Isentropic exponent

The isentropic exponent k is defined as ratio of pressure fluctuations and corresponding fluctuations of the density at isentropic conditions and may be calculated, for example, by measurements of the velocity of sound [12,13]  

For an ideal gas, the isentropic exponent according to Eq. (15.28) can be transferred into the ratio of specific heat capacities at constant pressure and volume (see Table 15.1). There are various calculation procedures in the literature for approximate 

In general, the isentropic exponents take very high values at large reduced pressures the description of this factor on the assumption of an ideal gas behavior is then no longer permissible. The calculation by means of measured specific heat capacities according to the isentropic exponent defined in Table 15.1 leads to almost equal values even at very high reduced pressures. 

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It has played a dual role, one in Equation 2.18 on specific heat ratio and the other as an isentropic exponent in Equation 2.53. In the previous calculation of the speed of sound. Equation 2.32, the k assumes the singular specific heat ratio value, such as at compressor suction conditions. When a non-perfect gas is being compressed from point 1 to point 2, as in the head Equation 2.66, k at 2 will not necessarily be the same as k at 1. Fortunately, in many practical conditions, the k doesn t change very... 

Suction temperature Discharge temperature Suction pressure Discharge pressure Isentropic exponent Specific gravity Percent clearance ... 

I p = pressure ratio k = isentropic exponent r, = volume ratio... 

In the case of adiabatic flow we use Eqs. (9-1) and (9-3) to eliminate density and temperature from Eq. (9-15). This can be called the locally isentropic approach, because the friction loss is still included in the energy balance. Actual flow conditions are often somewhere between isothermal and adiabatic, in which case the flow behavior can be described by the isentropic equations, with the isentropic constant k replaced by a polytropic constant (or isentropic exponent ) y, where 1 < y < k, as is done for compressors. (The isothermal condition corresponds to y= 1, whereas truly isentropic flow corresponds to y = k.) This same approach can be used for some non-ideal gases by using a variable isentropic exponent for k (e.g., for steam, see Fig. C-l). 

Just as for isothermal flow, this is an implicit expression for the choke pressure (P ) as a function of the upstream pressure (Pi), the loss coefficients (J] Kf), and the isentropic exponent (7c), which is most easily solved by iteration. It is very important to realize that once the pressure at the end of the pipe falls to P and choked flow occurs, all of the conditions within the pipe (G = G, P2 = P, etc.) will remain the same regardless of how low the pressure outside the end of the pipe falls. The pressure drop within the pipe (which determines the flow rate) is always Pt — P when the flow is choked. 

You have to feed a gaseous reactant to a reactor at a constant rate of 1000 scfm. The gas is contained at 80°F and a pressure of 500psigin a tank that is located 20 ft from the reactor, and the pressure in the reactor fluctuates between 10 and 20 psig. You know that if the flow is choked in the feed line to the reactor, then the flow rate will be independent of the pressure in the reactor, which is what you require. If the feed line has a roughness of 0.0018 in., what should its diameter be in order to satisfy your requirements The gas has an MW of 35, an isentropic exponent of 1.25, and a viscosity of 0.01 cP at 80°F. 

Figure C-1 Steam values of isentropic exponent, k (for small changes in pressure (or volume) along an isentrope, pVk = constant).

The thrustor was considered to consist of two sections 1) where the mixture is formed and 2) where combustion takes place and the pressure is generated. The principal mechanism involved in the combustion process was assumed to be successive ignition, but other mechanisms such as turbulent frontal combustion were also considered. The analysis yielded two instability criteria, expressed in terms of the Mach number in zone 1, the velocity ratio in zones 1 and 2, the isentropic exponent in zone 2, the activation energy, the temperature of the cold gas, the pressure upstream of the combustion zone, and the pressure drop due to the combustion... 

Detonation Parameters Chapman-Jouguet Pressure, Energy, and Isentropic Exponent from Water Shock Measurements 11... 

In reality, many compressor conditions are neither purely isothermal nor isentropic, but somewhere in between. This can be taken into account by using the isentropic Equation (5.149) and replacing the isentropic exponent A by a polytropic constant y (where 1 < y < A ), which is a function of the compressor design as well as the properties of the gas. 

Zeuner s equation for the saturated region gives the isentropic exponent as ... 

This book contains tables of the properties of water and steam from 0 to 800 and from 0 to 1000 bar which have been calculated using a set of equations accepted by the members of the Sixth International Conference on the Properties of Steam in 1967. Properties which are tabulated include the pressure, specific volume, density, specific enthalpy, specific heat of evaporation, specific entropy, specific isobaric heat capacity, dynamic viscosity, thermal conductivity, the Prandtl number, the ion-product of water, the dielectric constant, the isentropic exponent, the surface tension and Laplace coefficient. Also see items [43] and [70]. 

Young s and bulk moduli in Pa, mass density in kg.m isochore compressibility in Pa , dimensionless isentropic exponents, y = C /C -... 

Type of gas molecule Molar heat capacities Isentropic exponent... 

Name (synonyms) Isobar molar heat capacity (300K) Isochor molar heat capacity (300K) Isentropic exponent (300K) Thermal conduct ivity (298K) Attraction constant Co-volume Critical pressure Critical tempera- ture Critical density Critical compress. factor Solubility water (0°C) Refractive index (589nm)... 

K = Isentropic exponent, typically 1.3 for a lean natural gas L = Mechanical leakage correction factor, % (see Fig. 25-13)... 

According to EN-ISO 4126-7, the isentropic exponent k is to be related to the entry conditions (k = ko). Since no additional information has been provided for the calculation, it is obvious to compute the isentropic exponent as well as the sizing... 

The isentropic exponent and the specific heat capacity for ideal and real gases are given in Table 15.1. 

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