Adiabatic expansion factor

Ya = adiabatic-expansion factor for flow nozzles and venturi tubes... 

For the discharge of compressible fluids from the end of a short aiping length into a larger cross section, such as a larger pipe, vessel, or atmosphere, the flow is considered adiabatic. Corrections are applied to the Darcy equation to compensate for fluid property changes due to the expansion of the fluid, and these are known as Y net expansion factors [3]. The corrected Darcy equation is ... 

Figure 9-2 Expansion factor for adiabatic flow in piping systems, (a) k = 1.3 (b) k- 1.4. (From Crane Co., 1991.)...

Figure 4-14 The expansion factor Kg for adiabatic pipe flow for y = 1.4. From AICHE/CCPS, Guidelines for Consequence Analysis of Chemical Releases (New York American Institute of Chemical Engineers, 1999).

For the flow of gases, expansion factor Y, which allows for the change in gas density as it expands adiabatically from pi to p, is given by... 

Equation (26-137) is recognized as the expression for all-gas flow by adiabatic expansion across an orifice or nozzle. The factor k is the expansion coefficient for the adiabatic flow equation of state ... 

The expansion factor is defined as the molar density of the reagents divided by the molar density of the products in an explosive mixture. The expansion factor is a measure of the increase in volume resulting from combustion. The maximum value of the expansion factor is for adiabatic combustion. 

Fuel Formula Maximum Flame Speed (m/s) Adiabatic Flame Temperature (K) Expansion Factor Autoignition Temperature (°C)... 

The Expansion Factor Y. This corrects for density changes between taps. Y depends on the adiabatic exponent (k = CJC ), absolute pressure ratio (AP/P ), and the ratio, p, between restriction diameter and the inside pipe diameter. For liquid flow, Y = 1.0. For gas flow, Buckingham derived the equation [3] ... 

It is desired to quench the coagulation of an aerosol composed of very small panicles dp (p)- If the rate of coagulation is to be reduced to 1% of its original value by isoihemial. constant pressure dilution with particIc-frce gas, dctcnninc the dilution ratio. The rate is to be reduced by the same factor by a reversible adiabatic expansion. Determine the volume e.xpansion ratio assuming the gas is ideal. 

For the measurement. of compressible flow of gases, the adiabatic expansion fromp, to P2 pressure must be allowed for in Eq. (3.2-7). A similar equation and the same coefficient C are used along with the dimensionless expansion correction factor Y (shown in Fig. 3.2-3 for air) as follows ... 

For the fluid to expand, the channel must be convergent (Dz < 0) under subsonic conditions (Ma < 1) and divergent (Dz > 0) under supersonic conditions (Ma > 1). Note that Eq. (31) has a singularity at Ma = 1 and changes its sign when the flow speed u z) crosses the speed of sound Msnd- Because Dz = 0 in a cylindrical channel, an adiabatic expansion must be driven by friction (or else the trivial solution dp/dz = 0 is obtained). The friction factor / in Eq. (30) is always positive thus, if one starts at subsonic conditions, flow can never be accelerated beyond the speed of sound inside a cylindrical duct. Flow that attains exactly the speed of sound at the exit of the duct is called choked flow. As we... 

Sethna [1981] considered two limiting cases. The calculation of action in the fast flip approximation (a>j CO ) proceeds by utilizing the expansion exp ( — cu,-1t ) 1 — cu t. After substituting the first term, i.e. the unity, in (5.72) we get precisely the quantity which yields the Franck-Condon factor in the rate constant. The next term cancels the adiabatic renormalization and changes KM)... 

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