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Equation (6) can be improved by considering how the pressure drop coefficients f ci
actually
depend on the Reynolds number. In our case, owing to the turbulent flow condition into the (core and
heat exchangers) smooth channels, the following Blausius correlation [14] can be used:
−0.25
= 0.32
e
f c
R
were
e
≡
REYNOLDS NUMBER
=
D e
ρ v
µ
=
Q
m
D e
S µ
e
(8)
and µ is the fluid viscosity, S e
is the equivalent flow area of the considered channel or component and
D e
is the corresponding equivalent diameter.
By considering the (8) Blausius correlation, the equation (6) becomes:
1.75
m
Q
∆P
∝
ρ
= ρ
0.75
v
1.75
µ
0.25
(9)
The improved model (9), besides the hypothesis (7), needs only the following further
approximation:
0.25
µ i
0.25
µ
≈ 1
2.2 Gravitational pull and energy balance in steady conditions
In steady state convection, the kinetics energy dissipated by pressure drop is compensated by the
work made by the gravity field along the entire loop. By considering unit volumes, we can write this
balance in terms of pressure drops:
∆P g
= ∆P
where the gravitational pull ∆P g
is defined as:
∆
P g
≡
∫
r r
ρ g • d s
(10)
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