Almost everyone working on pressure drop coefficients of perforated
plates encounters the work of I.E. Idelchick {1}. A plethora of
graphs or equations  some of which are impossible to evaluate quickly
 must then be addressed. To simplify this issue for the reader,
this month's Technical Data page has been designed to provide an
overview of this information.
When focusing on thin perforated plates with sharpedged orifices,
diagrams 81 and 85 in [ref. 1] should be consulted. Here a condensed
compilation of the pressure drop coefficient
(Greek letter 'zeta') can be found defined as =
p / (1/2
u_{1}^{2}),
with u_{1} the velocity of
air on the upstream face of the plate and
the air density. Various ingredients for the calculation of (f,Re)
as a function of the open area fraction f (0<f<1;
f=1 means a fictitious 100% open plate) and the Reynolds
number Re=u_{0} d_{h}
/v are provided as an analytical function, in part as graph
or table. The Reynolds number must be calculated with the hydraulic
diameter d_{h} of an orifice
as the length scale and the velocity of air in the hole u_{0}
as the typical velocity. Assuming that the plate contains circular
orifices, the geometrical diameter is equal to the hydraulic diameter.
The equation of continuity f u_{0}
= u_{1} can be used to obtain
the Reynolds number from the approach velocity u_{1}
as Re= u_{1} d_{h}
/(f v).
Exactly which table or which combination of tables and diagrams
is applied depends upon the Re. There are 4 regimes:
Re>10^{5}
=(diagram.
[81 in ref. 1]) 
(1) 
30 < Re < 10^{4}...10^{5}
=(diagram.
[85 in ref. 1] and diagram. [81]) 
(2) 
10 < Re < 25 = =
((4) and diagram. [85 in ref.1] and diagram. [81]) 
(3) 
Re<10 =30
/ (f^{2} Re ) 
(4) 
The fully developed turbulent regime is covered by Eq. (1), the
laminar one by Eq. (4). Eqs. (2) and (3) are suitable for the transitional
regime. For free convective situations Eq. (2) should be used. The
original values from [1] were used by the author to elaborate analytical
fit functions for all values for f and Re. These functions
(f,Re) are
plotted in two diagrams: Fig. 1 for 0.1 < f <
0.5 and Fig. 2 for 0.6 < f < 0.95. in
a double logarithmic system. We observe that the data does not provide
a continuous function (f=const.,Re)
but jumps between the Reintervals (1) and (4).
Fig. 1. Pressure drop coefficient of
perforated plates function of log Re and free area ratio f, for
0.1 < f < 0.5. Note the logarithmic
scaling on the vertical axis. The black square denotes the position
of the example given in the text.
For example, to calculate (for a plate with holes of diameter d=3
mm, pitch (distance hole center to hole center) s=4 mm and
an air velocity of u_{1} =
0.5 m/s,. f turns out to be f=
d^{2} /(4 s^{2})
= 0.44. Re= u_{1} d/(f
v) 230.
Figure 1 can be used to find 4.
Fig.2. Pressure drop coefficient of
perforated plates for 0.6 < f < 0.95.
Reference
1. 
I.E. Idelchik, Flow Resistance,
Hemisphere Publishing Corp., New York 1988 
