Economic Aspects of Decision Making in Reliability Assessment of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 209

8.3 COMPONENTS OF MOST ECONOMIC DESIGN

The most economic alternative is usually the best compromise between the investment and
operational costs. For example, if a transportation pipe convening the flow, Q , (in m 3 /s) is to
be designed along the length, L , the head loss that will be generated during the operation is
ΔH (in mwc). The cost of energy needed to deliver the flow at required pressure will be
calculated as:

ρ
1000

gQH

p

EC = T × e

8.4

× η

where H p is the pumping head that includes the static head H st composed of the minimum
pressure p end /ρg at the pipe end, and elevation difference of the upstream and downstream end
ΔZ i.e.:

p

8.5

H = H + ∆ H ; H =

end

± ∆ Z

p st st

ρ g

Furthermore, e is the unit price (per kWh) of the energy needed to compensate the pipe head
loss, T is the time component, and η the pumping efficiency. The static head can be neglected
in the calculation of optimal pipe diameter. Hence, the annual costs of the energy wasted per
metre length of the pipe become:

9 81 × 24 × 365 × Q ∆ H e e ∆ H

EC = ≈ 24 × Q 8.6

3600

× L η η L

By using the Darcy-Weisbach equation and assuming the friction factor λ of 0.02:

2 3

e 0 02 × Q e Q − 9

EC = 24 × Q ≈ 3 × 10 8.7

5 2 5

η 12 . × D × 3600 η D

Applying liner relation between the pipe cost and diameter, the total annual costs including
investment and operation of the pipe become:

3

e Q − 9

A = a × D × a + 3 × 10 8.8

n / r

5

η D

The most economic diameter will finally be calculated from δA/δD = 0 for Equation 8.8:

3

e Q e

− 9

a × a = 5 × 3 × 10 ⇒ D = 0 05 Q

8.9

6

n / r

η D

6

η a a

n / r

The above simplified derivation considers fixed energy costs and fixed flow rate over the
entire design period. The growth of these parameters should obviously be taken into account,
if any.