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Minimum cost parameters

Minimum cost.
The minimum cost of the system obviously corresponds to the smallest possible intercepting tanks and the smallest possible pipe diameter. To determine that cost, iterative calculations are necessary because both tank size and pipe diameters are directly related to rates of flow and the characteristics of solids, but, concurrently, tank size and proportions determine the rate of flow due to the buffering action on toilet flushings and the characteristics of unretained solids.

Computations made in the Cartagena study, working with discreet particles of clay or lime (the omnipresent material in the areas under study) with specific weight of 2.65, led to a set of basic parameters for minimum cost of tanks and sewers. The particle size to which minimum cost parameters correspond is 0.02 mm.

Further verifications with prices in Cartagena and for other projects, including the pilot projects of Granada and San Zenón, proved that these parameters are still correct in spite of drastic changes in prices in Colombia throughout the years since 1982.

Unit load.
The unit load for sewer design was worked out for cylindrical tanks, which were adopted as being cheaper than rectangular tanks under the assumption that they would be prefabricated in massive production for the South-Eastern Zone and Pasacaballos.

The rate of flow of the unit load is produced by the simultaneous discharge of all the fixtures, that is, the toilet, the kitchen sink the laundry trough and the shower. Colombian faucets and shower valves discharge around 0.1 l/s each for normal inhouse service heads (8-10 m water head). For the three fixtures the compound discharge is, then, 0.3 l/s.

For the unit tank adopted for that project, (0.90 m diameter, 1.48 m length for average occupancy of 6.8 people per house) the maximum possible discharge increment was 0.028 l/s for tank water-closet flushings (17 liters) and 0.007 l/s for pour-flush toilets (4 liters). The compound rates are, therefore, 0.328 and 0.307 l/s respectively.

For rectangular tanks of equivalent capacity to the cylindrical ones, the maximum discharges are less for obvious reasons: they are wider at liquid level and produce less over-elevation of liquid level with toilet flushings.

Since there is so little variation in maximum discharge in relation to the type of toilet and tank shape, a conservative unit load of 0.328 l/s, rounded to 0.33 l/s, was then adopted as a basic parameter for ASAS design.

Simultaneity equation and design loads.
For the determination of the design load for sewers, different methods of figuring out the probability of simultaneous discharges were considered. In Angelo Gallizio's "Instalaciones Sanitarias", published in Spanish in 1964 by Editorial Cientifico-Médica from Barcelona, a system to determine water demand and drainage in large buildings was found suitable because it takes into account three parameters to reflect more precisely the buffering effect of the intercepting tanks: peak duration, interval between repetitive discharges and duration of discharge.

Gallizio's equation is:

log Ar-1 - log B = log Crn


i      = interval between repetitive discharges
t      = duration of the discharge
h     = duration of peak
A    = i/t, (i, t in minutes)
B     = h/i, (h, i in hours)
Crn     = number of possible combinations of "r" units out of a total of "n".

The equation was adapted under the following considerations. Although the influence of toilet flushings on the maximum rate of discharge from intercepting tanks is small, they determine the actual maximum value, so the interval between uses of toilets was taken as "y".

The maximum discharge value prevails only for an instant, but to be conservative the approximate time for the tanks to evacuate the volume of one flushing was adopted for "t" values. Valves for "H" and "i" were based on observations and surveys.

The curve of simultaneity for 2 hours peaks, i = 10 minutes and t = 1 minute, is shown in figure 5.1. Tables with valves of n, r, r/n and the corresponding design flows, have been prepared. They are not included for reasons of space.

Number of houses
Figure 5.1: Simultaneity curve for sewer design flows

Sensibility analysis with different values for t and i, and with H varying between 1 and 2 hours produced very close values for r/n. This means that the discharge loads computed by this method and the capacity of sewers dimensioned will normally not be exceeded. As may be seen, the curve tends to be asymptotic to 23.5% values. With t = 30 seconds, it goes closer to 23%. For values of "t" approaching one second, the curve tends to drop to 4%.

It was considered too risky to use these low simultaneities even though the maximum discharge from intercepting tanks really last seconds, so the more conservative values, as in figure 3, were adopted for ASAS projects. The monitoring of the Grananda and San Zenón pilot projects must contribute to elucidate this question. It might make ASAS even more economical.

Although sewers are usually laid above water table, infiltration flows are added to the design load with rates of 0.1 l/s/Ha for vitrified clay pipe and 0.05 l/s/Ha for plastic pipe. Storm drains are not permitted to be connected to tanks or sewers but 0.5 l/s/Ha are also added to design flows. These rates are half of the specified in Cartagena for conventional sanitary sewers. As a fact, infiltration flows can be reduced even more but the risk of abusive connections makes recommendable to include these flows.

Minimum velocity and slope.
The low content of fine particles in the effluents of intercepting tanks admits velocities as low as 20 cm/s in sewers. Nevertheless, it is not advisable to adopt a slope less than 0.1%, (equal to 1 cm fall each 10 m) because of practical installation limitations. This fall can be easily measured with enough precision with a hose level. (A hose level is a garden hose of enough length, with glass or transparent plastic tubes in both ends that is normally used in Colombia by masons and pipelayers. The hose is filled with water. The water level in both tubes is the reference to measure elevation falls).

This slope induces velocities of more than 20 cm/s for 3" and greater diameters for full flowing pipes and for unit load of 0.33 l/s. For 2" PVC pipes the minimum slope is a little less then 0.2%. Since velocities increase when pipes are not full, minimum slopes adopted were 0.2% for 2" pipes and 0.1% for larger pipes. Verifications with tractive force theory proved these parameters adequate for 0.02 mm particles.

Average number of occupiers per house.
This is the basic parameter to design the capacity for sludge and scum of the intercepting tanks. This parameter is determined dividing the population of the area by the total number of houses. Normally it should correspond to the number of occupiers of the most frequent house in terms of occupancy. It can be established with a census of population and houses or, more easily but less accurate, with a survey. Figures in Cartagena were 6.8 and in Granada and San Zenón, 5.76 and 5.78, rounded up to 5.8.

There is no logical reason to increase minimum slope. As for the particle size of 0.02 mm, it has proved adequate to produce the minimum ASAS cost in all projects. Besides, tanks to retain that size of particles are small enough. Only if experienced rates of accumulation of sludge and scum are greater than the ones deducted in the Cartagena project, tank dimensions are to be enlarged.

As may be seen, the number of free flowing fixtures have the heaviest weight in determining the unit load. For projects with different number and type of fixtures, this must be taken into account.

These basic parameters were also adopted for the Granada and San Zenon projects and the other projects designed by the consultant because general conditions were not as severe but similar to those of the Cartagena projects.

As a conclusion, it can be stated that basic parameters of ASAS makes this technology applicable for areas with any socio-economic level and that the numeric values set for the Cartagena project are applicable in places with more or less similar conditions to those in Cartagena, Granada and San Zenón.

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