## Coefficients and Default Values

Most statistical models use coefficients and default values developed from series of field testing. It is important; however, that the operator understands the nature of the coefficients and default values, how and why they were applied to the calculation so that they make any necessary changes for local conditions.

Coefficients and default values often used may include

• Typical flow rates of each category of leaks and breaks at some standard pressure (normally 70 psi or 50 m).

• Typical background leakage for mains if in good condition (per mi/hr, at some standard pressure, this can be measured in an area where all locatable leaks have just been repaired—see ICF calculations in Sec. 10.6).

• Typical background leakage for service connections if in good condition (at some standard pressure can also be measured as above—see ICF calculations in Sec. 10.6).

• Typical numbers of residents using toilets at 3 to 4 a.m. each morning (or other relevant minimum night-flow period).

• Typical toilet flush volume (toilet use is one of the largest residential individual uses and the most common use of water at night other than in areas where irrigation is being undertaken).

• Typical toilet leakage.

• FAVAD N1 values for different types of leaks and pipe materials.

• FAVAD N3 values for pressure dependant and nondependant consumption.

• ICF values for estimating background leakage volumes and separating them from reported and unreported breaks volumes.

A simple example showing the need for care when applying coefficients and defaults values is shown below:

A night flow analysis model is used to estimate the amount of leakage present in a zone. The zone consists of residential properties and no commerce or industry (infrastructure and system data).

One of the key factors in this model is to identify estimated legitimate night consumption and subtract it from the night flow. To do this the model makes some assumptions based on preprogrammed coefficients and default values. In our example, the model was built in the United Kingdom and is being applied in the United States.

The model assumes that most of the use at night in a residential zone is from toilet flushes. In our example, the toilet flush volume was 1.5 gal per flush (default value). However in the zone in which the model is being applied the toilets have not been retrofitted and the flush is really 4 gal (default value).

So the model will ask for the population in the zone and multiply this by the estimated number of people active at night. Let's say 6% (coefficient) during our analysis window of 3 to 4 a.m. in the morning.

If the population in our zone were 6000 (infrastructure and system data) then the model would assume that 6% were active at some time during that period, which would be 360 active flushes.

The model then identifies the flush volume from the default value and multiplies this by the number of active flushes. In our example this would be 360 flushes multiplied by 1.5 gal per flush, which would equal 540 gal used between 3 and 4 a.m. in the morning, which is 540 gal/hr or 9 gal/min.

However a closer estimation using the correct flush volume would be 360 flushes multiplied by 4 gal per flush, which would equal 1440 gal, used between 3 and 4 a.m. in the morning, which is 1440 gal/hr or 24 gal/min.

If the measured night flow was 50 gal/min (field data) the model would then subtract the estimated legitimate usage and identify the rest as leakage. If the coefficients and default values were incorrectly applied as shown above the model would identify the example zone as having 41 gal/min of leakage, where as really it would only have 26 gal/min of leakage.

Then there are the allowances for leaking toilets; what percent of households have leaking toilets, what is the typical leak flow rate. Leaking toilets are a significant component on night consumption in North America and many other countries.

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