PRINCIPAL OF GASES, GAS LAW FLOW OF
GASES AND VENTURI PRINCIPAL
Presenter Dr Andre Mwana-Ngoie
• Gas pression
• absolute temperature
• Boyles low
• Charles low
*All substances(Matter) are composed of
small particles (molecules);
is measured of space;
that the molecules occupy (volume) is
derived from the space in between the
molecules and not the space. The
molecules contain themselves
• There are 3 states of matter
• The molecules are in constant motion
• This motion is different for the 3 states of
Solid - Molecules are
held close to each
other by their
attractions of charge.
They will bend
and/or vibrate, but
will stay in close
Liquid - Molecules
will flow or glide
over one another,
but stay toward the
bottom of the
Motion is a bit more
random than that of
• Gas - Molecules are in continual straight-line
• The kinetic energy of the molecule is greater
than the attractive force between them, thus
they are much farther apart and move freely
of each other.
• When the molecules collide with each other,
or with the walls of a container, there is no
loss of energy.
• distinguished from the solid and liquid states
-relatively low density and viscosity(‘light’)
because molecules are spread apart over a
large volume. (density = mass / volume)
– Density order: solid > liquid >>> gases
– Gases flow freely because there are no effective
forces of attraction between the gaseous particles
– Because of this gases and liquids are described
– relatively great expansion and contraction with
changes in pressure and temperature
The spontaneous tendency to become
distributed uniformly ...
NB ;The main distinguishing property of gases is
their ability to be compressed into smaller and
smaller because of the ‘empty’ space between
◦ (almost impossible to compress a solid)
• The pressure of a gas is causes by collisions of
the molecules with the walls of the container.
• The magnitude of the pressure is related to
how hard and how often the molecules strike
• The "hardness" of the impact of the molecules
with the wall will be related to the velocity of
the molecules times the mass of the molecules
For example - if the number of gaseous
particles in a container is doubled, the gas
pressure is doubled
because doubling the number of molecules
doubles the number of impacts on the side
of the container so the total impact force
per unit area is also doubled.
This doubling of the particle impacts doubling
the pressure is pictured in the two diagrams
2 x particles
P x 2
• The absolute temperature is a measure of the
average kinetic energy of its molecules.
• If two different gases are at the same
temperature, their molecules have the same
average kinetic energy If the temperature of a
gas is doubled, the average kinetic energy of
its molecules is doubled
• Gases have no surface, and no fixed shape or
volume, and because of lack of particle
attraction, they always spread out and fill any
container (so gas volume = container volume).
• A gas will fill whatever container that it is in.
eg of this is a
opened in a
room and the
The (advanced) kinetic theory of gases is founded on the following six
(i)Gases are composed of minute discrete particles
(ii)The particles are in continuous chaotic motion
moving in straight lines between very frequent
collisions with each other and the sides of the
container (approximately 109/s).
(iii) The bombardment of the container walls by the
particles causes the phenomenon we call pressure
(i.e. force of impacts/unit area).
(iv)The collisions are perfectly elastic i.e. no energy
loss on collision due to friction.
(v)At relatively low pressures the average distance
between particles is large compared to the
diameter of the particles and therefore the inter-
molecular forces between the particles is
(vi)The average kinetic energy of the particles is
directly proportional to the absolute temperature
on the Kelvin scale (K).
• Consider volume of gas within asyringe
• Collision btn the molecule and the walls of the
container results in an absolute pressure P
which in this case is a typical atmospheric
pressure=100kPa or 1 bar) .
• When volume increase and temperature
remains constant .
• The average kinetic energy of the gas molecules
• This means that the speed of the molecules, remains
• If the speed remains unchanged, but the volume
increases, this means that there will be fewer
collisions with the container walls over a a given time
• Therefore, the pressure will decrease
• Mathematically Boyle's law can be expressed as
P1V1 = P2V2
• V1is the original volume
• V2 is the new volume
• P1 is original pressure
• P2 is the new pressure
• Effect of a temperature increase at constant
• An increase in temperature means an
increase in the average kinetic energy of the
• There will be more collisions per unit time,
furthermore, the momentum of each collision
increases (molecules strike the wall harder)
Therefore, there will be an increase in pressure.
If we allow the volume to change to maintain
constant pressure, the volume will increase with
increasing temperature .
V / T =constant
V is the volume
T is the absolute temperature (measured in Kelvin)
• Important: Charles's Law only works when the
pressure is constant.
Note: Charles's Law is fairly accurate but gases
tend to deviate from it at very high and low
• The combined gas law is a combination of
Boyle's Law and Charles's Law; hence its name
the combined gas law.
• This can be written as PV / T = constant. Since
for a given amount of gas there is a constant
then we can write P1V1 / T1 = P2V2 / T2.
The Third perfect gas law
• The third gas law indicates that at constant
volume the absolute pressure on the gas
varies directly with the absolute temperature
or P / T = constant.
• Therefore at constant volume a doubling of
temperature results in a doubling of pressure
P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature (in Kelvin)
P2 is the final pressure
V2 is the final volume
T2 is the final temperature (in Kelvin)
This equation is useful if you have the current
volume, temperature, and pressure of a gas, and if
you have two of the three final values of the gas.
• For the gas law above one varible must be
• For these condition to apply heat energy must
be added or removed from the gas for the
change to occur .
• An adiabatic process is one in which the
changes in volume and pressure of a given
mass of gas take place such that heat is
neither allowed to enter nor leave the gas.
• E.g. IF a cylinder is connected to an
anaesthetic machine and turned on quickly
the pressure in the connecting pipes and
gauges rises rapidly.
• thus the gas is compressed adiabatically and a
large temperature rises with increased risk of
• a cylinder is connected to a pressure regulator
which is used to set a cooling rate.
For a simple substance, during an adiabatic process in which the
volume increases, the internal energy of the working substance must
Effusion and Diffusion are the two ways that gases
mix with other gases.
Diffusion is a process in which a gas enters a
container with another gas and the two mix to form
a uniform mixture.
Effusion occurs when a gas moves through a small
hole in its current container into another container.
An example of diffusion is the ammonia mentioned
earlier where the ammonia moves into the room
with the air
Dalton's law of partial pressure
Two gas laws describe partial pressure. Dalton's
law of partial pressure
• states that the total pressure of a gas is equal
to the sum of its partial pressures(that is, the
pressure exerted by each component of the
• air is composed mostly of nitrogen and
• Along with these are small components
carbon dioxide and gases collectively known
as the rare or noble gases.
• Hence, the total pressure of a given quantity
of air is equal to the sum of the pressures
exerted by each of these gases.
Henry's law states
• Henry's law
• states that the amount of gas dissolved in a
liquid is directly proportional to the partial
pressure of the gas above the surface of the
• This applies only to gases such as oxygen and
hydrogen that do not react chemically to
• On the other hand, hydrochloric acid will
ionize when introduced to water:
• one or more of its electrons will be removed,
and its atoms will convert to ions, which are
either positive or negative in charge.
STP is Standard Temperature and Pressure. STP is Oo
Celcius and 1 atmosphere of pressure.
Gases properties can be compared using STP as a
To obtain the pressure of gas collected over water
the partial pressure of the water must be taken into
The reason for this is as the gas bubbles through the
water the gas picks up water vapor.
• The amount of water vapor the gas picks up
only depends on the temperature.
• To calculate the pressure of the gas the partial
pressure of the water must be subtracted
from the pressure in the container.
The ideal gas
• The ideal gas law is a combination of all the gas
laws. The ideal gas law can be expressed as
PV = nRT.
• P is the pressure in atm
• V is the volume in liters
• n is the number of moles
• R is a constant
• T is the temperature in Kelvin
• The constant R is calculated from a
theroretical gas called the ideal gas. The most
commonly used form of R is .0821 L * atm / (K
• This R will allow the units to cancel so the
equation will work out.
• The ideal gas law is the equation of state of a
hypothetical ideal gas.
The modern form of the equation is:.
where p is the absolute pressure of the gas;
V is the volume;
is the amount of substance;
R is the Regnault constant, better known as
universal gas constant; and
T is the absolute temperature
In SI units, p is measured in pascals; V in cubic
metres; n in moles; and T in kelvin. R has the
value 8.314472 J·K−1·mol−1 .
Deviations from real gases
• The equation of state given here applies only
to an ideal gas, or a real gas that behaves like
an ideal gas.
• Since it neglects both molecular size and
• the ideal gas law is most accurate for
monatomic gases at high temperatures and
• This can be clearly seen in the diagram
• If the gases conformed to the ideal gas law
equation PV=nRT, the product PV should be
constant with increasing pressure at constant
temperature, clearly this is not the case.
• for any gas the lower its pressure and the
higher its temperature, the more closely it
will be 'ideal', i.e. closely obey the ideal gas
• Also the smaller the molecular mass or the
weaker the intermolecular forces, the gas will
be closer to ideal behaviour.
Flow of gases
– Flow by definition is the quantity of the gas or
fluid which passes a point in unit time.
In equation form,
F = Q/t
– where F is equal to the mean flow
– Q = the quantity (mass or volume) and
– T = time.
– The rate of change of a parameter, such as Q, is
specified as Q dot or
Definition: laminar flow -- "Streamline flow of a fluid
in which the fluid moves in layers without
fluctuations or turbulence so that successive
particles passing the same point have the same
– It occurs at low Reynolds numbers, i.e. low
velocities, high viscosities, low densities or small
dimensions.... Laminar flow may be visualized in
accord with the diagram below.
• The flow is greatest in the centre as the side of
the tube is approached the flow
becomes slower until it approaches zero
• In order to drive a fluid through the tube the
pressure different must be present across the
• This principal can be used to measure
resistance with gas flow
• The relationship above illustrates that
Pressure is proportiona to Flow [ P ] and
• where R presents the resistance of the tube.
If the flow is constant, i.e. is constant then the magnitude of the resistance
caused by the constriction can be determined from P1 and P2. The resistance
would be (P1-P2)/ Q = R.
Graphs for turbulent and lamumina
For turbulent flow, a nonlinear
relationship exists between flow and
pressure as shown below:
Relationships between flow and
• Turbulent flow may occur if there is sharp
increase in the flow through the tube.
• These fluctuations are superimposed on the
underlying regular (average) flow.
• Other factors affecting the type of flow
include viscosity, density and the diameter of
• These factors may be combined to give index
known Reynolds number.
• Reynolds number = (v Pd) /n ,
• where v is the linear fluid velocity
• ,P is the density,
• d is the tube diameter, and
• n is the viscosity
– Recalling that the Reynolds number is a ratio of
inertia forces (momentum) to viscous forces,
– smaller Reynolds numbers are consistent with
relatively larger viscous forces which would
predispose to laminar flow.
– Larger Reynolds numbers then indicate
dominance of momentum forces which
predispose to turbulence.
◦ Generally, Reynolds numbers less than about
2000 correspond to laminar flow,
◦ whereas Reynolds number is greater than
about 3000 characterize turbulent flow
◦ Reynolds numbers between 2000 and
3000 reflect unstable flow that can
transition between laminar and turbulent
– Furthermore, with turbulent flow, since pressure
to flow relationships do not exhibit linearity,
resistance will not be constant.
– In the turbulent flow case, resistance
measurements must be specified in terms of the
particular flow rate.
– Physiologically, during breathing, airflow
resistance will depend on the air flow rate
Graphs for turbulent
For turbulent flow, a nonlinear relationship exists
between flow and pressure as shown below:
factors predisposed to relatively
laminar vs. turbulent flow behavior
***Effect of reducing the tube diameter on the
Small changes in the diameter of an endotrachial
tube would have large effects on resistance and
then flow, assuming constant pressure.
– Hemodynamically, changes in vasomotor tone,
causing vasoconstriction, have similar large
• At constant pressure reducing the length of
the tube increase the flow of gas.
• flows may be laminar in which fluids move in
thin layers or turbulence reflecting irregular
motion with the velocity fluctuations
• Flow may change from lamina to turbulent if a
consriction is reached resulting in increased
• Viscosity of the fluid affect the flow.eg blood
viscosity increases if the patients haemoglobin
or fibrinogen raise
• Raise in viscosity reduces blood flow giving
risk of vascular occlusion.
• Viscosity increases at low temperature,
increasing age and following treatment with
low molecular weight dextan.
• An important clinical consideration has to do
with a change in the relationship between
flow and pressure as flow transitions from
laminar to turbulent.
• In particular, for turbulence flow inside
pathways that have rough internal edges, flow
appears about proportional to the square root
of pressure or a doubling of flow requires a
quadrupling of pressure.
• Laminar and turbulent flow in anesthesia: The
diagram above notes the critical flows for air and for
an anesthetic mixture containing nitrous oxide (60%)
• Transition between laminar and turbulent flow
exhibits dependencies on gas velocity.
• Furthermore gas velocity will be dependent on other
factors including volume flow, tubing diameter and
• Within the patient airway, gases tend to be
more humidified and at a higher temperature,
factors that reduced density ,Critical flow
values then will exhibit dependencies on
temperature and humidity.
• The figure above indicates that the
critical flow represented in l/min
correlates fairly well with airway
• For example anesthetic flow through a 10mm
internal diameter endotracheal tube would
transition from laminar to turbulent flow
when the flow rate would increase to above
about 10 l/min.
• Similarly if the tracheal diameter is about 15
mm, then the transitional flow to turbulence
would occur at flow rates above about 15
• Within normal breathing cycle, higher flows,
peaking at over 50 l/min would be associated
with turbulence while laminar flow would be
typical elsewhere in the respiratory cycle.
• The figure above indicates a greater likelihood
that air flow would remain laminar compared
to the combination of nitrous oxide + oxygen.
• Within the respiratory tract, the narrower,
smaller flow pathways in the lung, typically in
the lower part of the respiratory tract, would
predispose to laminar flow.
• Corrugated surface of anaesthetic tubing
induces turbulence at a lower flow than a
• Any sharp bends or angle increase the
incidence of turbulence flow,
• Eg turbulence at the connector of an
Elbow adapter between anesthetic
circuit and endotracheal tube .
• For "quiet breathing", much of the respiratory
tract flow would be laminar; however
speaking or coughing or sighing (deep breath)
would induce turbulence. Sharp tubing
bends and rougher(corrugated) internal
surfaces also predispose to turbulence as
suggested at the connecting site for an
endotracheal tube (below):
• Some equipments have a tube with a
constriction in which across section area
gradually decreases and then increase, this
instrument is a venturi meter
• If the pressure along the tube is measured it is
found that the pressure at the narrowest part
is lower than other areas
• This fall of pressure at the constriction
(narrow)is called venturi effect.
• The Venturi effect is the reduction in fluid
pressure that results when a fluid flows
through a constricted section of pipe.
• The Venturi effect is named after Giovanni
Battista Venturi (1746–1822).
• The Venturi effect is a jet effect;
• Eg as with an (air) funnel, or a thumb
on a garden hose, the velocity of the
fluid increases as the cross sectional
area decreases, with the static
pressure correspondingly decreasing.
How does it arises
• Flowing fluid contains energy in two forms
kinetic energy associated with flow and
potential energy associated with pressure.
• At a constriction there is a considerable
increase of fluid velocity hence a gain in
• A gain in kinetic energy can only occur if there
is a fall in potential energy ,This is because the
total energy present must remain constant.
• According to the laws governing fluid
dynamics, a fluid's velocity must increase as it
passes through a constriction to satisfy the
conservation of mass,
• while its pressure must decrease to satisfy the
conservation of energy.
• Thus any gain in kinetic energy a fluid may
accrue due to its increased velocity through a
constriction is negated by a drop in pressure.
• As the tube widens the fluid velocity falls
together with its kinetic energy hence the
potential energy and the pressure rises.
• IF you have a pressure gauge at the
constriction which is removed and leave the
tube open at this area
• The pressure at this point is below
atmospheric pressure , air or fluid will be
entrained through this opening(INJECTOR)
• Kinetic energy can also be converted to heat
energy by the friction of the moving fluid with
• For the system to work efficiently the friction
force which cause change in pressure between
two terminal end must be small so that
negligible amount of heat energy is lost.
• This will balance the two energy.
• Bernoulli's theorem:
• P1 + 1/2P v1
2 = P2 + 1/2 Pv2
• where v = flow velocity, P1or 2 = pressure
andP = density.
• (this form is for a horizontal "tube" such that
gravitational contributions may be omitted)
• Also, A1v1=A2v2 where A is the circular cross-
sectional area and v = flow velocity
• The Venturi oxygen mask is based on the
Venturi principal in that relatively rapidly
moving oxygen molecules pull along
(entrainment) air molecules by two processes:
1. the first process is based on the Bernoulli effect
in which there is a relative reduction in pressure
associated with the higher oxygen velocity from
– 2. and the second involves friction between the
high-speed oxygen molecules in the lower speed
air molecules which has the effect of pulling air
molecules into the higher speed stream of
– Translational momentum transfer occurs as the
air molecules increased their velocity.
This injector therefore dilutes oxygen with air
provides clinically useful concentraions
Venturi Mask (oxygen molecules: blue; air
• Entrainment ratio can be calculated as a
function of the entrainment flow to the
driving (oxygen) flow.
Entrainment ratio = (entrainment flow) / (driving flow).
• If the ratio were 8:1, then 8 l/min of air would
be entrained by the driving gas (oxygen) of 1
• Factors that could change the entrainment
• transient obstruction at the outlet of te
• change back pressure, which would ultimately
change the flow and so the resulting oxygen
• Bernoulli's Principle states that as the speed
of a moving fluid increases, the pressure
within the fluid decreases.
• for an inviscid flow, an increase in the speed
of the fluid occurs simultaneously with a
decrease in pressure ( a decrease in the fluid's
potential energy . )
• For Bernoulli's Principle to apply, the fluid is
assumed to have these qualities:
-fluid flows smoothly
-fluid flows without any swirls (which are called
-fluid flows everywhere through the pipe (which
means there is no "flow separation")
-fluid has the same density everywhere (it is
"incompressible" like water)
• As a fluid passes through a pipe that narrows
or widens, the velocity and pressure of the
• As the pipe narrows, the fluid flows more
• Bernoulli's Principle tells us that as the fluid
flows more quickly through the narrow
sections, the pressure actually decreases
rather than increases!
• Bernoulli's principle can be derived from the
principle of conservation of energy.
• This states that, in a steady flow, the sum of
all forms of mechanical energy in a fluid along
a streamline is the same at all points on that
• This requires that the sum of kinetic energy
and potential energy remain constant.
• If the fluid is flowing out of a reservoir the
sum of all forms of energy is the same on all
streamlines because in a reservoir the energy
per unit mass (the sum of pressure and
gravitational potential ρ g h) is the same
• Fluid particles are subject only to pressure and
their own weight[
• If a fluid is flowing horizontally and along a section of
a streamline, where the speed increases it can only
be because the fluid on that section has moved from
a region of higher pressure to a region of lower
• if its speed decreases, it can only be because it has
moved from a region of lower pressure to a region of
higher pressure. Consequently, within a fluid flowing
horizontally, the highest speed occurs where the
pressure is lowest, and the lowest speed occurs
where the pressure is highest.
• This demonstration of Bernoulli's Principle .
While blowing through the narrow part,
remove your finger that is holding the ball
inside the inverted funnel.
• The ball will hover in the funnel until your
breath runs out.
A ping pong ball is contained in an inverted funnel. Blowing into
the small tube
end of the funnel causes the ping pong ball to rise to the top
(narrow end) of the funnel.
• Basic physics and measurements in anaesthesia by P d
• Textbook of Anaesthesia by smith
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