Jökull - 01.12.1966, Side 43

standard error of 3%. The absolute accuracy
is still somewhat uncertain. Somewhat less satis-
factory results have been obtained with the
argon dilution method, but prospects of im-
provement appear good.
CONCLUSIONS
It cannot be claimed that an easy and suf-
ficiently accurate method of assessing the dis-
charge from a well is yet available. Nevertheless,
during the last five years a better understand-
ing of two-phase critical flow in parallel ducts
has increased the likelihood that a method can
be devised on this basis. The rnajor impedi-
ment, as the above and other analyses show,
is the extreme difficulty of disentangling the
transient inter-related effects which occur late
in the expansion as the pipe exit is approach-
ed. Subject to this, if dilution methods, which
are now showing promise, can be perfected,
there should be available in the future two
different but complementary techniques.
APPENDIX
An Analytical Derivation of a Polytropic
Expansion Index for Equilibrium Flow
The polytropic equilibrium expansion of a
high-quality two phase mixture may be assumed
to obey the law
pvni’=C, (A. I)
where np is a constant, or, at least, a very
slowly varying function of p.
Hence
and since
we have
v dp
p dv ’
v 52 xv
g’
dv
dp
dvg
dp
+ vg
dx
dp’
(A.2)
(A. 3)
and multiplying by — p/v we obtain
1 p dvg p dx
ni> vg dp x dp
(A.4)
At equilibrium the first factor on the r.h.s. of
(A. 4) is simply 1 / n where ng is the polytropic
coefficient for the expansion of dry saturated
steam, that is ng = 1.06 (expansion along the
line x = 1).
In computing the second factor on the r.h.s.
of (A. 4) we observe that this factor will in
general be considerably smaller than the first
one. Moreover we can therefore disregard kine-
tic energy terms and write
x = (h0-
and since
dx dx dT
dp — dT dp
dx _ d / h
dp dT \ r
hf)/r
we obtain
\ dT
/ clp
(A.5)
(. 6)
We will now assume that r is a slowly varying
íunction and put hf = cfT. Moreover, we will
use the Clausius-CIapeyron equation
dT Tvg
dp Jr
and hence (A. 6) becomes
dx ct Tvg cfTvg V’g
dp = " "r” ' Jr = ~ JÍ+ ’ ,= “ Jr2~
and therefore
p dx pr h(vg pvghf
x dp “ (h0 — hf) Jr2 “ Jr(h0-hf)
Hence, equation (A. 4) gives
0.94
Pvghf____
Jr(h0 — hf)
(A. 7)
A CKNO WLED GEMENTS
The separating and measuring plant employ-
ed by the Electricity Authority, Iceland, was
designecl by Mr. Sveinn S. Einarsson to whom
the authors are indebted for his collaboration.
The salt and argon experiments currently in
progress in lceland are under the supervision
of Mr. S. Björnsson and Mr. S. Benediktsson.
Tlie work leading to this review paper was
done following vacation consultancies in Ice-
land by one author (D.J.R.) who acknowledges
JÖKULL 197