the head loss ratio in water distribution: case study … · the fraction of head loss due to...

$: The Head Loss Ratio in Water Distribution: Case Study … · The fraction of head loss due to fittings in the first index ... terms of the head loss coefficient k of the fitting as$
Journal of Advanced & Applied Sciences (JAAS), 2 (3): 105-116, 2014 ISSN: 2289-6260

© 2014 Academic Research Online Publisher.

Research Paper

105 | P a g e

The Head Loss Ratio in Water Distribution: Case Study of a 96- Unit

Residential Estate

John I. Sodik , Emmanuel M. Adigio

b

aDepartment of Mechanical Engineering, Rivers State University of Science and Technology, Port Harcourt, Nigeria

bDepartment of Mechanical Engineering, Niger Delta University, Wilberforce Island, Amassoma, Nigeria

*Corresponding author. Tel: +2348033101488

E-mail address: [email protected]

A b s t r a c t

Keywords:

Loss through pipe fittings,

Design flow rate,

Residential estate.

The paper presents a case study of water distribution to a 96-unit residential housing

estate with a total design flow rate of 24 l/s and a first index pipe run of 705m. A

useful method of distribution pipe sizing and estimation of the frictional and fitting

loss components is presented. The fraction of head loss due to fittings in the first index

pipe run is found to be 0.392 of the total loss. This fraction falls in the region predicted

by an earlier study.

Accepted: 14 May2014 © Academic Research Online Publisher. All rights reserved.

1. Introduction

In a related paper, the fraction of the total head loss

which constitutes that through pipe fittings for the

first index pipe run was computed for a water

distribution system serving a 448-bed student hostel

building [1]. The relevant fluid mechanics equations

employed to obtain the frictional and fittings loss are,

respectively, the Hazen-Williams equation expressed

for plastic pipe material as [2]

lf

h /3

101374.1

x 85.1867.4 qd

(1)

where hf = frictional head loss (in m)

l = pipe length (m)

d = pipe diameter (m)

q = flow rate )/( 3 sm

and the D’Arcy-Weisbach equation expressed in

terms of the head loss coefficient k of the fitting as

[3]:

2408256.0 qkdph

(2)

The result of that study agreed well with an earlier

one which studied the effect of varying the available

distribution pressure on the fraction of loss due to

pipe fittings [4].

http://www.aropub.org/journals/journal-of-advanced-applied-sciences-jaas/

John I. Sodiki et al./Journal of Advanced & Applied Sciences (JAAS), 2 (3): 105-116, 2014

106 | P a g e

The present case study is one in which water is

distributed to a 96 – unit residential estate. The

frictional and fitting loss components in the first

index pipe run are calculated using the methods

employed in the case of distribution to the student

hostel building [1]. The fraction of the head loss due

to fittings is obtained and compared with typical

values obtained from earlier studies.

2. Distribution system to the residential estate

The residential estate layout is shown in Fig. 1. The

estate comprises of the following building blocks,

each on two floors: six terrace house blocks, each

housing six number of 5 - bedroom duplexes (i.e. 6 x

6 =36 housing units); two terrace house blocks, each

housing four number of 5 - bedroom duplexes (i.e. 2

x 4 = 8 housing units); fourteen semi –detached

house blocks, each housing two number of 5-

bedroom duplexes (i.e. 14 x 2 = 28 housing units);

two blocks of 1 – bedroom flats, each housing eight

flats (i.e. 2 x 8 = 16 housing units), and two blocks of

3 – bedroom flats, each housing four flats (i.e. 2 x 4 =

8 housing units). The total number of housing units

(and households) is thus 96. In addition, there are a

gate house and a service yard which also includes

recreational facilities.

In the analysis of the distribution system, the other

water draw-off equipment which are external to the

buildings and which are not in normal operation

during building use (such as the fire hydrants and

drain valves) are not considered; even though they

are shown on the system layout. However, on

conclusion of the pipe sizing exercise, pipes of

adequate sizes are usually extended to supply those

equipment.

As observed from Fig. 1, the longest run of pipe work

from the overhead reservoir (which is the first index

run) is that from point A at the reservoir through

points B, C, D, E, - - - up to point Q shown in Figs. 1

and 2 and up to point W shown in Fig. 2. Fig 2 is an

isometric sketch showing the first index pipe run

which terminates at a water heater on the upper floor

of the last semi-detached building. The water

distribution plans of this last building are shown in

Figs. 3 and 4. In Figs. 1 and 2 the pipe sections are

designated with boxes as follows: the number in the

left of the box is the pipe section number, that on the

top right is the measured pipe length (in m) while that

on the bottom right is the design flow rate through

section (in l/s) (obtained as explained in section 3

below).

3. Pipe sizing and estimation of head losses

In this study, pipe sizing and estimation of head loss

components are done following the same methods

elaborated in earlier published works [1, 4] and

illustrated here. The appliance loading units which

account for the non-simultaneous discharge from all

the installed appliances are taken as 2 for a water

closet, 10 for a bath tub, 1.5 for a wash basin, 4 for a

sink, 3 for a shower and 1 for a urinal [5].

Cumulative loading units are thus calculated for the

different building blocks in Table 1 . These are then

aggregated for each distribution pipe section as

shown in Table 2. The flow rates through different

pipe sections are obtained from the graph of flow rate

versus loading unit of Fig 5 [5]. The graph of Fig. 5

is also useful for pipe sizing in terms of standard pipe

outside diameters. However, as inside pipe diameters

need to be obtained for this study, the graph of Fig. 6

[5] is used instead.


107 | P a g e

LEGEND

1-B Block of 1 -bedroom flats

3-B Block of 3 - bedroom flats

SD Block of Semi-detached units

T4 4-units terrace housing block

T6 6-units terrace housing block

GH Gate house

ESY Estate service yard

House connection valve chamber

Gate valve

Air valve

Drain valve

Fire hydrant


108 | P a g e


109 | P a g e


110 | P a g e


111 | P a g e

Table 1: Calculation of Loading Units per Building

Block Type Flats in Block No. of Appliances Per Flat Total No. of Appliances in Block Loading Units Per Appliance Type Total

Loading

Units

Per

Block

Type Number wc bt wb ks bs sh ur wc bt wb ks bs sh ur wc bt wb ks bs Sh ur

Block of 1-

Bedroom

Flats

1-bedroom 8 3 1 3 1 - 1 - 24 8 24 8 - 8 - 48 80 36 32 - 24 - 220

Block of 3-

Bedroom

Flats

3-bedroom 4 5 3 5 1 1 1 - 20 12 20 4 4 4 - 40 120 30 16 16 12 - 234

Semi-

Detached

Block

5-bedroom

Duplex 2 6 3 6 1 1 2 - 12 6 12 2 2 4 - 24 60 18 8 8 12 - 130

4-Unit

Terrace

House

Block

5-bedroom

Duplex 4 6 1 6 1 1 4 - 24 4 24 4 4 16 - 48 40 36 16 16 48 - 204

6-Unit

Terrace

House

Block

5-bedroom

Duplex 6 6 1 6 1 1 4 - 36 6 36 6 6 24 - 72 60 54 24 24 72 - 306

Gate House 1-bedroom 1 1 - 1 - - 1 - 1 - 1 - - 1 - 2 - 1-5 - - 3 - 6.5 Estate

Service

Yard

Multi-

purpose

(Office,

Shops and

Recreational

Facilities)

1 9 - 8 1 - 8 3 9 - 8 1 - 8 3 18 - 12 4 - 24 4.5 65.5

Key

wc : water closet

bt : bath tub

wb : wash basin

ks : kitchen sink

bs : belfast sink

sh : shower , ur : urinal


112 | P a g e

Table 2: Calculation of Head Loss Components

Pipe

section

no.

Loading

units

Design flow

(l/s)

Pipe

length (m)

Permissible ⁄

Diameter

(mm)

Actual ⁄

Frictional

head loss,

Fittings

(other than reducers)

Reducers

(mm x mm)

Loss through

fittings,

(m)

1 5037.5 24.00 22.5 0.01 150 0.0060 0.135 4 elbows, 1 gate valve, 1

tee

- 0.493

2 4972.0 22.00 16.5 0.01 150 0.0055 0.091 1 tee - 0.158

3 2728.0 16.00 58.0 0.01 150 0.0035 0.203 1 elbow, 1 gate valve, 2

tees

- 0.209

4 2364.0 14.00 39.0 0.01 125 0.0075 0.293 2 tees 150 x 125 0.270

5 2000.0 12.50 38.0 0.01 125 0.0070 0.266 2 tees - 0.211

6 1650.0 9.50 38.0 0.01 125 0.0040 0.152 1 gate valves, 2 tees - 0.130

7 1300.0 8.00 112.0 0.01 125 0.0030 0.336 2 elbows, 2 gate valves,

1 tee

- 0.087

8 1170.0 7.50 33.0 0.01 100 0.0075 0.248 1 tee 125 x 100 0.098

9 1040.0 7.00 33.0 0.01 100 0.0070 0.231 1 gate valve, 1 tee - 0.091

10 910.0 6.80 33.0 0.01 100 0.0065 0.215 1 tee - 0.076

11 780.0 5.70 33.0 0.01 100 0.0045 0.149 1 tee - 0.053

12 690.0 5.00 33.0 0.01 100 0.0040 0.132 1 tee - 0.041

13 520.0 4.00 33.0 0.01 100 0.0025 0.083 1 gate valve, 1 tee - 0.030

14 390.0 3.50 33.0 0.01 75 0.0080 0.264 1 tee 100 x 75 0.068

15 260.0 2.70 33.0 0.01 75 0.0050 0.165 1 tee - 0.038

16 130.0 1.40 33.0 0.01 65 0.0035 0.116 1 tee 75 x 65 0.019

17 82.5 1.20 8.0 0.01 50 0.0095 0.076 1 elbow, 1 tee 65 x 50 0.055

18 56.5 0.84 20.0 0.01 50 0.0045 0.090 1 elbow, 1 tee - 0.026

19 37.0 0.67 41.0 0.01 50 0.0030 0.123 2 elbows, 2 gate valves,

2 tees

- 0.036

20 30.0 0.50 11.0 0.01 40 0.0085 0.094 2 elbows, 1 gate valve, 2

tees

50 x 40 0.031

21 6.0 0.22 2.0 0.01 32 0.0050 0.010 1 tee 40 x 32 0.016

22 1.5 0.10 3.0 0.01 25 0.0040 0.012 3 elbows, 1 gate valve 32 x 25 0.006

704.5 3.484 2.242

113 | P a g e


114 | P a g e

Now, elevation difference between the reservoir

outlet connection and highest sanitary appliance

(in pipe section 22 of Fig. 2) = 7m; and the

measured total length of first index run (from

Table 2) = 704.5m

permissible maximum head loss per meter run

LH =

5.704

7= 0.01

This LH / value is utilized with the sectional

flow rates to obtain pipe sizes from Fig. 6. For

instance, in pipe section 19, the flow rate is

0.67l/s and a 50mm pipe size is selected at point

A in Fig. 6. The actual LH / value on the

horizontal axis is thus 0.003; and the frictional

head loss being the product of this value and the

pipe section length of 41m is 0.123m.

The summary of the pipe sizing calculations is

given in Table 2. Having obtained the pipe sizes,

locations of reducers are indicated and other pipe

fittings (i.e. elbows, tees and valves) in the first

index run are also specified such as to achieve

system functionality.

Now, the K-values for use in Eqn. 2 are 0.75 for

elbows, 0.25 for gate valves and 2 for tees [6].

For reducers, K-values are given in terms of the

ratio of upstream diameter d1 to downstream

diameter d2 as in Table 3 [6]. In pipe section 17,

for instance, there are one elbow, one tee and one


115 | P a g e

65mm x 50mm reducer (with d1/d2 = 1.30, and a

corresponding K-value of 0.125 obtained by

interpolation in Table 3). Applying Eqn. 2,

hp for pipe section 17 = 0.08256 (0.75 + 2 +

0.125) x 0.05-4

x (1.2 x 10-3

)2 = 0.055m

as the design flow q = 1.2 x 10-3

m3/s.

From Table 2 the total frictional loss is 3.484m

while that through fittings is 2.242m. Therefore,

the fraction of the total loss which accounts for

that through fittings is 0.392.

Table 3: Values of K for Reducers, in Terms of Ratio of Upstream Diameter (d1) to Downstream Diameter (d2) [6]

Ratio d1/d2 k

1.2 0.08

1.4 0.17

1.6 0.26

1.8 0.34

2.0 0.37

2.5 0.41

3.0 0.43

4.0 0.45

5.0 0.46

4. Discussion of results

In an earlier study which modelled the variation

of the head loss component due to fittings with

length of first index run, number of buildings and

total flow rate [7], it was observed that for the

utilized maximum length of run, number of

buildings and flow rate, respectively, of 305m,

16 and 5.6l/s a loss fraction due to fittings equal

to about 0.49 occurred. That fraction being

greater than 0.392 obtained in the present case

study is expected due to the much longer index

pipe run of about 705m utilized in the present

study (with a corresponding larger numbers of

buildings and a higher flow rate) in relation to

number of installed pipe fittings. This reduction

in the loss fraction due to fittings with increased

first index run had also been predicted by Fluids

Handling Inc. [8] when they indicated that

extensive pipe runs normally increase the head

loss fraction due to pipe friction with a

corresponding reduction in the fraction due to

fittings.

5. Conclusion

The paper has presented a case study which

illustrates a useful method of pipe sizing and

estimation of head loss components in water

distribution systems. The fraction of head loss

component due to fittings obtained is expected,

following from the results of an earlier study.


116 | P a g e

References

[1] Sodiki JI, Adigio EM, The head loss ratio in

water distribution: case study of a 448-bed

student hostel. Journal of Innovative Systems

Design and Engineering. 2014; 4(5): 91-100

[2] Sodiki JI, A representative expression for

swimming pool circulator pumps selection.

Nigerian Journal of Engineering Research and

Development 2002; 1 (4): 24-35

[3] Sodiki JI, Design analysis of water supply

and distribution to a multi-storey building

utilizing a borehole source. Nigerian Journal of

Industrial and Systems Studies 2003;2 (2): 16-32

[4] Sodiki JI, The effect of system pressure on

head loss components (Part 1: water distribution

within buildings). International Journal of

Scientific and Engineering Research 2013; 4

(11): 881-903

[5] Institute of Plumbing, Plumbing services

design guide. (Section A), Essex 1977: 6-7

[6] Giles RV, Fluid mechanics and hydraulics.

1977, McGraw-Hill, New York: 252 – 253.

[7] Sodiki JI, Modeling of head loss components

in water distribution to a group of

buildings.Journal of Basic and Applied Scientific

Research 2013; 3(12): 342-351

[8] Fluids Handling Inc, Calculating pump head

2008. [Online] Available: http://www.fluidh.com

http://www.fluidh.com/

the head loss ratio in water distribution: case study … · the fraction of head loss due to...

Documents