Fluid volume, calculation

Solid Density. SoHds can be characterized by three densities bulk, skeletal, and particle. Bulk density is a measure of the weight of an assemblage of particles divided by the volume the particles occupy. This measurement includes the voids between the particles and the voids within porous particles. The skeletal, or tme soHd density, is the density of the soHd material if it had zero porosity. Fluid-bed calculations generally use the particle... 

Explosion energy can be calculated by employing a slight variation on Eq. (6.3.26), by multiplying expansion work per unit volume by fluid volume, instead of multiplying expansion work per unit mass by fluid mass. Both propane and butane must be considered. This gives, for example, for vapor energy for the 50% fill-ratio case ... 

The total fluid volume that must be filled into a unit parenteral container is typically greater than the volume that would contain the exact labeled dose. The fill volume is dependent on the viscosity of the solution and the retention of the solution by the container and stopper. The USP provides a procedure for calculating the fill dose that is necessary to ensure the delivery of the stated dose. It also provides a table of excess volumes that are usually sufficient to permit withdrawal and administration of the labeled volume. 

In the following paragraphs a method is developed that models and predicts the temperature effects in an extruder. It is then followed by an example to demonstrate the use of the new dissipation model. This model is then extended for use as a control volume calculation method that allows the prediction of fluid temperatures as a function of the axial direction. 

The concentration (c) of a solution corresponds to the amount (D) of substance dissolved in a volume (V) thus, c = D/V. If the dose of drug (D) and its plasma concentration (c) are known, a volume of distribution (V) can be calculated from V = D/c. However, this represents an apparent volume of distribution (Vapp), because an even distribution in the body is assumed in its calculation. Homogeneous distribution will not occur if drugs are bound to cell membranes (5) or to membranes of intracellular organelles (6) or are stored within the latter (7). In these cases, Vapp can exceed the actual size of the available fluid volume. The significance of Vapp as a pharmacokinetic parameter is discussed on p. 44. 

Using this equation, the ratio of the fluid volume to the solid mass needed to achieve a desired fluid-phase equilibrium concentration (X) can be calculated. We can achieve a lower liquid-phase concentration level by using a lower Vim ratio, using, for example, a higher amount of solid. Thus, equilibrium calculations result in the maximum V/m ratio that should be used to achieve the desired equilibrium (final) concentration. But, how much time do we need to achieve our goal in a batch reactor This is a question to be answered by kinetics. 

Now we need the corresponding expression for advective transport. Note that the advective velocity along the x-axis, vx, can be interpreted as a volume flux (of water, air, or any other fluid) per unit area and time. Thus, to calculate the flux of a dissolved chemical we must multiply the fluid volume flux with the concentration of... 

This may be rearranged to permit one to calculate the radial position of a given fluid volume element at the start of an iteration given the linear and radial position of that element at the conclusion of the iteration ... 

In the Hornsey (1956) procedure, the sample was minced thoroughly, and a 10 g sample was mixed in a tall beaker (to prevent undue evaporation) with 10 ml of a solution of 40 ml acetone and 3 ml water. Total fluid volume was 50 ml, including the 7 ml water in the sample. This procedure was preferred over dilution of sample to 50 ml final volume, since calculations were simplified and correction for the volume of insoluble meat tissues was avoided. Later workers have modified the procedure, using smaller samples and less solvent. Pearson and Tauber (1984) used a 2 g sample and capped test tubes to prevent acetone evaporation, and Carpenter and Clark (1995) used 5 g samples. 

The IAD I(a,t) in a chemical reactor is specially interesting and it does not seem that sufficient attention has been paid to the possibilities offered by this function. For instance, let us consider a semi-batch reactor, and let Q(t) be the feed flowrate of an incompressible fluid. The instantaneous fluid volume is V = /q Q(tf)dtf, from which the IAD is written I(a,t) = Q(t-a)/V. I(a,t) can be used to calculate the chemical conversion in different segregation states. Consider a species of concentration C produced with the rate t. If the mixture is assumed to be well mixed at the molecular scale, one obtains the familiar mass balance equation... 

The concentration and hence the viscosity and density (of the aqueous sucrose, e.g.) at any point in the spin fluid are calculated from the concentrations and volumes in the gradient apparatus and the dimensions of the rotor. 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

Many modifications of the original Redlich/Kwohg equation that appear in the literature are intended for special-purpose applications. The SRJt equation, developed for vapor/liquid equilibrium calculations, is designed specifically to yield reasonable vapor pressures for pure fluids. Thus, there is no assurance that molar volumes calculated by the SRK equation are more accurate than values given by the original Redlich/Kwong equation. 

Answer The properties of the fluid are calculated using AQUAlibrium and are as follows density 903 kg/m3 and molar mass 41.248 kg/kmol. Use simple geometry to calculate the volume of the pipe ... 

The micropore volume within the range corresponding to the size of molecules of the applied pycnometric fluids was calculated from ... 

X 10 moles trypsin per liter fluid volume. To demonstrate the feasibility of using the Ford method to determine the active-site of our immobilized enzyme systems, trypsin CVB-PHEMA-PABS-carbamate was treated in a circulation reactor with NPGB and the titration is Illustrated in Figure 4. The amount of p-nitro-phenol produced by the burst is equal to the amount of the active immobilized trypsin which, for this particular system, turns out to be 31% of the total bound enzyme. Active-site titrations of soluble trypsin were performed according to Chase and Shaw (16), and the active molecules for free trypsin was found to be 70% of the total protein involved. Consequently, the retention of active molecules for the immobilized enzyme was calculated 45%. The specific activity is 17% (Table III) for the same system so the efficiency of the system, based on the actually available active sites, was 38%. Thus, 62% of the initially active trypsin bound has lost its activity upon binding. 

The volume of distribution is not a real volume. It is a proportionality constant, relating the total amount of drug present in the organism to its plasma concentration at the same moment. It is the fluid volume in which the total amount of drug in the body should be dissolved to give rise to the same concentration as measured in the plasma. This calculated volume does not necessarily correspond to an identifiable physiological volume, and can be much larger than the volume of total body water. It is therefore called apparent volume of distribution. 

Finally, the method used to calculate the volume of distribution may be influenced by renal insufficiency. The three most commonly used volume of distribution terms are volume of the central compartment (Ec), volume of the terminal phase (E, E jea). and volume of distribution at steady state (Eis). The central compartment volume is calculated as the intravenous bolus dose divided by the initial plasma concentration. E for many drugs approximates extracellular fluid volume and thus may be increased or decreased by shifts in this physiologic volume. Renal insufficiency, especially oliguric acute renal failure, is often accompanied by fluid overload and a resultant increased Ec due to reduced renal elimination of water and sodium. Uaiea Or E is Calculated as the total body clearance divided by the terminal elimination rate constant (k or /3). This volume term represents the proportionality constant between plasma concentrations in the terminal elimination phase and the amount of drug remaining in the body. E is affected by both distribution characteristics, as well as by the elimination rate constant. The third volume term, the steady-state volume of distribution (Ess), is calculated as (AUMC x dose)/AUC , where AUMC is the area under the first moment of the concentrationtime curve and AUC is the area under the concentration-time curve... 

---