Keywords: water distribution systems, demand variations, peaking factor, normal distribution, lognormal distribution, reliability analysis.

In the literature few studies can be found in which the variation of demand has been considered for reliability analysis purposes. Consideration of the probabilistic nature of demand should lead to more realistic assessments of the performance of water distribution systems. In the past most of the design and reliability analysis methods for water distribution systems were based on a fixed value of demand [1,2,3,4,5,6,7]. There is little information in the literature on this fixed demand value and how it can be calculated.

Some researchers have highlighted the issue of the probabilistic nature of demand and made an assumption that the demands are having a normal distribution. Mays [8] used randomly generated water consumption data to model the distribution pattern of water consumption data. Different types of distributions were used in the simulation model for examining the sensitivity of the system and the nodal reliability to the distributions. Khomsi et al. [9] used real demand data for their reliability analysis and they stated that the demand is behaving as normal distribution. However they have not given certain details such as the significance level used for the test. Therefore it can be concluded that no study has attempted to clarify the actual behavioural pattern of the water demand for real water consumption by validating of the models in a comprehensive way.

This paper attempts to solve this problem by analysing some sets of household demand data statistically. Various demand data were analysed, and it was found that possible distributions for the data are the normal and lognormal distributions. Therefore, given historical water consumption data, the mean value of demand can be calculated and multiplied by a peaking factor. For any distribution system depending on its size and whether it is urban or rural it is possible to find an appropriate peaking factor. This provides a means of determining the fixed demand value that can be used to calculate the reliability of water distribution systems using any of the techniques which use a single demand value. Modelling the demands statistically then provides a mechanism for determining the probability that any critical demand values used for assessing system performance will be exceeded. Consequently, confidence levels can be obtained for the corresponding reliability values.

1

Alperovits E and Shamir U, (1977). `Design of optimal water distribution systems', Water Resources Research, 13, (6), 885-900. doi:10.1029/WR013i006p00885

2

Fujiwara O and De Silva A U, (1990). `Algorithm for reliability based optimal design of networks', ASCE, Journal of Environmental Engineering, 116, (3), 575-587. doi:10.1061/(ASCE)0733-9372(1990)116:3(575)

3

Fujiwara O and Tung H, (1991). `Reliability improvement for water distribution networks through increasing pipe size', Water Resources Research, 29, (7), 1395-1402. doi:10.1029/91WR00882

4

Tanyimboh T T, Tabesh M and Burrows R, (2001). `Appraisal of source head methods for calculating reliability of water distribution networks', ASCE, Journal of Water Resources Planning and Management, 127, (4), in press. doi:10.1061/(ASCE)0733-9496(2001)127:4(206)

5

Tanyimboh T T, Burd R, Burrows R and Tabesh M, (1999). `Modelling and reliability analysis of water distribution systems', Water Science and Technology, 39, (4), 249-255. doi:10.1016/S0273-1223(99)00078-5

6

Tanyimboh T T and Templeman A B, (1993). `Optimum design of flexible water distribution networks', Civil Engineering Systems, 10, (3), 243-258. doi:10.1080/02630259308970126

7

Tanyimboh T T and Templeman A B, (1998). `Calculating the reliability of single source networks by the source head method', Advances in Engineering Software, 29, (7-9), 499-505. doi:10.1016/S0965-9978(98)00016-7

8

Mays L W, (1994). `Methodologies for reliability analysis of water distribution systems', Computer Modelling of Free Surface and Pressurised Flows, Chaudray M H and Mays L W (editors), Kluwer Academic Publishers, Netherland, 485-517.

9

Khomsi D, Walters G A, Thorly A R D and Ouazar D, (1996). `Reliability tester for water distribution networks', ASCE, Journal of Computing in Civil Engineering, 10, (1), 11-19. doi:10.1061/(ASCE)0887-3801(1996)10:1(10)

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