is set to the desired % of oxygen, and it is adjusted first
-Then the total flow rate is adjusted independently by another dial (the
black knob).
-Therefore, the percentage of ~ is fixed and there is no need to readjust
the flow of 02 manually whenever the flow rate is changed.

Flow valves
They constitute an important landmark of the anesthesia machine
because they divide the machine into two gas circuits
• The high-pressure circuit: is the part of the machine that is
upstream from the flow control valves and consists of the pipeline
system, the gas cylinders and the tubes connecting them to the
machine
• The low-pressure circuit: is the part of the machine that is
downstream from the flow control valves and consists of the
flowmeters, the vaporizers and the common gas outlet that receives
all gases and vapors from the machine

Flow and Flowmeter

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