230
Dynamics
of
the Vascular System
where m is the mass of the injectate,
C,
is the concentration, and t is time.
Inject
m
mg
v
-
velocity
a!
-'I
-
;
-v
1
LL-I
-
Detector
-
Detector
-
c---
I
I
0
-T4
Genesis of the
dilution
curve
Fig.
8.1.1 1:
Principle
of
the dye dilution technique and the genesis
of
the dye dilution
curve
of
concentration
vs.
time. From Geddes
(1984).
The Stewart-Hamilton principle states that if a known concentration
of
indicator
is
introduced into a flow
stream
and
its
temporal
concentration
is
measured at a downstream site, then the volume flow
can be calculated. The Stuart-Hamilton principle relates the flow
(Q)
to
the mass (m) of indicator injected and the concentration (c(t)) of the
indicator measured downstream at time t:
m
Q=
m
(8.1.19)
