Turbulent Flow
the velocity profile across the lumen is lost
flow becomes directly proportional to the square root of the driving pressure
therefore, as pressure flow is not linear, resistance is not constant, and the flow at which the
resistance is measured must be specified
other factors in turbulent flow may be summarised,
where,
k
=
a constant
r
=
rho, the
density
of the fluid in kg.m
-3
thus, radius has less of an effect on turbulent flow
the likelihood of the onset of turbulent flow is predicted by,
Reynold's number
(Re)
=
ρ
vd
η
where,
d
=
the diameter of the tube
v
=
the velocity of flow
ρ
=
rho
, the density of the fluid in kg.m
-3
η
=
eta
, the viscosity of the fluid in Pascal seconds
empirical studies show that for cylindrical tubes, if Re > 2000 turbulent flow becomes more likely
for a given set of conditions there is a
critical velocity
at which Re = 2000
Clinical Aspects
thus the transition from laminar to turbulent flow depends on the mixture of gases present
in the patient's airway the gases are humidified, contain CO
2
and are warmed
the net effect is an increase in the critical velocity, due to a reduction in density due to warming
of the gases
for a typical anaesthetic mixture,
critical flow (l/min)
~
airway diameter (mm)
as breathing is cyclical, with peak flows > 50 l/min, turbulent flow usually predominates during
peak flow, while laminar flow is present during other times in the respiratory cycle
due to the great reduction in velocity in the bronchi and smaller airways, flow through them tends
to be laminar
in general, during quiet breathing flow tends to be laminar, while during speaking, coughing, or
deep breathing flow becomes turbulent in the larger airways
Q
.
=
k
.
r
2
.
δ
P
ρ
l
Anaesthesia Equipment
2