Liquid compression effects

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

Derived from an analytical model for flat, infinitely thick liquid layer Effects of gas compressibility included Effects of gas/liquid ratio, liquid viscosity, and nozzle geometry not included X and Xm can be determined from the universal curves for metals in P29] for subsonic gas flow and in [330] for sonic/supersonic gas flow ... 

The number of formulae representing the effect of temperature on latent heat, and empirical formulae for latent heats, is large, and latent heat is a quantity which is peculiarly adaptable to representation by empirical formulae, some of which agree with experiment for one group of liquids and fail for others. In the following, 4 and 4/ are the total and internal ( l.VIIIL) latent heats in g.cal. per g., L =M1 and Qg the densities in g./ml. of liquid and vapour, vt, Vg the specific volumes of liquid and vapour in ml. /g., p the vapour pressure, T the abs. temp., Tb the b.p. abs., Tc the critical temperattire, pc the critical pressure, Vc the critical volume, Qc the critical density, d —TjTc r=TdT, c or Cp is the specific heat, M=mol. wt., a=coefiicient of expansion of liquid, =compressibility of liquid, k, K, ki, k2, Aq, B, m, , /q, s are constants. 

For most reservoir liquids the effect of liquid compression is more than counterbalanced by the effect of solution gas so that the viscosity decreases with pressure until the saturation pressure is reached. A fm-ther increase in pressure will cause an increase in viscosity due to compression of the liquid as is shown in Figure 75. 

One of the authors once examined apparent molar volume of physisorbed phase in nanopores and found that the molar volume would become smaller against the increase in the chemical potential in the equilibrium bulk phase up to a saturated concentration, which was able to be modeled as a compression caused by attractive potential from pore walls [5]. If such kind of jamming would be the case, the strength of pore wall potential energy must considerably affect the freezing behavior within a pore subjected to saturated vapor This condition also corresponds to a pore system immersed in pure liquid. This effect was studied in pores of the simplest geometry. 

Here, u represents a characteristic velocity of the flow and usotmd is the speed of sound in the fluid at the same temperature and pressure. It may be noted that usound for air at room temperature and atmospheric pressure is approximately 300 m/s, whereas the same quantity for liquids such as water at 20°C is approximately 1500 m/s. Thus the motion of liquids will, in practice, rarely ever be influenced by compressibility effects. For nonisothermal systems, the density will vary with the temperature, and this can be quite important because it is the source of buoyancy-driven motions, which are known as natural convection flows. Even in this case, however, it is frequently possible to neglect the variations of density in the continuity equation. We will return to this issue of how to treat the density in nonisothermal flows later in the book. 

D. Holzman, The Variation of Sonic Velocity in Two-Phase Mixtures Considering the Effect of Liquid Compressibility, Internal memorandum, Aerojet-General Corp, (1960). 

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