Pumping saions and waer ranspor Hydraulics: heoreical background c555 February 8, 8
Hydraulics of waer ranspor hrough pipes: conen Waer ranspor hrough pipes mahemaical descripion drinking waer ranspor > rigid pipe Sewerage ranspor > open channel flow Waer hammer Pumps and moors Nework calculaion February 8, 8
Waer flows from a high level o a lower level Free waer surface hydraulic grade line Open reservoir Open channel Open reservoir February 8, 8 3
Waer flows from a high level o a lower level Free waer surface hydraulic grade line Weir Open reservoir Open channel Open reservoir Pump Pipe Ouflow February 8, 8 4
Waer ranspor hrough pipes flow ypes Closed pressurised flow Fully filled closed pipes Waer pressure higher han amospheric Open channel flow Parly filled pipe Free waer surface Main difference: Open channel accommodaes sorage in profile February 8, 8 5
Heads in a pipe-pump sysem Saic head o compensae level differences Dynamic head: o compensae Fricion loss ΔH W Deceleraion loss ΔH S Local losses H dynamic H saic February 8, 8 6
Mahemaical descripion Coninuiy equaion: mass balance: Ingoing mass ougoing mass over a cerain period of ime d in 1 ou February 8, 8 7
Mahemaical descripion Mass balance: in *d ou * d d* d Incoming ougoing sorage Dividing by and wih limi ransiion: February 8, 8 8
Mahemaical descripion Momenum balance 1: cceleraion erm : Convecive erm 3: Graviaional/pressure erm 4: Fricion erm p g c R 1 3 4 February 8, 8 9
February 8, 8 1 Mahemaical descripion Momenum balance u * me D u u c p g u u u u u R c p g π
Drinking waer ranspor: fully filled closed pipes Two possible flow ypes: Rapid changing boundaries for pressure and/or volume flow: waer hammer Slow changing boundaries for pressure and/or flow: fricion flow Rigid column: uniform and saionary flow / prismaic pipe / waer incompressible elasiciy pipe negligible / Newon s fluid February 8, 8 11
February 8, 8 1 Rigid column: Coninuiy becomes nd consequenly u u u u
February 8, 8 13 Rigid column: momenum balance 1 wih ; ; ; R C p g u D u u c p g u u D u u c p g u u u u u π π
February 8, 8 14 Rigid column: Darcy Weissbach D L D g L p p R C p p R C d p R C p g C g L o L o 5 5 1 8 1 and inegraing over L,86 8 1 λ π λ λ
fer some mahemaical eercises Darcy Weissbach: No ime dependency ΔH H Whie-Colebrook H 1 1 k log N λ 3D L λ D u g λl,86 5 D February 8, 8 15 1,3 Re λ
Moody diagram February 8, 8 16
Local losses Energy loss due o deceleraion and release of sreamlines ΔH u ξ g D u u 1 D 1 Deceleraion area February 8, 8 17
Local losses ΔH u ξ g Deceleraion area February 8, 8 18
Source: Idel cik February 8, 8 19
Source: Idel cik February 8, 8
Pressurised ranspor Pressure H 1 ΔH H H 1 Pipe L u λ D g λl,86 5 D Pressure drop ΔH H Pump L, D, λ Demand February 8, 8 1
Sewer ranspor Three flow condiions occur: Open channel flow Fully filled closed pipe Transiion siuaion Modelling is very challenging February 8, 8
February 8, 8 3 Sewerage ranspor: open channel flow ) ( )*, ( Flow surface dependan on widh in ime and place : Momenum equaion : ) ( balance: Mass h B R c p g h
February 8, 8 4 Sewer ranspor: open channel flow Mass balance Coninuiy equaion ) ( h h B R c h g
Schemaic model sewer sysem February 8, 8 5
Schemaic model urban drainage sysem February 8, 8 6
Transiion beween open channel and fully filled Physical (and mahemaical) insabiliy Open channel flow Transiion o surcharged flow February 8, 8 7
The Preissmann slo: preserve open channel flow δ is,1 o 5% of diameer Keeps open surface Valid hrough sree level Inroduces sysemaical error February 8, 8 8
Waer hammer: fully filled flow Sudden changes in boundary condiions: Increase/decrease in velociy Pump rip Take ino accoun compressibiliy of waer and elasiciy of he pipe February 8, 8 9
Waer hammer v February 8, 8 3
Waer hammer Furher eplanaion Ivo Pohof WL Delf Hydraulics February 8, 8 31
Summary Drinking waer, normal condiions Rigid column, closed pipes: Darcy-Weissbach Time independen Sewerage waer, normal condiions Open channel flow Time dependan Transiion phase: Preissmann slo Waer hammer Time dependan Special analysis Pracical and consrucion measures February 8, 8 3
To ge some feeling of dimensions ssume a pipe Lengh 5 km Diameer 5 mm Flow 4 m 3 /h Pressure drop? February 8, 8 33
To ge some more feeling ssume wo pipes Conneced parralel Same lambda s, pressure drop, lengh Volume flow Diameers pipe 1 :D, pipe : *D Wha is he raio beween he flows hrough he pipes? February 8, 8 34
Few quesions How much will pressure drop wih doubling of flow? Wha effec has increasing roughness on pressure drop? Wha has more effec: increasing roughness or decreasing diameer? February 8, 8 35