Volumetric expansion

Kea.tlte, Keatite has been prepared (65) by the crystallisation of amorphous precipitated silica ia a hydrothermal bomb from dilute alkah hydroxide or carbonate solutions at 380—585°C and 35—120 MPa (345—1180 atm). The stmcture (66) is tetragonal. There are 12 Si02 units ia the unit cell ttg = 745 pm and Cg = 8604 pm the space group is P42. Keatite has a negative volumetric expansion coefficient from 20—550°C. It is unchanged by beating at 1100°C, but is transformed completely to cristobahte ia three hours at 1620°C. 

Vorticity The relative motion between two points in a fluid can be decomposed into three components rotation, dilatation, and deformation. The rate of deformation tensor has been defined. Dilatation refers to the volumetric expansion or compression of the fluid, and vanishes for incompressible flow. Rotation is described bv a tensor (Oy = dvj/dxj — dvj/dxi. The vector of vorticity given by one-half the... 

R, = volume generation rate, ftVmin P = volumetric expansion coefficient, ftVlb-°F Q = heat input rate, Btu/min Cp = hquid heat capacity, Btu/lb-°F... 

Djj. The Grashof number Nq, = Dj pgpAto/p" were is equivalent diameter, g is acceleration due to gravity, p is coefficient of volumetric expansion, p is viscosity, p is density, and Atg is the difference between the temperature at the wall and that in the bulk fluid. Nq, must be calculated from fluid properties at the bulk temperature. 

P = coefficient of volumetric expansion Atfj = the difference between the temperature at the wall and that in the bulk fluid... 

Flame speed was observed to be nearly constant, but increased with the scale of the experiment. Because mixing with air was limited, a volumetric expansion ratio of approximately 3.5 was observed. The maximum pressure observed was found to be scale dependent (Figure 4.5). 

Because the Raj and Emmons (1975) expression for tv cannot be applied in a straightforward manner, the expression given here differs from that recommended by Raj and Emmons (1975). It should be emphasized that w, which represents the inverse of the volumetric expansion due to combustion in the plume, is highly... 

Pu/Ph designates the volumetric expansion ratio of burnt to unburnt gases... 

For simple nth-order kinetics where volumetric expansion effects may be significant, equation 8.1.8 becomes... 

If we had erred and not included the effect of volumetric expansion on reaction, we would have calculated a space time of 18.6 sec, which would have been offby 38%, and this error would propagate through the remainder of the calculations below. 

Consider the general case of a reaction accompanied by a volumetric expansion or contraction. The time necessary for a plug to travel from inlet to outlet of a tubular reactor is given by... 

Unlike the situation in the PFR, there is always a simple relationship between the mean residence time and the reactor space time for a CSTR. Since one normally associates a liquid feed stream with these reactors, volumetric expansion effects are usually negligible (SA = 0). 

Under optimum conditions at this temperature, what fraction of the inlet benzene ends up as maleic anhydride What is the yield of maleic anhydride based on the amount of benzene reacted Neglect volumetric expansion. 

Douglas and Bischoff (23) have considered the influence of volumetric expansion effects on the yields obtained with dispersion. 

Since there is a change in the number of moles on reaction, the volumetric expansion parameter d will be nonzero. Consequently,... 

The volumetric expansion parameter S may thus be taken as 0.9675. The product distribution will vary somewhat with temperature, but the stoichiometry indicated above is sufficient for preliminary design purposes. (We should also indicate that if one s primary goal is the production of ethylene, the obvious thing to do is to recycle the propylene and ethane and any unreacted propane after separation from the lighter components. In such cases the reactor feed would consist of a mixture of propane, propylene, and ethane, and the design analysis that we will present would have to be modified. For our purposes, however, the use of a mixed feed would involve significantly more computation without serving sufficient educational purpose.)... 

Au is the difference between the liquid and glassy volumetric expansion coefficients and the temperatures are in kelvin. "The WLF equation holds between I], or / f 10 K and abftut 100 K above 7A,. Above this temperature, for thermally stable polymers, Berry and Fox (28) have shown that a useful extension of the WLF equation is the addition of an Arrhenius term with a low activation energy. 

The volumetric expansion rate Qv through the relief resulting from thermal expansion is... 

The volumetric expansion rate Qv is subsequently used in an appropriate equation to determine the relief vent size. 

The cooling coil in a reactor has a surface area of 10,000 ft2. Under the most severe conditions the coils can contain water at 32°F and can be exposed to superheated steam at 400°F. Given a heat transfer coefficient of 50 Btu/hr-ft2-°F, estimate the volumetric expansion rate of the water in the cooling coils in gpm. 

Crowl and Louvar (9) have shown that the volumetric expansion (or flow) rate for a liquid contained in process equipment that undergoes thermal expansion from heat input is given by ... 

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