Hydraulic time constant

Equation (5.32) is a simple linear relationship between the liquid holdup on a tray, M , and the liquid flow rate leaving the tray, L . The parameter P is the hydraulic time constant, typically 3 to 6 seconds per tray. 

By introducing the hydraulic time constant, r, we have the following equality... 

In this equation Tl can be considered to be a liquid hydraulic time constant. /I is a dimensionless combination of Ti and rv . = -(tv/Tl) and describes the influence of the vapor flow on the hquid flow (dLjdv) in order to give the same hold-up. represents the... 

As expected, the hydraulic time constant is completely determined by the term from Eqn. (16.52) which describes the mass above the weir. Thus it depends largely on the liquid flow and the hold-up fraetion. The equation for Tk becomes ... 

Gravity-flow reflux, surge tank with Sutro weir, tt > 3-5 minutes. Make sure the reflux line has a sufficiendy high hydraulic resistance. Note that tt is the hydraulic time constant of the surge tank with Sutro weir ... 

The liquid hydraulic time constant ( 3) is included by using a linearized form of the Francis weir formulation, and 3 is set to 6 s. 

The model optimized based on steady-state analysis allows for a dynamic real-time simulation of the entire absorption process. Because dynamic behavior is determined mainly by process hydraulics, it is necessary to consider those elements of the column periphery that lead to larger time constants than the column itself. Therefore, major elements of the column periphery, such as distributors, stirred tanks, and pipelines, have been additionally implemented into the dynamic model. 

For this case the simple analysis of Section 16.2 must be extended to take into accoimt the lags between the column feed point and the column base. Let us suppose that there are n trays between these two points and that hydraulic lag of each tray is first order with a time constant Ttr (see Chapter 13). Typical values are in the range of 3-8 seconds. It has been shown elsewhere (Chapter 12 of reference 1) that a number of equal lags may be approximated by dead time ... 

An anaerobic digester is a no-recycle complete mix reactor. Thus, its performance is independent of organic loading but is controlled by hydraulic retention time (HRT). Based on kinetic theoiy and values of the pseudo constants for methane bac teria, a minimum HRT of 3 to 4 days is required. To provide a safety factor and compensate for load variation as indicated earlier, HRT is kept in the range 10 to 30 days. Thickening of feed sludge is used to reduce the tank volume required... 

To monitor the motors performance, a plot can be made in real time of the mechanical horsepower versus the hydraulic horsepower. The curve should be similar to the MHP curve of Figure 4-315 since, according to equation 4-233, at constant Q, the hydraulic power is proportional to AP, An example is shown in Figure 4-317 where measurements have been made at various RPM. 

The figure illustration shows occurrence of clogging by plotting data from an observation well (OW) and compare that to the production well (PW). In this case the production well shows a decreased specific capacity while the observation well shows a steady level versus time. The only explanation is then that the resistance for water to enter the production well is increasing. The increased resistance will lower the drawdown inside the well, while the groundwater table outside the well is kept constant. This will increase the hydraulic gradient (the driving force) between the well and the aquifer and hence maintain a constant flow rate. 

It is important to know from Equation 27.7 that the performance of a complete mix with recycle system does not depend on hydraulic retention time. For a specific wastewater, a biological culture, and a particular set of environmental conditions, all coefficients Ks, b, Y, and km become constant. It is apparent from Equation 27.7 that the system performance is a function of mean cell residence time. 

Here the Ac is the channel cross-section flow area, and the factor, fRe, is a numerical constant computed and tabulated for various channel geometries. The characteristic dimension has been replaced by a hydraulic diameter defined as four times the flow area divided by the channel perimeter. 

Fabricator acetyla- feed brine Hydraulic, P meation constant, A times total rejection... 

With the first experiment, conducted with chloride, you want to determine the hydraulic parameters of the column. At time t=0, the chloride concentration at the input is set to Cjn = 100 mg L 1 and then kept constant. Time series of chloride concentrations are measured at the outlet of the column. The results are given in Table 25.3. Determine the porosity and the dispersion coefficient Eiis of the column. 

The continuous-flow nonsteady state measurements can be made after the reactor has reached steady state, which usually takes at least 3 to 5 times the hydraulic retention time under constant conditions. Then an appropriate amount of the compound to be oxidized (e. g. Na2S03) is injected into the reactor. An immediate decrease in the liquid ozone concentration to c, 0 mg L-1 indicates that the concentration is correct. Enough sulfite has to be added to keep cL = 0 for at least one minute so that it is uniformly dispersed throughout the whole reactor. Thus a bit more than one mole of sodium sulfite per mole ozone dissolved is necessary. The subsequent increase in cL is recorded by a computer or a strip chart. The data are evaluated according to equation 3-24, the slope from the linear regression is - (2/,/Vj + KLa(03)). 

Steady state can be assumed to have been reached when cL and cG are constant for at least 30 minutes. As already mentioned before, the average time required for the reactors to reach steady state is approximately three to five times the hydraulic retention time. 

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