certain  temperature,  which  can  be  obtained  by empirical

according to Eqs。 (1) – (4), the derivation of air humidity at outlet of cylinder is

expressions or look-up the table。 For Eq。 (1), when the condensation  doesn’t  occur,  we  can  instead  the absolute

humidity with initial absolute humidity。 Empirical expression is as follows:

With the increasing of s0, the saturation or super saturation is easier to reach。 s0 was defined as a comprehensive parameter。 Hence, the local speed of  sound

is   considered   as   constant,   then   A/V   is   an important

comprehensive parameter。

We can assume as follows[11]: (1) Viscous of air in pipe is very small and can be regard as ideal gas; (2) The pressure, temperature and density in cylinder is uniform; (3) There is no heat transfer between air and pipe wall, namely, the pipe wall is heat insulation, the flow of air in pipe is adiabatic

reversible;  (4)  The  temperature  of  air  in  pipe  is   radial

4。2 Proposed comprehensive parameter based

on natural frequency and average speed

The average velocity of air um during discharge[3] is expressed as follows:

uniform distribution; (5) The relation ρ • (∂u/∂t) » u    •

(∂p/∂x) stands while the flow is unsteady flow。

According   to   fluid   net   theory,    the   pressure     and

temperature in Eq。 (1) can be derived from Eq。 (3) and

where  A1is  the  effective  section  area  at  the  outlet   of

container,   Zc    is   the   characteristic   impedance   of pipe,

According  to Eq。 (5), the partial derivatives of   average

velocity to s0 and l/a can be obtained as follows:

where is the density of compressed air, u is the axial velocity, t is the time, ps is the initial absolute pressure of compressed air, p0  is the pressure variation of   compressed

air at the beginning moment/initiation of discharging, s0 is a comprehensive system parameter, s0 = A • a/V。 a is the local speed of sound, n is the polytrophic exponent, Rg is the gas constant, s  is the initial density of compressed  air,

is the reflectance for flow resistance at the end of pipe,

here, ≈ −1。

Pressure, temperature, and corresponding saturated vapor pressure, relative humidity and the derivation of relative humidity at arbitrary time and position can be derived from Eqs。 (1) – (4), hence[3]

The above results show that the effect trend of s0 and l/a on average velocity is the same。 The larger s0 is, the bigger l/a and the lower average velocity are, the easier internal condensation occurs。 Therefore, s0l/a = Al/V  was proposed as a comprehensive parameter of evaluating condensation and its physical interpret is motion performance of compressed air。 The comprehensive parameter is called dimensionless volume of discharging pipe and used to analyze internal condensation and external condensation instead of volume of container。 The discharging  process  can  be  considered  to  the  spreading

process of decompression wave in system with natural frequency of fluid network theory[11]。 The system in Fig。  3,