Ben-Gurion University of the Negev Jacob Blaustein Institutes for ...

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3.5.1 Positive Cij
Given a pipeline network of a specific diameter and with a specific friction index, the
cost of transportation depends on pumping costs which are strictly related to electricity
costs. The amount of energy required to move every unit of water depends on the
specific arc of transportation in which the water is moving. The energy applied depends
on: 1) the distance between source i and destination j; 2) the difference in elevation
between source i and destination; 3) the diameter and the type of the pipe utilized, other
factors were neglected. Maintenances costs were not included in the computation.
Let us consider total required head (minor losses due to bends, valves, etc, are
neglected), ∆ H,
to be given by:
where
∆H
= ∆Z
+ ∆h
f
∆ Z = difference in elevation between a source and a destination (m);
∆hf= pressure friction losses (m)
The energy requirements at the pump used to convey the water to demand site are
given (Jensen, 1983) by:
HP=
Where:
Q∆H
2. 7η
H = pressure head, (m)
HP = the power of the pump in horsepower (1HP=0.746 kW)
Q = flow rate (m 3 /h)
η = pump efficiency ( %)
The energy loss ∆hf (m) in pipes depends on several factors, water flow, pipe’s length,
pipe's materials and shape.
The gradient of the energy loss in a pipe is usually expressed in ‰ (part per thousand)
J(‰), as:
J f
= 1000*
∆ h / L
The gradient of the head loss J(‰), due to friction is assessed by Hazen-Williams
equation (Jensen, 1983) :
1.
852
J = 1.
131*
10 ( Q/
C)
D
12 −4.
87
J = gradient of the head loss (‰);
Q = flow rate (m 3 /h);
D = internal diameter of a pipe (mm);
(11)
(12)
(13)
(14)