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

Transcription

1 Journal of Advanced & Applied Sciences (JAAS), 2 (3): , 2014 ISSN: Academic Research Online Publisher. Research Paper The Head Loss Ratio in Water Distribution: Case Study of a 96- Unit Residential Estate John I. Sodik, Emmanuel M. Adigio b a Department of Mechanical Engineering, Rivers State University of Science and Technology, Port Harcourt, Nigeria b Department of Mechanical Engineering, Niger Delta University, Wilberforce Island, Amassoma, Nigeria *Corresponding author. Tel: address: jisodiki_partners@yahoo.com 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 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 d = pipe diameter (m) 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] h f / l x10 d q (1) where h f = frictional head loss (in m) 3 q = flow rate ( m / s) and the D Arcy-Weisbach equation expressed in terms of the head loss coefficient k of the fitting as [3]: 4 2 h p kd q (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]. l = pipe length (m) 105 P a g e

2 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. 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. As observed from Fig. 1, the longest run of pipe work from the overhead reservoir (which is the first index 106 P a g e

3 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 107 P a g e

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7 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 Type Number wc bt wb ks bs sh ur wc bt wb ks bs sh ur wc bt wb ks bs Sh ur Loading Units Per Block Block of 1-1-bedroom Bedroom Flats Block of 3-3-bedroom Bedroom Flats Semi- Detached Block 5-bedroom Duplex Unit Terrace House Block 6-Unit Terrace House Block 5-bedroom Duplex 5-bedroom Duplex Gate House 1-bedroom Estate Service Yard Multipurpose (Office, Shops and Recreational Facilities) Key wc : water closet bt : bath tub wb : wash basin ks : kitchen sink bs : belfast sink sh : shower, ur : urinal 111 P a g e

8 Pipe section no. Loading units Design flow (l/s) Pipe length (m) Table 2: Calculation of Head Loss Components Permissible Diameter (mm) Actual Frictional head loss, Fittings (other than reducers) Reducers (mm x mm) Loss through fittings, (m) elbows, 1 gate valve, tee tee elbow, 1 gate valve, tees tees 150 x tees gate valves, 2 tees elbows, 2 gate valves, tee tee 125 x gate valve, 1 tee tee tee tee gate valve, 1 tee tee 100 x tee tee 75 x elbow, 1 tee 65 x elbow, 1 tee elbows, 2 gate valves, tees elbows, 1 gate valve, 2 50 x tees tee 40 x elbows, 1 gate valve 32 x P a g e

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10 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 H L = This 7 = H / L 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 H / L 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 d 1 to downstream diameter d 2 as in Table 3 [6]. In pipe section 17, for instance, there are one elbow, one tee and one 114 P a g e

11 65mm x 50mm reducer (with d 1 /d 2 = 1.30, and a corresponding K-value of obtained by interpolation in Table 3). Applying Eqn. 2, h p for pipe section 17 = ( ) x x (1.2 x 10-3 ) 2 = 0.055m as the design flow q = 1.2 x 10-3 m 3 /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 Table 3: Values of K for Reducers, in Terms of Ratio of Upstream Diameter (d 1 ) to Downstream Diameter (d 2 ) [6] Ratio d 1 /d 2 k 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 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. 115 P a g e

12 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): [2] Sodiki JI, A representative expression for swimming pool circulator pumps selection. Nigerian Journal of Engineering Research and Development 2002; 1 (4): [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): [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): [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: [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): [8] Fluids Handling Inc, Calculating pump head [Online] Available: P a g e