Discharge coefficient C_D0

The discharge coefficient of the holes of a perforated tube without grazing flow: the ratio of the actual flow rate through a hole to the ideal flow rate at the same pressure difference. It sets the initial loss coefficient $K_0 = 1/(\sigma C_{D0})^2$ and is the upper limit of the grazing-flow discharge coefficient.

Last updated 2026-11-03

Theory

A jet leaving a sharp-edged hole contracts, so it carries less flow than the hole area multiplied by the ideal velocity; $C_D$ quantifies this reduction. For a thin plate $C_D$ is typically 0.6-0.7; in a thicker wall the jet partly reattaches inside the bore, which raises the coefficient.

On Auto, the program interpolates bilinearly, equation (1), in a table of measured steady-flow discharge coefficients:

rows of wall thickness $t$ = 0.5, 0.8, 1.0, 1.25, 1.5, 2.0 and 2.5 mm;
columns of hole diameter $d$ from 0.6 to 5 mm;
values between 0.72 and 0.91.

Outside the table the nearest edge value is used; the program never extrapolates beyond the table.

With the grazing correction enabled (Grazing correction), the coefficient applied on each face is $\min(C_{De}, C_{D0})$ : grazing flow lowers the coefficient, and as the grazing flow becomes small it returns to $C_{D0}$ . In a flow + acoustics run the same value is used as the acoustic model's $C_D$ (Discharge coefficient C_D (acoustics)).

Equations

C_{D0} = \sum_{a,b \in \{0,1\}} w_a(t)\,w_b(d)\,C_{i+a,\,j+b}, \qquad K_0 = \frac{1}{(\sigma\,C_{D0})^2}

(1)

where	meaning	unit
$C_{i,j}$	Table value at thickness row $i$ and diameter column $j$ bracketing $(t, d)$	-
$w_a, w_b$	Linear interpolation weights in $t$ and $d$ (clamped to the table)	-
$\sigma$	Open-area ratio	-
$K_0$	Initial loss coefficient	-

Default and rule

Default: Auto: interpolated in the hole-diameter × wall-thickness tableComputed by the program
Rule: Auto (table interpolation). A value between 0.05 and 1 entered by the user overrides the table.
Source: The table contains Elnady's measured DC-flow discharge coefficients as a function of hole diameter and wall thickness: Table 1 of Paper III (Elnady and Boden, 2004) of his doctoral thesis (Elnady, 2004); the related journal paper is (Elnady et al., 2010). The measured samples cover $d$ = 0.6-2.4 mm and $t$ = 0.8-2.4 mm; the remainder of the table is Elnady's extrapolation. The table values are not reproduced here; refer to the thesis.

Valid range 0.05 ≤ C_D0 ≤ 1

Values

0.05 to 1. A user value replaces the table for the CFD and, in a flow + acoustics run, for the acoustic model.

Extrapolated table cells

Outside $d$ = 0.6-2.4 mm or $t$ = 0.8-2.4 mm the table value is Elnady's extrapolation; the boundary-condition card indicates this.

Theory

Equations

Default and rule

Valid range 0.05 ≤ C_D0 ≤ 1

Related 6

References 3