Liquid mass density

For liquids the equations in mass units are convenient because liquid mass densities are genemlly weak functions of composition, so that the approximation ip/it = dpldz = 0 is made and i>. = 0 by Eq, (A). Equation (B) is then... 

The distance the spray extends away from the tank wall is assumed to be 1.5 m over the full height of the cascade. This is a reasonable minimum figure based on observations on water cascades. Wind girders part way down the tank can increase the width to in excess of 3 m but any broadening of the liquid cascade increases the total induced air flow and tends to reduce the maximum vapour concentration. Given the cross section of the cascade and the total liquid release rate the liquid mass density can be calculated. 

Given the liquid mass density the volume flow of entrained air can be taken from a plot such as that shown in Figure 16. The height over which air is entrained is not the full height of the tank because it typically takes several metres for primary aerodynamic break up to be complete and there is likely to be re-entrainment of contaminated air from the splash zone in the last few metres of fall. It has therefore been assumed that air is entrained over a minimum height of 6 m. For very high tanks (>15 m) this may be an underestimate leading to minor underestimates of airflow and overestimation of risk. 

For a one-component fluid, the vapour-liquid transition is characterized by density fluctuations here the order parameter, mass density p, is also conserved. The equilibrium structure factor S(k) of a one component fluid is... 

Density — the mass per unit volume of any substance, including liquids. The density of a liquid determines whether a spilled material that is insoluble in or immiscible with water will sink or float on water. Knowledge of this behavior is essential in checking whether to use water to suppress a fire involving the material. 

L = liquid mass flow, Ib/sec V = vapor mass flow, Ib/sec Pv = vapor density, Ib/ft at flowing conditions Pi = liquid density, Ib/ft... 

L liquid mass rate G - gas mass rate A.. liquid density Po - gas density... 

L = liquid mass rate, lb/sec G = vapor or gas mass rate, lb/sec Pg = gas density, Ib/ft at conditions Pl = liquid density, lb/ft at conditions A = area, ft tower cross-section area... 

L — Liquid mass rate G — Gas mass rate Pi — Liquid density Pg — Gas density... 

For an ideal gas, the total molar concentration Cj is constant at a given total pressure P and temperature T. This approximation holds quite well for real gases and vapours, except at high pressures. For a liquid however, CT may show considerable variations as the concentrations of the components change and, in practice, the total mass concentration (density p of the mixture) is much more nearly constant. Thus for a mixture of ethanol and water for example, the mass density will range from about 790 to 1000 kg/m3 whereas the molar density will range from about 17 to 56 kmol/m3. For this reason the diffusion equations are frequently written in the form of a mass flux JA (mass/area x time) and the concentration gradients in terms of mass concentrations, such as cA. 

When trying to understand and to manipulate matter and materials, chemistry does not start by looking at the natural world in all its complexity. Rather, it seeks to establish what have been termed exemplar phenomena ideal or simplified examples that are capable of investigation with the tools available at the time (Gilbert, Borrlter, Elmer, 2000). This level consists of representatiorrs of the empirical properties of solids, liquids (taken to include solutions, especially aqueous solutiorts), colloids, gases and aerosols. These properties are perceptible in chemistry laboratories and in everyday life and are therefore able to be meastrred. Examples of such properties are mass, density, concentration, pH, temperatrrre and osmotic presstrre. 

Equations (4.1) or (4.2) are a set of N simultaneous equations in iV+1 unknowns, the unknowns being the N outlet concentrations aout,bout, , and the one volumetric flow rate Qout- Note that Qom is evaluated at the conditions within the reactor. If the mass density of the fluid is constant, as is approximately true for liquid systems, then Qout=Qm- This allows Equations (4.1) to be solved for the outlet compositions. If Qout is unknown, then the component balances must be supplemented by an equation of state for the system. Perhaps surprisingly, the algebraic equations governing the steady-state performance of a CSTR are usually more difficult to solve than the sets of simultaneous, first-order ODEs encountered in Chapters 2 and 3. We start with an example that is easy but important. 

Baker (Bl) developed a flow pattern map for horizontal gas-liquid systems that is shown in Fig. 5. The coordinates are functions of gas and liquid mass flow rates, phase densities, liquid viscosity, and surface tension. Using the same coordinates, Cichy et al. (C5) have presented a modification of the flow-pattern maps of Govier and co-workers (B6, G2, G3) for vertical gas liquid systems. 

The ongoing work on sludge-blanket and draft-tube reactors requires demonstration of sufficient gas-liquid mass transfer to provide the necessary oxygen needed in high cell density reactors. 

X = (pc2)-1 in place of its isothermal counterpart, where p is the mass density of the liquid and c is the speed of sound. With this modification, the agreement between theory and experiment improves somewhat yet some fundamental difference remains unexplained. 

Two spherical particles, one of density 3000 kg/m3 and diameter 20. im, and the other of density 2000 kg/m3 and diameter 30 (im start settling from rest at the same horizontal level in a liquid of density 900 kg/m3 and of viscosity 3 mN s/m2. After what period of settling will the particles be again at the same horizontal level It may be assumed that Stokes Law is applicable, and the effect of added mass of the liquid moved with each sphere may be ignored. 

It may be assumed that the volume of the liquid phase does not change appreciably as the reaction proceeds, although, in practice there will be some departure from this assumption. If the reaction is considered complete at the stage when 1 kmol C2H2 (molecular mass = 26 kg/kmol) has been added to 1 kmol C7H8 (molecular mass = 92 kg/kmol), then per 1 kmol of toluene, the total mass in the reactor will have increased from 92 kg initially to 118 kg of product having a mass density similar to that of the original toluene. 

In this liquid phase reaction, it may be assumed that the mass density of the liquid is unaffected by the reaction, allowing the material balance for the tubular reactor to be applied on a volume basis (Section 1.7.1, Volume 3) with plug flow. 

Here, r gas is the viscosity of the gas surrounding the liquid droplet and pliquid is the mass density of the liquid. Figure 17.4 shows the steady-state velocity of a water droplet in air as a function of the droplet radius. The quadratic dependence on the droplet radius gives rise to a dramatic slow down, thus making visualization of falling microdroplets practical. 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

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