Open-area ratio

The fraction $\sigma$ of the wall area that is open (total hole area divided by wall area). It sets the loss coefficient $K$ of a perforated tube, and of a perpendicular plate defined by its open-area ratio; $K$ grows roughly as $1/\sigma^2$ . For a perforated tube the acoustic model uses the same value.

Last updated 2026-11-03

Theory

Through a perforated wall the gas accelerates from the face velocity $U_n$ to the hole velocity $U_n/\sigma$ (and further in the contracted jet). The loss is a fraction of the jet's dynamic head, so $K$ on the face velocity scales with $1/\sigma^2$ :

Perforated tube: the whole jet head is lost, equation (1) (Elnady et al., 2010). The starting value with $C_{D0}$ is shown as Jet loss K0 (read-only); the grazing update lowers $C_d$ during the run.
Perpendicular plate, thin sharp-edged: equation (2), Idelchik's zero-thickness plate (Idelchik, 2008).
Perpendicular plate, thick: equation (3), Idelchik's Diagram 8-4, which also needs $t/d$ (see Plate formula).

The card shows the estimated $K$ of a plate, or $K_0$ of a tube, as $\sigma$ is typed.

Equations

K_{tube} = \frac{1}{(\sigma\,C_d)^2}

(1)

K_{thin} = \frac{\left(0.707\,(1-\sigma)^{0.375} + 1 - \sigma\right)^2}{\sigma^2}

(2)

K_{thick} = \frac{\left(0.5 + \tau(t/d)\sqrt{1-\sigma}\right)(1-\sigma) + (1-\sigma)^2 + \lambda\,t/d}{\sigma^2}, \qquad \lambda = 0.02

(3)

where	meaning	unit
$\sigma$	Open-area ratio	-
$C_d$	Discharge coefficient of the holes	-
$\tau$	Jet-reattachment coefficient of Diagram 8-4, a table in $t/d$	-
$t$	Wall thickness	m
$d$	Hole diameter	m
$\lambda$	Friction factor of the hole bore used by the diagram's table	-

Default and rule

Default: 0.1
Rule: 0.1 (10 % open area), the schema value; enter the real ratio of the part.
Source: Tube law: (Elnady et al., 2010) eq. 24 with (Rogers and Hersh, 1975). Plate formulas: (Idelchik, 2008). The thick-plate diagram is taken from the 1960 edition; the thin formula is the later editions' form (the 1960 Diagram 8-1 uses $\sqrt{1-\sigma}$ and gives about 6 % less at $\sigma = 0.4$ ; the program keeps the later form so that existing results do not change).

Valid range 0 < σ ≤ 1

Values

$0 < \sigma \le 1$ . Muffler perforates are typically 0.03-0.3.

Small open area

$K$ rises as $1/\sigma^2$ : at $\sigma = 0.03$ the tube's $K_0$ is above 1000, and the solved pressure drop becomes very sensitive to $\sigma$ . Measure it on the part.

Plate formulas

Idelchik's formulas assume sharp-edged holes at $Re \ge 10^5$ ; the low-Reynolds correction is not applied.

Theory

Equations

Default and rule

Valid range 0 < σ ≤ 1

Related 6

References 3