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where ai' asi'
ted perimeter
di = 4-di
and Ei are the
of ith section,
(—a
s i
flow area, solid cross
respectively. Hence, d
sectional
and di
area, and
are related
In the above development, the reference scales for the velocity and tem-
perature change have been used. The simplest way to obtain these scales are
to use the steady state solutions. By taking the heated section as a repre-
sentative section, one can obtain the following solution for temperature rise.
ATqCtu (aso)(17)
ppo o
where subscript o denotes the heated section. Substituting the above expres-
sion into the steady state momentum integral equation, the solution for the
velocity becomes
uo
1/3 2s(o) Qaso
pCph ao
29i/A1)
VI.2.2 General Similarity Laws
(16)
(18)
The similarity criteria between two different systems can be ob-
tained from a detailed consideration of the similarity groups developed above
together with necessary constitutive relations. In the following analysis,
subcript R denotes the ratio between the model and prototype. Thus
*m
_ ---- *R for model
4p 4, for prototype '
In general, the solid materials need not be
and prototype. However, for simplicity the use
structures is assumed in the present analysis.
336
the same between the
of the same materials
This implies that
(19)
model
for
wet-
by