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OPTIMIZATION OF PUMPING FRESH WATER

THROUGH LONG ROUTE

Here in this case we will apply the geometric programming for optimizing the cost of

pump station and optimizing the variable design such as drop pressure and the suitablediameter and the proper length for each division along the pipe line .

There are another several variables could be optimized for this case study, but forsimplification and in the aim of showing the geometric programming technique in

optimization they are neglected.

A water pipeline tends to be extended 4!m across a desert from a water table at

AlDisseh areasouth of H."#, to Amman city through the long route using several pumps

along the 4"m.

The pipeline, as shown schematically in figure $%& conveys 0.2 m3sof water.

The first costs of pipeline are '

!"s# "$ ea%h &'m& ()0000*0.00032 +P,.2-Ds

!"s# "$ /00 m "$ &i&e( ,/0 E01 D ,.)-Ds

Where +P ( &ress're r"& i4 ea%h &i&e se%#i"4 5Pa

D ( iame#er "$ &i&e5 m

Ass'me a $ri%#i"4 $a%#"r "$ 0.02 $"r %"mmer%ial lar6e iame#er '%#ile &i&es

(se geometric programming on a constrained ob)ective function to select the number of

pumps and the pipe diameter that results in the minimum total first cost for the system.

Fi6're , S%hema#i% ia6ram "$ &'m&i46 r"'#e

Pr"%e're

,7 8e 8ill a&&l9 #he 6e"me#ri% &r"6rammi46 $"r "imi:i46 #his %ase7

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*f4designates the number of pump +and +pipe sections, the total cost is

Y= n (50000+0.00032 P 1.2+ 140 E06 D 1.5)

And '

n= 400,000/L-here is the length of each pipe section in meters .the pressure drop in each pipe

section is'

The statement of the problem is

/inimize the ob)ective function'

Y= (400,000/L) (50000+0.00032 P 1.2+ 140 E06 D 1.5)

0ub)ect to

&r";ie #ha#

L: -w1 w2 - Mw4=0

p: 1.2w2 + Mw4=0

D : 1.5w3+5 Mw4=0

w1 + w2+w3 =1

5Mw4=M

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Using Matlab s!t"a#$ sl%ing t&$ !i%$ $'atins t !in t&$ !i%$ n*n"ns

"1=0.035 "2= 0.1-23 "3= 0.6-2 M= 0.230 M"4 = 0.230

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U4i;ersi#9 "$ >"ra4

PM P7E8

9$:$t#i;