Volume time constant

In a process loop with a pneumatic controller and a large process time constant. Here the process time constant is dominant, and the positioner will improve the linearitv of the final control element, Some common processes with large time constants that benefit from positioner application are liquid level, temperature, large volume gas pressure, and mixing,... 

G = air flow rate, mass/time L = waste flow rate, volume/time X = concentration of pollutant in waste, massA ohime H = Henry s constant for the pollutant in water, volume/mass... 

In all the above conditions, the rotor would heatup much more rapidly than the stator due to its low thermal time constant (t), and its smaller volume compared to that of the stator, on the one hand, and high-frequency eddy current losses at high slips, due to the skin effect, on the other. True motor protection will therefore require separate protection of the rotor. Since it is not possible to monitor the rotor s temperature, its protection is provided through the stator only. Separate protection is therefore recommended through the stator against these conditions for large LT and all HT motors. 

Samant and Ng [28] compared various scale-up rules for agitated reactors. They suggested that a scale-up rule of power per unit volume and constant average residence time (where the power per unit volume and average residence time cannot be increased) is the most suited in many operations. However, this still may not improve or preserve the performance of the systems. Therefore, adequate consideration must be given to a tradeoff between performance and operating constraints. 

FIGURE 8.1 Model of a central recirculating system used for calculating the connection between contaminant concentrations, airflow rates, contaminant source strength, q, and air cleaner efficiency, rj. Cj p is the concentration in the supply (outside) air, c is the concentration in the room, c is the concentration in the returned air, (JaMot the total flow rate through the room, ic is the ratio between recirculated airflow rate and total air flow rate, T is the time constant for the room, and V is the room volume. 

In order to have effective exchange of air in important locations in a room, the age of the air in those locations should be low. The basis for comparison is the complete mixing scenario. That scenario gives the same age for any air volume selected in the room, identical to the nominal time constant for the ventilation airflow,. A steady-state scenario is assumed. See Sutcliffe for an overview of definitions related to age of air. The various air exchange efficiency indices are presented in Table 8.6. 

In the case of a temperature probe, the capacity is a heat capacity C == me, where m is the mass and c the material heat capacity, and the resistance is a thermal resistance R = l/(hA), where h is the heat transfer coefficient and A is the sensor surface area. Thus the time constant of a temperature probe is T = mc/ hA). Note that the time constant depends not only on the probe, but also on the environment in which the probe is located. According to the same principle, the time constant, for example, of the flow cell of a gas analyzer is r = Vwhere V is the volume of the cell and the sample flow rate. 

The kinetics of alkaline hydrolysis of an ester can be followed by the pH-stat method, in which the pH is held constant by adding a solution of strong alkali to the reacting ester solution. The volume of alkali added in order to keep the pH constant is recorded as a function-time. Find the volume function needed to determine the rate constant that is, given the volume-time data for this type of experiment, what plot or calculation will yield the rate constant ... 

An alternative, simpler expression can be obtained as follows. Using the chain rule, the temperature derivative of the volume for constant value of the relaxation time is expressed as... 

Thus the time constant for the process is equal to the mean residence or holdup time in the tank and has units of time, (volume/volumetric flow rate). 

The dynamic error existing between and Cr depends on the relative magnitudes of the respective time constants. For the reactor, assuming a first-order, constant volume reaction... 

K = electrical conductivity of solution Vf = flow rate volume/time of solution through ES capillary y = surface tension of solvent e = permitivity of solvent Co = permitivity of vacuum e/ o = dielectric constant of solvent... 

Robert Boyle (1627-1691) studied the effect of changing the pressure of a gas on its volume at constant temperature. He measured the volume of a given quantity of gas at a given pressure, changed its pressure, and measured the volume again. He obtained data similar to the data shown in Table 11-1. After repeating the process many times with several different gases, he concluded that... 

The tryptophane is extracted from the aqueous solution by repeatedly shaking in a separatory funnel with 25-cc. quantities of ra-butyl alcohol water is added from time to time to keep the volume approximately constant (Note n). The butyl alcohol extract is distilled under reduced pressure. After the water present has distilled over, the tryptophane precipitates in the distilling flask and may cause bumping. When all water has been removed, as is indicated by non-formation of drops on the side of the condenser, the distillation is stopped, and, after cooling, the tryptophane is filtered off and washed with a little fresh butyl alcohol. Such extractions ami distillations are con-... 

Tap density (ptap) is an extension of bulk density measurements, and the procedure used to measure the tap density again varies from lab to lab and can affect the final results. To measure tap density, a graduated cylinder is filled with powder and the weight and volume are recorded. The difference observed between procedures is the number of taps used for the measurement. In some cases, a particular number of taps is used, such as 200 [65], 500 [66], or even 1000 taps [67]. Other procedures involve tapping the cylinder for a number of times, recording the volume, and repeating the procedure until the volume remains constant [68]. This method ensures more consistent results. 

Butadiene is dimerized at 350 C in the gas phase according to second order kinetics. Data were taken at constant volume, time in minutes and total pressure in Torr, starting, with pure butadiene. 

Evaluate the various rates of change of the table at the time that the rate of reaction is ra = 0.1 lbmols/(h) (cuft) when the reaction proceeds at (a) constant volume (b) constant pressure. 

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