Evaluation of Methodologies for Determination of Economical Pipe

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 08 Issue: 02 | Feb 2021 www.irjet.net p-ISSN: 2395-0072

Diameter of Water Pumping Mains

Gebremedhin Mulatu Gessa

Lecturer, Department of Hydraulics and Water Resources Engineering, Wolaita Sodo University, Ethiopia

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Abstract - Pipes represent a large proportion of

capital invested in water pumping system undertakings

and proper sizing of the pumping main play an

important role in the overall design of any water

supply system. Therefore, determination of pipe

diameter for pumping mains shall have to be

judiciously selected not only from the point of view of

its hydraulic performance but also from the point of

view of its installation and operation costs necessary to

ensure the required function and performance

throughout its designed lifetime. It should also be

designed to reduce pumping costs through economical

combination of pipe diameters, pumping head and

pump requirements. It is therefore, the purpose of this

paper to analyse the methodologies commonly used for

optimization and determination of economical pipe

diameter of a simple water pumping main taking Metti

Town Water Sypply system as a case study area with

the expectation that the knowledge of the

interdependence of the variables involved might

produce a better understanding of the problem and,

perhaps, lead to better designs.

Key Words: Water supply system, Water pumping main,

Optimization, Economical pipe diameter, Water pumping

head

1. INTRODUCTION

The essential design objectives for pumping mains are

assessing hydraulic capacity under various flow conditions,

facilitating best management practices in the operation of

the pumping system, and providing for the buried

infrastructure’s long-term physical resiliency. It therefore

requires the appropirate dimensioning of pipe diameter in

addition to the selection of materials that provide the highest

efficiency. The appropriate dimensioning depends on the

determination of water flow velocity, flow rate, pipe

diameter and head loss in the pumping main. Since flow rate

is a parameter determined in the project demand analysis,

three parameters remain to be defined. However, there are

only two equations available for this task, the mass and

energy conservation equations, which are functions of flow

rate and pipe diameter, meaning the dimensioning is a

hydraulically undetermined problem.

Pipe network optimization problems can be classified in

numerous ways. The two most meaningful classifications

concern whether the flow distribution is initially fixed (fixed

versus variable flow pattern), and whether the system's

energy is provided by gravity or pumping (gravity versus

pumped systems).

In gravity systems, the least costly piping system will

dissipate all excessive head thus keeping pipe size, and

hence cost, to a minimum. In pumped systems, the available

head is not fixed but can be altered by changing pump head

with the associated changes in energy and pumping

equipment costs.

2. MATERIALS AND METHODS

2.1. Methods Used for Determination of Economical

Diameter

In history, different reserchers have come to pipe

optimization models that rely on some technique from the

field of operations and researchs to find optimal solutions. In

order to apply the solution technique, however it is

necessary to simplify the field problem to make it fit the

solution technique and was impossible to incorporate

reliability considerations into design in an unarbitrary and

computationally efficient manner. These methodologies have

traditionally been guided by rule of thumb that includes

different hydraulic factors such as flow velocities, water

pressure and flow conditions for different combination of

pipe diameters.

Now a days, the economical pipe size for pumping main can

be computed using either computer aided rigorous pipe

optimization analysis or by adopting empirical formula

proposed by various scholars.

2.2. Methods Using Empirical Equations

Several authors have published formulae and nomographs

for the estimation of the economic pipe diameter, Genereaux

(1937), Peters and Timmerhaus (1968) (1991), Nolte (1978)

and Capps (1995). Dupuit (1854) proposed that the

economic pipe diameter could be expressed by:

Where: D is the economic pipe size; k is a parameter that

depends, among others, on the costs of the material,

transportation, manhour, electric power, and system

operation and maintenance; and Q is the required flow rate.

Dupuit suggested a value of 1.60 for k, based on the prices of

coal, pipes, manpower and services at that time.

Other famous formulation which is dominantly practiced in

Ethiopia for the calculation of the economic pipe diameter is

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 08 Issue: 02 | Feb 2021 www.irjet.net p-ISSN: 2395-0072

Lea’s emperical formula (Garg, S. K.). Lea’s equation is

expressed as;

Where; D is economical diameter in meters, a is coefficient

ranging from 0.97 to 1.22 and Q is the amount of water to be

pumped in cubic meter per second. This relation gives

optimum flow velocity varying between 0.8 to 1.35 meter

per second.

2.3. Rigorous Economic Analysis

In rigorous economic analysis, the total cost of pipe and

pumping are worked out at different assumed velocities and

a graph plotted between the annual cost and the size of the

pipe. This analysis requires the flow in the pipe is known

beforehand and finding the most economical combination of

pumping capacity, pumping main diameter and pumping

head to at the lowest annual cost.

For a given discharge of water to be pumped there are two

options to be considered for the economical determination

of the pipe diameter. In one hand it can be done through a

pipe of large diameter at low velocity or in the other hand

through a pipe of small diameter at high velocity. Using a

large pump will unnecessarily add to the cost of the pipe and

if the diameter of the pipe is kept low, the velocity of flow

will have to be measured, which will increase frictional loss

and will also require more power for pumping thereby

increasing the cost of pumping.

An optimum pipe diameter shall be worked out which will

provide an economical pumping of the required quantity of

water. The economical diameter therefore, is the one which

minimizes the total cost meaning, investment cost of pipes

(placement and installation costs), cost of pump and energy

cost of operation (operation and maintenance costs).

Therefore, the total cost of pumping main depends mainly on

the cost of the pipe, the pump and construction of the

pumping station, and the cost of the energy required for the

pumps to work during the entire lifespan of the system.

3. METHODOLOGY

3.1. Case Study: Definition of Project Conditions

For the evaluation of the methods discussed above, Metti

town water supply, sanitation and hyegine project pumping

system located in Gambella Regional State, Ethiopia, is

considered. The porject consists of pumping water to the

350m

service reservoir with a design discharge of 20Lit/s

from the well field. For the case study, the pipe material is

selected to be Ductile Cast Iron (DCI) pipe.

The follwing data summarized in the table below is used for

the analysis in which Q is the project flow in cubic meters

per second, L is the cummulative length of pumping main in

meters and H is static head of the systems in meters.

Table 1 Project parameters

Source

Q (Lit/sec)

L (m)

H (m)

Borehole (BH)

4863.58

183.75

The objective here is to determine what type of pipe size

should be installed for minimum total annual cost. This can

be achived either by using empirical approch or rigorous

economic method meaning, calculate the total annual cost as

a function of the summation of cost of pipe per year and cost

of pumping per year.

For the determination of dynamic head of the pumping

system, Hazen-Williams equaiton is adopted as follows;

Where C is coefficient of roughness for DCI pipe (130), g is

acceleration due to gravity (9.81m/s

) and D is the

economical diameter of pumping main(m). Minor head

losses due to valves and fittings is taken to be 5% of head

loss due to friction.

Taking the calculated duty point of pumps; Pump

discharge(Q) and total head (H

) & assumed value of overall

pump and motor efficiency η, the required pump and motor

power is calculated using the following formula:-

Where,  is specific gravity of water (9.81KN/m

), Q is the

design discharge to be pumped (m

/s), H

is the total

pumping head (m) and  is efficiency of the pump (0.65)

Assumptions

The following assumptions hold in the present approach for

the economic pipe size analysis.

 For evaluation of cost of pipe and pumping, water flow

velocity is taken to be in the range of 0.8m/s and 2m/s

 Acutal present prices of Ethiopian market is considered

for the cost of pipe, pump, installation, operation and

maintenance and energy.

 Electricity as a source of energy and its local prices are

used in this paper for the evaluation of the cost of

energy. The price of electricity is 0.5 Ethiopian Birr

(ETB) per kWh for households and 0.816ETB per kWh

for businesses which includes all components of the

electricity bill such as the cost of power, distribution and

taxes.

3.2. Economical Pipe Diameter Calculation

Based on the methods of analysis discussed in previous

paragraphs the empirical formula proposed by two scholars

and rigorous economic analysis using the annual cost of pipe

and energy as the main factors is used for evaluation of

determination of economical pipe diameter of the case

project.

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 08 Issue: 02 | Feb 2021 www.irjet.net p-ISSN: 2395-0072

Empirical Analysis

In this analysis, inserting the values of design flow directly

from the water demand analysis to the equation proposed

and claculating for both upper and lower values of the

costant is calculated. Then, market available pipe diameter

size laying in the range of calculated higher and lower sizes

is taken as to be the economical pipe diameter that will

inreturn minimizes the total annual cost of the system. The

flow velocity in the economical pipe diameter calculated

shall also be calculated for its hydraulic feasibility.

Cost Functions of Rigorous Economic Analysis

The rigorous calculations in this research cover the cost of

pipes, annual energy and maintenance. According to

Prabhata K. Swamee and Ashok K. Sharma (2008), the

above-mentioned types of costs cannot be simply added to

find the overall cost or life-cycle cost. These costs have to be

brought to the same units before they can be added. In net

present value analysis method, the current value of the

infrastructure can be calculated for the known infrastructure

associated future costs using a suitable discount rate. The

net present capital cost (P

) of a future expenditure can be

derived as

Where F is future cost, r is discount rate, and T is the

analysis period.

Pipe Cost

It is understood that various pipe sizes are commercially

availabe and the cost is calculated collecting price data of

each pipe sizes. The cost of fixtures and appurtenances are

assumed to be 10% of the cost of the pipeline. (Samra and

Essery, 2003). The cost of completed pipeline, meaning

transportation, excavation and installation cost is also

calculated taking 5% of the cost of the pipeline.

Cost of Pump and Pumping Station

Different pump models usually have similar cost since the

group and stage configurations depend on the variability of

the demand and not on the pipe features. The cost of the

pumping station is not of significance to be worked out as a

separate function and therefore, is not considered in this

paper.

Energy Cost

The cost of energy depends mainly on the variables such as

the volume of water to be pumped, the total pumping head,

the pump efficiency and also the velocity of flow adopted for

the given project. The pumping head is dependent on the

pipe size for the fact that the cost of energy decreases with

increasing pipe size due to reduced headloss and, therefore,

results in reduced pumping head and power consumption.

The annual recurring cost of energy consumed in

maintaining the flow depends on the discharge pumped and

the total pumping head H

produced by the pump. An

electrical cost could be calculated by multiplying the pump

size equation with operation hours. The calculated pumping

hour for the system is 8hrs/day or 2920hrs/yrar.

Multiplying the power by the number of pumping hours in a

year and the rate of electricity per kilowatt-hour, R

, the

annual cost of energy C

consumed in maintaining the flow

could be written as follows.

4. RESULTS AND DISCUSSION

4.1. Dupit and Lea’s Empirical Equation

For design discharge of 20Lit/s, Lea’s emirical equation gives

the economic pipe size as 137.18mmm for lower coefficient

value of 0.97 and 172.53mm for higher coefficient value of

1.22. Market available pipe size for calculated diameter sizes

in between 137.18mm and 172.53mm is 150mm. Now,

checking the velocity of flow through the pipe using

continuity equation,

Table 2: Pipe Diameters and Coresponding Flow

Velocity (m/s)

Nominal Pipe Diameter

(mm)

Velocity Through the Pipe

(m/s)

100

2.55

150

1.13

200

0.64

250

0.41

300

0.28

Figure 1: Variation of Flow Velocity with Pipe

Diameter

From the calculated result and the figure 1 above, it can

clearly seen that the velocity of flow through 150mm

diameter pipe size gives optimum value that meets the

design fow velocity and therefore, pipe size of DN150mm

can be selected to be the economical pipe diameter.

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 08 Issue: 02 | Feb 2021 www.irjet.net p-ISSN: 2395-0072

Using parameter k value as 1.60, the Dupit expression for

economical pipe diameter D=k√Q results in the pipe size of

226.26mm. Taking market avilable diameter of 200mm and

250mm and checking the velocity of flow, pipe diameter

results in 0.32 for 200mm 0.8m/s for 250mm pipe diameter.

4.2. Rigorous Economic Analysis

4.2.1. Pipe Size and Pipe Cost Relationship

It can be clearly seen from the table below that pipe cost

increases with increase in pipe diameter.

Table 3: Pipe Diameters and their Corresponding

Costs (Ethiopian Birr, ETB)

Nominal Pipe Size

(mm)

Total Pipe Cost

(ETB/Meters)

100

11,884

150

15,294

200

24,284

250

35,660

300

46,124

Figure 2: Variation of Pipe per meter Cost with Pipe

Diameter

4.2.2. Annual Energy Cost and Piipe Size

Relationship

Table 3: Pipe Diameters and Coresponding Annual

Energy Cost (ETB/year)

Nominal Pipe Diameter

(mm)

Csot of Energy

(ETB/year)

100

213,718

150

88,246

200

73,004

250

69,702

300

68,713

Figure 3: Variation of Annual Energy Cost with Pipe

Diameter

4.2.3. Total Annual Cost and Piipe Size Relationship

From the annual pipeline cost and energy cost relationships,

we have clearly seen when the larger the pipe diameter

becomes, the greater will be the capital charges. In addition,

the cost of energy goes down rapidly as the pipe size

increases resulting in pressure drop.

Figure 4: Total Annual Cost Versus Nominal Pipe

Diameter

The total cost is obtained by adding, the energy and piping

cost functions which are computed for each pipe size for the

design flow and taking derivative of the new combined

function with respect to diameter. This combination will

create the function representing the total annual cost of the

pipeline. As shown in Figure 4 above, a curve drawn results

in U-shape. The pipe diameter corresponding to this point at

the bottom of the U-shaped curve is the pipe which gives

minimum annual cost and the size at this point can be taken

as the economical pipe diameter.

Therefore, it can be seen from the graph minimum annual

total cost lays at coresponding pipe size of around 170mm.

But this pipe size is not market available and has to be

decided to be taken from either 150mm or 200mm checking

for the validity of meeting the design flow velocity criteria.

5. CONCLUSION

The aim of this study was to reach the economical pipe

diameter of the simple pumping main of Metti town water

supply, sanitation and hyegine project using empirical

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 08 Issue: 02 | Feb 2021 www.irjet.net p-ISSN: 2395-0072

equations and rigorous econmic analysis. The study shows

both methodologies resulted in slightly similar values of

economic pipe diameter.

The empirical equations preseneted by two scholars Dupit

and Lea uses flow of water and constants to reach the

economical pipe diameter checking for design flow velocity

range. In rigorous economic analysis, the relationship

between pipes and pumps creates many economic trade-offs

to consider. While a smaller pipe has lower capital costs, the

larger pump required to overcome the additional pressure

losses will cost more (both in capital and long-term

operating costs). Meanwhile, a larger pipe costs more

upfront, but enables lower operating costs as the pump does

not need to work as hard. Even with this simple example, it is

clear that there is a point where a perfectly sized pump

paired with a perfectly sized pipe can minimize system costs.

This point can be seen visually in Figure 4. Each pump-pipe

pair is informed by the essential design requirements,

placing each potential component pair on equal technical

footing.

In complex water pumping mains, the operating costs are

made up of many complex functions. Likewise, cost functions

for the fixed capital investment are very complex and also

made up of several factors. Thus, the resultant total cost

function may not be a simple curve, and it could be a

polynomial function with many local minimums and one

global optimal minimum total cost. One could understand

why this problem could be impossible to complete by hand

without using several risky assumptions.

Thus, it is essential for engineers to design the pumping

mains with precise economic specifications. The work

associated with operating a pump and the initial cost of pipe

are interrelated by the diameter of the pipe. Therefore,

designing a pipe with the appropriate diameter is crucial to

the optimization of the pumping mainline.

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