Conductance for Piping and Orifices

Conductance values will depend not only on the pressure and the nature of the gas which is flowing, but also on the sectional shape of the conducting element (e.g. circular or elliptical cross section). Other factors are the length and whether the element is straight or curved. The result is that various equations are required to take into account practical situations. Each of these equations is valid only for a particular pressure range. This is always to be considered in calculations.

a) Conductance for a straight pipe, which is not too short, of length l, with a circular cross section of diameter d for the laminar, Knudsen and molecular flow ranges, valid for air at 20 °C (Knudsen equation):

where

d = Pipe inside diameter in cm
l = Pipe length in cm (l ≥ 10 d)
p1 = Pressure at start of pipe (along the direction of flow) in mbar
p2 = Pressure at end of pipe (along the direction of flow) in mbar

If one rewrites the second term in C = 135(d^4/I)p + 12.1(d^3/I)⋅[(1 + 192 ⋅ d ⋅ p)/(1 + 237 ⋅ d ⋅ p)](l/s) in the following form

with

it is possible to derive the two important limits from the course of the function f (d · p):

Limit for laminar flow
(d · p > 6 · 10^(–1) mbar · cm):

Limit for molecular flow
(d · p < 10–2 mbar · cm) :

In the molecular flow region the conductance value is independent of pressure!

The complete Knudsen equation

will have to be used in the transitional area 10–2 < d · p < 6 · 10_(–1) mbar · cm. Conductance values f

or straight pipes of standard nominal diameters are shown in Figure 9.5 (laminar flow) and Figure 9.6 (molecular flow) below. 

Fig. 9.5: Conductance values for piping of commonly used nominal width with circular cross-section for laminar flow (p = 1 mbar) (Thick lines refer to preferred DN) Flow medium: air (d, l in cm!).

Fig. 9.6: Conductance values for piping of commonly used nominal width with circular cross-section for molecular flow. (Thick lines refer to preferred DN) Flow medium: air (d, l in cm!).

b) Conductance value C for an orifice A
(A in cm2): For continuum flow (viscous flow) the following equations (after Prandtl) apply to air at 20 °C where p_z /p_1 = δ:

Fig. 1.2 Flow of a gas through an opening (A) at high pressures (viscous flow)

for δ ≥ 0.528

and for δ ≤ 0,03

δ = 0.528 is the critical pressure situation for air

Flow is choked at δ < 0.528; gas flow is thus constant. In the case of molecular flow (high vacuum) the following will apply for air:

Cmol = 11,6 · A · l · s-1 (A in cm²)

Given in addition in Figure 1.3 are the pumping speeds S*_(visc) and S*_(mol) referenced to the area A of the opening and as a function of δ = p2 /p1. The equations given apply to air at 20 °C. The molar masses for the flowing gas are taken into consideration in the general equations, not shown here.

Fig. 1.3 Conductance values relative to the area, C*_(visc), C*_(mol), and pumping speed S*_(visc) and S*_(mol_) for an orifice A, depending on the pressure relationship p2/p1
for air at 20 °C.

Table 1.1 Conversion factors (see text)

When working with other gases it will be necessary to multiply the conductance values specified for air by the factors shown in Table 1.1.