Hydraulics and Engineering Applications - Report Example

Hydraulics and Engineering Applications Name: Course: Instructor: Institution: Date of Submission: Introduction The report presents the possible designs that will be used in supplying Wessex drinking water to the new 2000 development houses in Poundbury. The water will be supplied using two main routes. One route is from the pumping station located at Burton, which supply water from a regional main to the service reservoir will locate at Lambert’s Hill. Consequently, water will be supplied to the houses through gravity flow to the 2000 houses. The report presents an outline of the pipes including their designs. It presents an outline of the design of the pie from the pumped trunk main from the pumping reservoir in Burton to the service reservoir in Lambert hill through the application of the gravity flow. The designs will consider the costs of the pipes in relation to the route to be used for the pipes, the material of the pipes, and the diameter of the pipes. More importantly, in regards to the trunk main, the arrangement of the pump will be considered including the pressure surge protection. Investigations of Route The water supply to the 2000 houses in Poundbury will involve two main routes. The first route is from Burton’s pumping station to a service reservoir at Lambert’s Hill. The second route involves using the gravity flow of water from the service reservoir in Lamberts Hill to Poundbury houses. First Route: Burton to Lambert Hill In Burton the water is supplied from a regional main at the pumping station (PS) while in Lambert’s Hill, the water will be delivered to the service reservoir (SR). The route involves using the Burton road, all through to the Lower Burton Farm, to the Frome Whitfield lodge to reach Dorchester, which will be about 58m. The route will follow the path all through the Marabour Land Estate to use the path from Poundbury road to Bridport Road, which is Bridport Road that is about 103m, which will then connect to the Roman Road all through to the Lamberts’ Hill service reservoir, which is 154m from the point where Bridport Road connects to the Roman Road. It is also about 3m from the Roman Road to the reservoir (Ordanance Survey MAP, 2017). Burton Road (through lower burton farm, and Frome Whitfield lodge) to Dorchester =58m Minor road near (marabour land estate) to Poundbury road to Bridport road = 103m Bridport connects to the Roman Road that leads to Lambert hill reservoir = 154m Lambert Hill road to the reservoir = 3m Another alternative would be using the Burton Road to connect through the minor road near County Hall that would lead directly to the Roman Road and directly to the Lambert’s Hill service reservoir (OSM, 2017). Burton to County hall minor road = 56m County hall to Roman road = 84m Roman Road to Lambert hill reservoir = 155m. This route will be used to supply water to the Lambert reservoir through pumping method as the water is directly pumped from the PS to the SR. The route was selected due to the level and location of the service reservoir in Lambert Hill. The route selected helps in minimizing the length of the pumps to be used thoroughly, and the water pressure will be controlled easily if the water is pumped from the PS in Burton to the SR in Lambert Hill. Based on the routes choses above, the ground elevation and slope are the main determinants of the routes selection. In the next sections, the pipe designs and materials will consider the land use, maintenance and costs among others in their selections. Pipe Design The route requires a pumped trunk main pipe. The importance of this main is that it sustains the elevation difference between the input and output point. Pumped Main of Distribution Based on the figure above, the pumped main components include a pump, and distrbution main. The source of the water is the Pumping station (reervoir) that is located in Burton, to supply water to the service reservoir in Lambert. Thus, according to the Swamee methodology, the pumping design main is given through the cost function as presented in the following equation (Swamee & Sharma, 2000). On theother hand, the head loss is given through the equation below. fi in relation to Di presents that n= 1,2,3 and so on where ƛ = zero fi = constant when differentiated from Fi in order to equate it to zero. Thus, ƛ is an outcome of krpgQ1 The pumped main distribution data On the assumption that the terminal head pressure is 5m, the cost efficiency of the pumped pipe main using the cast iron material will be given. The standard parameters used include Km = 480; m = 0.935 Roughness of the pipe height = ɛ = 0.25mm based on the pmped main data in the table above. Kr/km = 0.02 Fi = 0.01 Second Route: From Lambert Hill Service Reservoir to Poundbury Development Houses The second route involves using gravity flow to supply water to Poundbury from Lambert’s Hill. The gravity flow is used since water will be moving from a low to a higher point to meet the anticipated demand of water in the 2000 houses been developed. The best available option involves using the main roman road to Bridport road which is 155m. From Bridport road to the junction connecting it to Poundbury road, which is 84m. From the main Bridport road to the minor bridport road that leads directly to the development houses in Poundbury, which is 94m. Therefore, Roman road to major Bridport road = 155m Major Bridport road to minor bridport road junction =84m Junction to minor Bridport road leading to Poundbury = 94m Pipe Design The pipe design is the gravity distribution main. The gravity distribution main is selected since the point of input (Burton PS) is at a upper level of elevation in relation to the points of withdrawal, which is the Lambert’s Hill SR and Poundbury (DC, 2015). The design of the pipe considered that high elevation difference between Burton and Lambert stipulating the pipe diameter will be small, which is an economical choice. Thus, the elevation difference is the key to the choice of using gravitational distribution main. The gravity main is adopted through determining the cost of the gravity main including the cost of the pipe. Gravity main = Fg The gravity main is thus adopted through using the equation below. Fg = KmLDm The head loss that the gravity main would encounter is expressed as hf = ZO – ZL – H = 8fLQ2/ Π2gD5 Thus, the diameter of the gravity main to be used from Lambert Hill to Poundbury will be given through the equation below. D = {8fLQ2 / Π2 g (zo – zl – H)}1/5 Cost of the Pumping Using the equation below, both the cost and diameter of the gravity distribution main is attained. Fg = KmL {8fLQ2 / Π2 g (Zo – Zl – H} m/5 The cost of the gravity main is given through the equation; Fp = KmLDm + krpgQho Pumping head is given as ho = H + ZL – ZO + 8fLQ2 / Π2 gD5 The material to be used for the gravity main is cast iron. Thus, the standard m for the cast iron pipes is 1.62, g =9.8m/s2 while f = 0.01 LHS and RHS = 19m Thus, using these standard values, the cost and diameter of the gravity pipe main to supply water from Lambert Hill SR to Poundbury will be given. The economic practicality of the gravity supply main stipulates that the leftward side of the inequity sign in the equation below should be higher than the right hand side critical value. Thus, the gravity distribution main should be cheaper and smoother pipes. When m < 2.5, the gravitational discharge can be large. The elevation difference from Lambert Hill to Poundbury is expressed as Zo – ZL = 20m H = the terminal head = 1m On the left hand side = ZO – ZL –H = 19m Thus, on the Right hand side = 11.48m Standard Kr/Km = 0.0185 units Fg = KmL {8fLQ2 / Π2 g (Zo – Zl – H} m/5 Fg = KmL {8 (0.01) LQ2 / Π2 9.8m/s2 (19m} 1.62/5 Fg = 1717.8km 19m > L/ 9.8 (5 / 1.62 +5) 5/1.62 (8fQ2/ Π2) 1.62/ 1.62 + 5 (mKm/5pKrQ) 5 / 1.62 + 5 Fp = 2027.0Km The critical discharge is given as Qc for both the pumped and gravity distribution main. Qc = [L / g (Z0 – Zl – H) {5/ m + 5} 5/m (8f/ Π2) m / m + 5 {mKm/ 5pKr} 5/ m+ 5] m+ 5/ 5-2m Qc = [ L / 9.8 (19) (5/ 1.62 + 5) 5/1.62 (8 (0.01 / Π2) 1.62/ 1.62 + 5 (0.0185) 5/ 1.62 + 5] 1.62 + 5 / 5 – 2m Critical discharge = 0.01503m3/s The great critical discharge stipulates that the gravity distribution main from Lambert to Poundbury is economic Fg = Fp = 503.09km Fg = 1717.8km and Fp = 2027.0Km Gravity Distribution Main Data Gravity Distribution Main n = links in the distribution main including the cost function, expressed as shown below. Pipe design The design of the pipe is related to the hydraulic operating conditions and the topographic features of the geographical area, economic parameters and fluid properties. The pipe sizing parameters include the demand of the water needed including the peak flow, max and min sizes of the pipe, materials and other conditions. The systems are designed to a life span equal to the maximum life of the pipes, which will then be replaced or redesigned (Walski, et al., 2001). The design parameters of the given pumped trunk main are given below. The pipeline mains are designed to meet the demand for the anticipated development in Poundbury. The diameter of the pipeline is large, which is selected to ensure it meets the demand of water at a peak period in the developed area. Thus, the selected diameter of the pipeline as perceived in the calculations above. The head loss of the pipes designed in relation to the diameter is given below. The pumped main pipe diameter using the HR Wallingford table gives a diameter of 250mm and gradient of 0.00022. Head loss = 0.00022 * 12000 = 2.64m Velocity = Q / A = 11.642 / Π * 2502/4 = 11.642 / (3.142 * 2502/4) = 11.642 / 49093.75 = 2.37m/s which is greater to the 1.5m/s Retention time = 12000 / (2.37 * 60 * 60) = 1.40 Thus, the retention time is 1hours, 40minutes, < 12hours The diameter of the pumped trunk main was larger, though expensive in purchasing. However, when compared to the operating costs of the larger diameter including friction, it was the best option. That is; with a larger diameter, the friction the piping system experiences is low. The diameter as presented above of the pumped trunk main is dependent on the friction, the pressure as will be shown below, which also includes the velocity flow and changes that the pipe can manage (Bombardelli & Marcelo, 2003). The friction of a piping system is given by Hazen Williams and Darchy Weisbach formulae Hazen Formula: Darchy Welsbach formula = The gravity main pipe diameter using the HR Wallingford table is given below (HR Wallingford, 2017). The selected diameter of the gravity main pipe is 150m at a gradient of 0.00950 [(0.00950 – 0.00900) * 22.754 – 22.093/ 22.755 – 22.093] + 0.0090 = 0.0005 * 0.661 / 0.662 + 0.00900 = 0.0095m/m 0.0095 * gradient design =heat loss of the gravity main 0.0095 * 12000 = 114m > the needed heat loss is 25.7 The head loss for the gravity main is equal to 114m Velocity = Q / A = 22.755 / Π * 1502/4 = 22.755 / (3.142 * 1502/4) = 22.755 / 176773.75 = 0.00129m/s which is less to the 1.5m/s Retention time = 12000 / (0.00129 * 60 * 60) = 2.583 Thus, the retention time is 2hours, 58minutes, < 12hours The pressure is >35m, leading to the installation of the PRV, which increases flow when the flow of water is low. Based on the table above, the required heat loss is 15m, where both the designed pipes meet the anticipated design for efficiency in supplying the water. The diameter of the gravity main is large though expensive. The anticipated future capacity is high, which stipulates it is cost effective basing on future demands. It is justified in that the larger the diameter of the pipe, the lower the friction levels, and the higher the capacity of the piping system to handle changes in flow velocities. Costs The gravity distribution main from Lambert to Poundbury is selected as the best option since it does not include the cost of pumping water (Dandy, et al., 2008). Cast Iron material was chosen since it is cheaper compared to other materials and easy to manufacture and use in the process (Keady, 1998). The material has a key advantage in that it is resistant to corrosion, and erosion, which stipulates when used it will not lead to problems of contaminating the water it is been used to transport. More importantly, the material has low damage risk during handling and construction. The standard pipe sizes are given by the British Standard Specifications. The standard pipe size design considers the discharge flow rate, which is given through the Pump The pump is selected through the head loss and total pressure that the head on the pump can handle. The head loss is given once the size of the pipe and material to be used has been selected as the head loss pressure occurs as a resultant of the fluid friction that the pipeline handles. Thus, the total pump head pressure is given through H = hts + hf H = dynamic pressure that can be overcome using the pumping Hts = the total static head also overcome by the pumping process Hf = head loss pressure caused by pipeline fluid friction Thus, the selection of the pump is dependent on total head that needs to be overcome in relation to the discharge rate of flow required. H is also given through the equation H = 96.75 +  Q2 to find  H = 96.75 + Q2 Q2 = units of peak demand week given in Ml/day As presented in the above calculations, Critical discharge (Qc) = 0.01503m3/s Pressure surge Pressure surge is triggered by velocity changes in the flow of the water in the piping system. The velocity change is an effect of the operations of valves and pumps as well as air expulsion from the piping system used. Air expulsion changes cause significant damages mainly to the piping system, and as such must be eliminated completely, which will be done through testing the piping system, prior to the actual application in supplying water using both routes. More importantly, during the design process, the materials used for the pipe should be flexible while encompassing the required size and placement of the valves. The accepted pressure surge of the cast iron, which is the material selected for the system is 97.3 (670) psl (kPa). Compared to other materials such as PVC, the pressure surge of the ductile iron is high. However, the material can withstand long-duration stresses without incurring damages. The pressure surges of the pipes used in the project wille calculated using the ISO equation given below. P = 2s / DR – 1 Where, P = The rated pressure the pipe has S = the design basis of the hydrostatic / safety factor (safety factor for long-term rating is 2:1 while short term safety factor is 2.5: 1). D = the standard dimensions of the pipe ratios. Thus, the maximum velocity flow needed to operate the Poundbury pipes should operate at a constant pressure of 165psl. Standard long term hydrostatic design basis of Ductile Iron = 1,600 Short term hydrostatic design basis of ductile iron = 42,000 Long-term rating of the system is equal to 2 (1,600 / 2) / 25 – 1 2 (800) / 24 1600 / 24 67 psi Short term rating of the pressure for the pipe 2 (42, 000 / 2.5) / 25 – 1 2 (16,800) / 24 33,600 / 24 1,400 psi Thus, the velocity change that could create a damaging pressure surge is given through the long term pressure rating been deducted from the short term value of the pressure rating. Thus, the pipes used to supply water to Poundbury through the two routes occurs at 1,400 – 67 =1, 333 psi Thus, the pressure surge of the pipes used is high, which stipulates that the pipes can handle high velocity flow changes without damaging the piping system. Therefore, the lifecycle of the piping system is improved, which is also reflected to the cost efficiency of implementing the system. Conclusions The project involves two main pumps, where one is the pumped distribution main that supplies water from the Burton PS to the Lambert Hill SR, while a gravitational main distributes water from Lambert hill SR to Poundbury. The two pipes have been selected in relation to the topography of the land. The pumped system was chosen for the first route since the PS main according to the Wessex Water cannot supply water to the local area of Poundbury. More importantly, the supply of water is also related to the elevation of the topography. The gravity main was chosen for the second route since it is the best choice when the entry point has a greater elevation, which is the case from Lambert Hill SR compared to the Poundbury withdrawal points. Consequently, it necessitates large pipe diameters for economic cost efficiency. The critical discharge/ elevation as calculated above presents that the gravity main has an economical cost. Thus, it is the best choice for supplying water from Lambert Hill SR to Poundbury. Cast iron is the material selected for the pipes since it resists erosion and corrosion highly. More importantly, the tensile strength of the cast iron as a ductile iron is high, which stipulates it has the ability to handle high pressure surges without encountering any damage. The material is also beneficial since it does not break or damage easily through handling and construction. References Bombardelli, F. A. & Marcelo, H. G., 2003. Hydraulic design of large-diameter pipes. Journal of Hydraulic Engineering, 129(11), pp. 839-846. Dandy, G., Walker, D., Daniell, T. & Warner, R., 2008. Planning and Design of Engineering Systems. 2nd ed. Abingdon: Taylor Francis. DC, 2015. Duchy of Cornwall. Poundbury Factsheet, pp. 1-20. HR Wallingford, 2017. HR Wallingford- Table 2 k=0.015MM, 30 -300mm pdf. Table 2. Keady, G., 1998. Colebrook-White formula for pipe flows. Journal of Hydraulic Engineering, 124(1), pp. 96-97. Ordanance Survey MAP, 2017. Dorchester CWS.Pdf. OSM, 2017. Dorchester OS50, pdf. Ordanance Survey Map (OSM). Swamee, P. K. & Sharma, A. K., 2000. Gravity Flow Water Distribution System Design. Journal of Water Supply, 49 (4), pp. 169 - 179. Walski, T., Chase, D. & Savik, D., 2001. Water Distribution Modelling. Waterbury, CT: Hestad Press. Appendices A3 Plan of Alternatives Design Calculation A) Pipe Diameters and Design Head-losses from Pipe and Fittings Pumped Main The pumped main pipe diameter using the HR Wallingford table gives a diameter of 250mm and gradient of 0.00022. Head loss = 0.00022 * 12000 = 2.64m Velocity = Q / A = 11.642 / Π * 2502/4 = 11.642 / (3.142 * 2502/4) = 11.642 / 49093.75 = 2.37m/s which is greater to the 1.5m/s Retention time = 12000 / (2.37 * 60 * 60) = 1.40 Thus, the retention time is 1hours, 40minutes, < 12hours Gravity Main The selected diameter of the gravity main pipe is 150m at a gradient of 0.00950 [(0.00950 – 0.00900) * 22.754 – 22.093/ 22.755 – 22.093] + 0.0090 = 0.0005 * 0.661 / 0.662 + 0.00900 = 0.0095m/m 0.0095 * gradient design =heat loss of the gravity main 0.0095 * 12000 = 114m > the needed heat loss is 25.7 The head loss for the gravity main is equal to 114m Velocity = Q / A = 22.755 / Π * 1502/4 = 22.755 / (3.142 * 1502/4) = 22.755 / 176773.75 = 0.00129m/s which is less to the 1.5m/s Retention time = 12000 / (0.00129 * 60 * 60) = 2.583 Thus, the retention time is 2hours, 58minutes, < 12hours Spreadsheets of NPV for Pumped Main (DI) and CAPEX for Gravity Main Net present value of the Pumped main Net present value of the Gravity main Calculation for System Curve H = 96.75 +  0.01503m3/s to find  Head Calculation GPM (gallons of water per minute) Tdh (time) Design Design flow 1000 110 Original Design   0 10 No flow   1500 206 1.4 * the design 110 - 10 * (1.4*1.4) + 10 = 206 500 46 0.6 * the design 110 - 10 * (0.6 * 0.6) + 10 = 46 750 82.25 0.85 * the design 110 -10 * (0.85 * 0.85) + 10 =82.25 Pump/ System Curve for 5 no 200 * 290 * 280 250 x 200 150 x point of operation 100 x x x 50 0 0 500 750 1000 1250 1500 1750 Assumed Pump curve System curve = Reservoir/ Pipe/ Vale Analysis for Pressure Surge Replication in the Mains Read More