Micro-perforate flow resistance

The pressure drop of the flow through a micro-perforated wall in the flow solution. Sub-millimetre holes are viscous: the drop is a Poiseuille (linear) term plus an inertial term, not the jet-loss formulas of millimetre holes.

Last updated 2026-11-11

Theory

The flow solution models every perforated wall as a pressure jump on a cyclic baffle, $\Delta p = (\mu D + \tfrac{1}{2}\rho I |U|)\,U\,L$ with $U$ the velocity through the wall face. For a micro-perforate both terms come from the papers of its acoustic model. The linear term is the zero-frequency limit of the acoustic hole impedance: the steady laminar flow in a tube of diameter $d$ Maa (1998), or between the walls of a slit of width $b$ Kabral et al. (2014). The inertial term is the quasi-steady form of the papers' amplitude-dependent resistance $|u_h|/(\sigma c)$ , which in steady flow is $\rho u_h |u_h|$ with the hole velocity $u_h = U/\sigma$ Allam and Abom (2011).

This is a law for flow THROUGH the wall. It is the same for a micro-perforated baffle across a duct, where all the flow crosses it, and for the wall of a micro-perforated tube, where the flow grazes the wall and the law sets only the small flow leaking through it. Unlike the perforated-tube law (Perforation type) it has no grazing-flow correction.

The linear term dominates while the ratio of the inertial to the viscous term, $Re_h\,d/(32\,t)$ for circular holes, stays below one. The card shows the hole and face velocity at which this happens. Above it the quadratic term takes over; the resistance is still computed, but the measured basis of the linear impedance no longer applies to the flow.

Equations

\Delta p = \mu\,\frac{32\,t}{\sigma d^2}\,U + \rho\,\frac{U |U|}{\sigma^2} \qquad \text{(circular holes)}, \qquad \Delta p = \mu\,\frac{12\,t}{\sigma b^2}\,U + \rho\,\frac{U |U|}{\sigma^2} \qquad \text{(slits)}

(1)

where	meaning	unit
$\Delta p$	Pressure drop across the wall	Pa
$\mu$	Dynamic viscosity	Pa s
$t$	Plate thickness	m
$\sigma$	Open-area ratio	-
$d, b$	Hole diameter, slit width	m
$U$	Velocity through the wall face	m/s
$\rho$	Density	kg/m³

D = \frac{32}{\sigma d^2}\ \text{or}\ \frac{12}{\sigma b^2}, \qquad I = \frac{2}{\sigma^2 t}, \qquad L = t, \qquad Re_h = \frac{u_h\,d}{\nu} < \frac{32\,t}{d}\ \text{or}\ \frac{12\,t}{b}

(2)

where	meaning	unit
$D$	Darcy coefficient of the jump	1/m²
$I$	Inertial coefficient of the jump	1/m
$L$	Jump length	m
$Re_h$	Hole Reynolds number	-

Default and rule

Default: computed from the hole size, thickness and open-area ratio
Rule: Computed when the wall's flow type is "Micro-perforated (laminar)" (Perforation type); the hole or slit size, the thickness and the open-area ratio are the same inputs as the wall's acoustic micro-perforate model, entered once.
Source: Maa (1998), eq. 3a; Kabral et al. (2014), eq. 2 (zero-frequency limit); Allam and Abom (2011), eq. 23 (amplitude-dependent term).

Valid range viscous (linear) while the hole Reynolds number stays below 32 t/d (circular) or 12 t/b (slits)

Linear range

When the expected hole velocity exceeds the linear limit shown on the card, the inertial term dominates; the setup check names the wall.

Not validated

This flow resistance has not been validated against a measured DC pressure drop of a micro-perforated plate: it is the zero-frequency and quasi-steady limit of the acoustic papers' equations. The measured data in hand do not test it: Lee et al. (2016) measured 3-15 Pa across silencers with micro-perforated linings, with the flow grazing the wall (the lined silencer behaves almost like a solid tube), and give no tap positions.

Theory

Equations

Default and rule

Valid range viscous (linear) while the hole Reynolds number stays below 32 t/d (circular) or 12 t/b (slits)

Related 6

References 4