Pressure drop for thin perforated plates

It is defined the pressure drop coefficient ( \zeta ) as:

\zeta = \Large \frac {\Delta p}{\frac{1}{2} \rho V_1}

Where:

• \Delta p : pressure drop through the plate.
• V_1 : air velocity on the upstream face of the plate.
• \rho : air density.

Pressure drop coefficient ( \zeta ) is function of the open area fraction or porosity ( f ) and the Reynolds number ( Re ). Porosity ( f ) is a factor whose values move between 0 and 1; f = 1 means a fictitious 100% open plate:

  Re = \Large \frac{V_0  d_h}{\nu}

Where:

• V_0 : air velocity in the orifices.
• d_h : hydraulic diameter or length scale.
• \nu : air cinematic viscosity.

If we assume circular orifices the geometrical diameter is equal to the hydraulic diameter.

We can use the equation of continuity:

f  V_0 = V_1

to get the Reynolds number ( Re ) from the approach velocity ( V_1 ):

  Re = \Large \frac{V_1  d_h}{f  \nu}

Depending on the Reynold number ( Re ), it is applied the corresponding formula or diagram for the four possible regimes:

Diagrams are expressed in a double logarithmic system.