Plate formula

For a perpendicular plate defined by its open-area ratio: Idelchik's formula for a plate of finite thickness (Diagram 8-4, uses $l/d$ = thickness / hole diameter) or his zero-thickness, thin sharp-edged plate (ignores $l/d$ ).

Last updated 2026-11-03

Theory

In a thin sharp-edged plate the jet separates at the hole edge and leaves the hole fully contracted. In a thicker plate the jet can reattach to the bore of the hole before it leaves, which recovers part of the contraction loss; the bore adds a friction loss. Idelchik's thick-plate diagram combines both: a coefficient $\tau(l/d)$ that falls from 1.35 at $l/d = 0$ to 0 at $l/d \ge 3$ , and a friction term $\lambda\,l/d$ (Idelchik, 2008).

The program interpolates $\tau$ linearly in the diagram's table and uses $\lambda = 0.02$ , the value the diagram's own table is computed with. At $l/d = 0$ the thick formula agrees with the thin one within 3 %. The thick formula needs the hole diameter, which the card then shows (Hole diameter).

Equations

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

(1)

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

(2)

where	meaning	unit
$\sigma$	Open-area ratio	-
$l$	Plate thickness	m
$d$	Hole diameter	m
$\tau$	Jet-reattachment coefficient, a function of $l/d$ given by the diagram (interpolated linearly in $l/d$ ; 0 for a long hole)	-
$\lambda$	Friction factor of the hole bore, 0.02	-

Default and rule

Default: thick plate (a new perforated wall); thin sharp-edged (a case file that stores none)
Rule: A new perforated wall uses the thick-plate formula. A case file without the key keeps the thin formula, so its results do not change.
Source: Idelchik's Diagram 8-4, "thickened grid (perforated plate or laths)", $l/d_h > 0.015$ , $Re \ge 10^5$ , from the 1960 edition's English translation (pp. 333-334); the implementation reproduces the diagram's own $\zeta$ table within 1 % (Idel'chik, 1966). 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 reproduce.

Valid range thick plate (l/d) | thin sharp-edged

Choice

Thick plate when the plate is at least a few tenths of the hole diameter thick (typical punched sheet); thin when the holes are much larger than the sheet thickness.

Reynolds number

Both formulas are for $Re \ge 10^5$ in the holes; the diagram's low-Reynolds correction (Diagram 8-2) is not applied.

Plate only

Not used for a perforated tube, nor when $K$ is typed.

Theory

Equations

Default and rule

Valid range thick plate (l/d) | thin sharp-edged

Related 5

References 2