Volume of the vessel

Here, the spatial integral is to be carried out over the entire volume of the vessel containing the gas, and for convenience we have changed the notation slightly. Now we differentiate//with time. 

When a solid such as charcoal is exposed in a closed space to a gas or vapour at some definite pressure, the solid begins to adsorb the gas and (if the solid is suspended, for example, on a spring balance) by an increase in the weight of the solid and a decrease in the pressure of the gas. After a time the pressure becomes constant at the value p, say, and correspondingly the weight ceases to increase any further. The amount of gas thus adsorbed can be calculated from the fall in pressure by application of the gas laws if the volumes of the vessel and of the solid are known or it can be determined directly as the increase in weight of the solid in the case where the spring balance is used. 

The heatable areas of the diyer are the vessel wall and the screw. The diyer makes maximum use of the product-heated areas—the filling volume of the vessel (up to the knuckle of the dished head) is the usable product loading. The top cover of the vessel is easily heated by either a half-pipe coil or heat tracing, which ensures that no vapor condensation will occur in the process area. In addition to the conical vessel heated area, heating the screw effectively increases the heat exchange area by 15-30 percent. This is accomphshed via rotary joints at the base of the screw. The screw can be neated with the same... 

Other methods for estimating the cost of vessels and fractionators can be used, but weight is usually the best. The cost of fractionators can be correlated as a function of the volume of the vessel times the shell thickness, with an addition for the cost of trays based on their diameter (Reference 13). Fractionator costs can also be correlated based on the volume of the vessel with the operating pressure as a parameter. This requires a great deal of data and does not give as good a correlation as weight. Hall et al. (Reference 14) present curves of column diameter vs. cost. 

The mass C is assumed to be the entire liquid inventory converted to gas. Liquid propane has a specific weight of 585.3 kg/m, and the volume of the vessel was 25 m. Therefore, for the 80% filled case ... 

When the volume of the vessel is divided by the flow rate, retention time and dilution rate are defined in the following equation ... 

It is required to store I kmol of methane at 320 K and 60 MN/m2. Using the following methods, estimate the volume of the vessel which must be provided ... 

The time required to pass through the high shear zone will be proportional to the volume of the vessel divided by the flow from the turbine. This will be porportional to 1/ND. With a turbine in turbulent flow, turnover is relatively rapid and all the fluid will pass through the impeller region in a relatively short period of time. The flow regime in an anchor or helically agitated vessel can be inferred from the flow studies by Smith and Peters (], 13j. These indicated... 

First, equipment costs do not increase linearly with size, since the amount of metal used is more closely related to the area than the volume of the vessel, and also the fabrication of a larger piece of equipment usually involves the same operations as a smaller piece, but each operation does not take twice as long. Second, actual construction costs are not twice as much. The piping of a 2 in. line does not take... 

For accurate temperature monitoring when conducting a temperature-controlled program, a minimum filling volume of the vessels is crucial. In the case of IR temperature measurement from the bottom of a vessel, only a very small amount of reaction mixture (ca. 50 pL) is sufficient to obtain a precise temperature feedback in a monomode instrument (CEM Discover series). On the other hand, a rectangular mounted IR sensor, as used in Biotage instruments (see Section 3.5) requires a certain minimum filling volume (200 pL for the smallest reaction vials see Fig. 3.21). 

It was found that there was an inverse relationship between the size of the vessel and the reaction rate. In each case the time required for the reaction to go to 65 % completion was determined. It was shown that the rate of the reaction increases as the pressure increases, since the pressure is inversely related to the volume of the vessel. 

A The volume of the vessel is 0.09841 L. We substitute other values into the expression for molar mass. 

The siphon purging process starts by filling the vessel with liquid — water or any liquid compatible with the product. The purge gas is subsequently added to the vapor space of the vessel as the liquid is drained from the vessel. The volume of purge gas is equal to the volume of the vessel, and the rate of purging is equivalent to the volumetric rate of liquid discharge. 

Space time (r) is usually applied only to flow situations, and is the time required to process one reactor volume of inlet material (feed) measured at inlet conditions. That is, t is the time required for a volume of feed equal to the volume of the vessel (V) to flow through the vessel. The volume V is the volume of the vessel accessible to the fluid, t can be used as a scaling quantity for reactor performance, but the reaction conditions must be the same, point-by-point, in the scaling. 

The tanks-in-series (TIS) model for arbitrary flow through a vessel assumes that it can be represented by flow through a series of N equal-sized stirred tanks with BMF in each tank (Figure 19.11). N is the adjustable parameter of the model. Its value describes the degree of mixing in the vessel. As N increases from 1 to °°, the flow represented in the vessel varies from BMF to PF in fact, PF is virtually achieved for N > 30. The volume of the vessel modeled, V, is equal to the sum of the volumes of the N tanks ... 

Since the the volumes of freeboard and dished head are equal, the volume of the vessel equals that of the straight side. 

An improved method for determining the AIT of solids has been described, and the effect of catalytically active inorganics on the reactivity and ignition temperature of solid fuels has been studied. Sodium carbonate markedly lowers the ignition temperatures of coal and coke [7], The volume of the vessel (traditionally a 200 ml flask) used to determine AIT has a significant effect on the results. For volumes of... 

An MSMPR crystalliser operates with a steady nucleation rate of n = 1013/m4, a growth rate, Gd = 10-8 m/s and a mixed-product removal rate, based on clear liquor of 0.00017 m3/s. The volume of the vessel, again based on clear liquor, is 4 m3, the crystal density is 2660 kg/m3 and the volumetric shape factor is 0.7. Determine ... 

If the volume of the vessel is designated by V and its surface area by S, and if a heat transfer coefficient h is defined, the amount of heat evolved over the whole volume per unit time by the chemical reaction is... 

The term outgassing refers to the liberation of gases and vapors from the vralls of a vacuum chamber or other components on the inside of a vacuum system. This quantity of gas is also characterized by the product of p V, A/here V is the volume of the vessel into which the gases are liberated, and by p, or better Ap, the inaease in pressure resulting from fhe infroduction of gases into this volume. 

In the rough vacuum region, the volume of the vessel is decisive for the time involved in the pumping process. In the high and ultrahigh vacuum regions, however, the gas evolution from the walls plays a significant role. 

The backing pump must be suitably rated with regard to the volume of the vessel and the desired pump-down time. This pump-down time is arranged according to the desired process duration if the process is to be finished after 12 -15 h, the pump-down time should not last longer than 1 h. The size of the backing pump may be easily calculated according to Section 2.3.1. 

We have to make a distinction here between electric controllers (e.g. PID controllers) with a proportional valve as actuator and mechanical diaphragm controllers. In a regulation system w/ith electric controllers the coordination between controller and actuator (piezoelectric gas inlet valve, inlet valve A/ith motor drive, butterfly control valve, throttle valve) is difficult because of the very different boundary conditions (volume of the vessel, effective pumping speed at the vessel, pressure control range). Such control circuits tend to vibrate easily when process malfunctions occur. It is virtually impossible to specify generally valid standard values. 

---