Page 163 - Water Loss Control

Modelling W ater Losses 141

proportional to the orifice area A and the real fluid exit speed V (which varies with the
f f
square root of the static pressure h, and a discharge coefficient C ):
d
Q = C A 2 gh (10.1)
f d f
However, if the area of the orifice, and/or the coefficient of discharge C , also
d
changes with pressure, then the flow through the orifice will be more sensitive to pres-
sure than the “square root” relationship predicts. So Eq. (10.1) can be expressed as

Q = k p x (10.2)
f f
where x is the leakage exponent
p is the static pressure
k is the leakage coefficient
f
As there is no international convention for the exponent, the IWA Water Losses Task
Force uses the alphanumeric characters N1 for the exponent in Eq. (10.2); obtaining the
following expressions:
Q ≅ P N1 (10.3)
f
Q ⎛ P ⎞ N1
f 1 = ⎜ 1 ⎟ (10.4)
Q ⎝ P ⎠
f 0 0
where Q f 1 is the leak flow rate after the change in pressure
Q is the leak flow rate before the change in pressure
f 0
P is the pressure after implementing the change
1
P is the pressure before implementing the change
0
This general form of equation [Eq. (10.4)] between leak flow rate L and pressure P
has been used since 1981 in Japan, where a weighted average exponent of 1.15 is used. 4
A different relationship (the leakage index curve) was used in the United Kingdom
from 1979, but after May (1994) the fixed and variable area concept, now known as FAVAD
[Eqs. (10.3) and (10.4)], are now recommended as best practice in the United Kingdom
and by the IWA Water Losses Pressure Management Team. 5

Measuring N1 in the Field
Values of the N1 exponent can be obtained from tests in distribution system zones, by
reducing inlet pressures in several steps at night, during the period of minimum con-
sumption. Leakage rates (L , L , and L ), obtained by deducting an appropriate allowance
0 1 2
for night consumption from the inflow rates, can be compared with pressures (P , P , P )
0 1 2
measured at the average zone pressure , to obtain estimates of the N1 exponent. Analyses
of more than 150 field tests in distribution zones in various countries (Table 10.9) have
confirmed that the exponent N1 is generally between 0.5 and 1.5, but may occasionally
reach values of 2.5 or more. A limited number of tests carried out to date in North Amer-
ica have produced N1 exponents within the range 0.5 to 1.5.
Tests in systems after all the detectable losses have been repaired or put out of service,
have generally produced higher values of N1, close to 1.5, for background leakage.
Table 10.9 clearly shows that leak flow rates in distribution systems are usually
much more sensitive to pressure than the traditional N1 value of 0.5. A physical expla-
nation for this apparent paradox was proposed by May in 1994, using the FAVAD
6