Constant specific volume

Horizontal and vertical lines are drawn through the initial condition point, as well. These lines, of course, represent the conditions of constant pressure and constant specific volume (1/p), respectively. They further break the curve into three sections. Sections I and II are further divided into sections by the tangent points (J and K) and the other letters defining particular points. 

Furthermore, in gels the elastic moduli K and p treated so far, those of the so-called skeletal frame in Biot s theory, are much smaller than the bulk moduli of fluid and polymer. Note that K accompanies no changes in the total volume of network + solvent, whereas K, p, and pfcl involve them and are much larger than K. From this fact, without changing the essential physics, we assume that the solvent and polymer have the same constant specific volume, so that... 

Section 8.2 gives the formula A/ — V AP for a change in pressure (AP) undergone by a liquid or solid with constant specific volume V. The value of V for liquid acetone may be determined as 0.0734 L/mol from the specific gravity (0.791) given in Table B.l. 

AH = TAP for solids and liquids, where V is the (presumably constant) specific volume of the solid or liquid. 

Moving on to compressible flow, it is first of all necessary to explain the physics of flow through an ideal, frictionless nozzle. Chapter S shows how the behaviour of such a nozzle may be derived from the differential form of the equation for energy conservation under a variety of constraint conditions constant specific volume, isothermal, isentropic and polytropic. The conditions for sonic flow are introduced, and the various flow formulae are compared. Chapter 6 uses the results of the previous chapter in deriving the equations for frictionally resisted, steady-state, compressible flow through a pipe under adiabatic conditions, physically the most likely case on... 

S.2.1 Steady-state flow through a nozzle with constant specific volume... 

Figure 5.2 shows the shape of the flow functions for the three main cases an expansion with constant specific volume, an isentropic expansion with n = 1.4, and an isothermal expansion. 

Hi) The flow functions for an isothermal expansion and an isentropic expansion have relatively similar values down to low pressure ratios, but the same is not true for the expansion at constant specific volume, where the flow function diverges significantly at... 

Equations (18.31), taken together with the assumption of constant specific volume (equation (18.29)), render equation (18.28) into the form... 

Tlie situation is similar, but a little more complex when the valve occurs some distance down the line. Now we need to consider the upstream and downstream sections of pipeline separately. Let us give them the labels (1) and (2), respectively. Figure 19.4 illustrates the situation. A constant specific volume will be assumed once more. 

The standard state-of-the-art steady-state process simulation is based on stream flows, which do not change with time. Therefore, flash calculations with other variables like constant specific volume or entropy are not provided. For the design of vessels and safety valves, the so-called isochoric flash is important. It uses the specific volume as the second fixed variable and determines the pressure which... 

The dielectric constants of amino acid solutions are very high. Thek ionic dipolar structures confer special vibrational spectra (Raman, k), as well as characteristic properties (specific volumes, specific heats, electrostriction) (34). 

Available data on the thermodynamic and transport properties of carbon dioxide have been reviewed and tables compiled giving specific volume, enthalpy, and entropy values for carbon dioxide at temperatures from 255 K to 1088 K and at pressures from atmospheric to 27,600 kPa (4,000 psia). Diagrams of compressibiHty factor, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, velocity of sound in carbon dioxide, viscosity, and thermal conductivity have also been prepared (5). 

For sources, units, and remarks, see Table 2-228. v = specific volume, mVkg h = specific enthalpy, kj/kg s = specific entropy, kJ/(kg-K) c = specific beat at constant pressure, kJ/(kg-K) i = viscosity, 10 Pa-s and k = tberni conductivity, VW(m-K). For specific beat ratio, see Table 2-200 for Prandtl number, see Table 2-369. 

Pi = upstream absolute pressure p2 = downstream absolute pressure R = gas constant T = absolute temperature M,, = molecular weight Di = upstream specific volume of gas Vo = downstream specific volume of gas... 

Constant Flow into Protected Equipment For the steady-state design scenario with a constant, steady flow of fluid from a pressure source that is above the maximum aUowed pressure in the protected equipment, volume is being generated within the equipment at a rate RV = F/ f. Substituting into Eq. (26-21) and noting that the specific volume of the vent stream is l/p, gives the required mass flow rate ... 

P = absolute pressure v = specific volume R = constant of proportionality T = absolute temperature... 

The heat evolution rate per unit mass, the vent capacity per unit area, physical properties (e.g.. latent heat of liquid, specific heat, and vapor/liqnid specific volumes) are constant. It allows for total vapor-liqnid disengagement of fluids that are not natural" surface active foamers. ... 

This is the state equation of an ideal gas, where p is pressure, v is specific volume, p is density, R is the gas constant, and T is absolute temperature. In an airflow there is a transfer of heat from one layer to another. This change of... 

Dehumidification only Decreased moisture content and specific volume constant dry-bulb temperature decreased wet-bulb temperature, specific enthalpy, and % saturation Not practical... 

Sensible cooling on ly Constant moisture content decreased specific volume, dry- and wet-bulb temperature, and specific enthalpy increased % saturation. When point 7 reaches the. 100% saturation line, the air )s saturated further cooling will result in moisture being removed from the air. C ooling coil and washer at dew point... 

Gases and Vapors Hydrocarbons Reference Symbols i Chemical Formula Mol. Wt. 1r> 1/7 I a Mol. Wt. Critical Conditions Boiling Point (F) 14,7 Psia Specific Volume Cu ft/lb 14.7 Psia 81 60F (Z Facior Accounted For) Latent Heat of Vaporization (Btu/lb 14.7 Psia) Specific heat Constant Pressure (Cp 60F) Specific heat Constant Volume Specific heat ratio K = Cp/Cv... 

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