Department of Hydro Sciences, Institute for Urban Water Management. Urban Water
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1 Department of Hydro Sciences, Institute for Urban Water Management Urban Water 1 Global water aspects Introduction to urban water management 3 Basics for systems description 4 Water transport 5 Matter transport 6 Introduction to water supply 7 Water extraction 8 Water purification 9 Water distribution 10 Introduction to wastewater disposal 11 Urban drainage 1 Wastewater treatment 13 Sludge treatment Peter Krebs Dresden, 010
2 Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 3 Water transport 3.1 Basics of hydromechanics 3. Pressurised flow pipe flow 3.3 Steady and uniform free-surface flow 3.4 Dynamic and non-uniform free-surface flow Urban Water Chapter 3 Water transport PK, 010 page
3 Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 3 Water transport 3.1 Basics of hydromechanics 3. Pressurised flow pipe flow 3.3 Steady and uniform free-surface flow 3.4 Dynamic and non-uniform free-surface flow Urban Water Chapter 3 Water transport PK, 010 page 3
4 Flow models 3D, turbulent Basic research Inestigation of local processes 1D, unsteady, non-uniform Numerical models in urban hydrology Historical eents Consequences of alternaties 1D, steady, uniform Easy to understand and handle Design and rough dimensioning Urban Water Chapter 3 Water transport PK, 010 page 4
5 Example of 3D flow simulation Secondary elocities by Large Eddy Simulation (LES) Urban Water Chapter 3 Water transport PK, 010 page 5
6 Steady and uniform flow (i) Steady Var 0 t Uniform 0 x A x 0 Normal flow Continuity Q 1 Q 1 A1 A Q x 0 Urban Water Chapter 3 Water transport PK, 010 page 6
7 Steady and uniform flow (ii) 1 1 A A S f SPr SP d dx 0 da dx 0 d h f d x d z d x 0,4 Unique relation between flow rate and water depth Q (m3/s) 0,3 0, 0,1 namely: no hysteresis 0 0 0,05 0,1 0,15 0, h (m) Urban Water Chapter 3 Water transport PK, 010 page 7
8 Urban Water Chapter 3 Water transport PK, 010 page 8 Reference horizon Δl S P z 1 Δh f S f g 1 g S Pr g p ρ 1 g p ρ z h f g g p z g g p z Δ ρ ρ Energy conseration (Bernoulli)
9 Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 3 Water transport 3.1 Basics of hydromechanics 3. Pressurised flow pipe flow 3.3 Steady and uniform free-surface flow 3.4 Dynamic and non-uniform free-surface flow Urban Water Chapter 3 Water transport PK, 010 page 9
10 Prandtl-Colebrook (Darcy-Weisbach) Friction slope S f λ D g 1 Friction loss h Δl Δ λ f D g Flow elocity 1 / f λ 1 ( g S D) Urban Water Chapter 3 Water transport PK, 010 page 10
11 Friction factor λ Smooth log. λ Re λ Transition 1 λ log Re λ k S D Rough 1 λ 1. 0 log k S D with Reynolds number Re D ν Urban Water Chapter 3 Water transport PK, 010 page 11
12 Friction factor λ Urban Water Chapter 3 Water transport PK, 010 page 1
13 Roughness coefficient k S Pipe material ks range (mm) new old Clay PVC Concrete Fibre cement Brickwork good condition Brickwork poor condition Rising mains Urban Water Chapter 3 Water transport PK, 010 page 13
14 Local losses Δh local k local g Fitting klocal (-) Pipe entry (sharp-edged) 0.50 Pipe entry (slightly rounded) 0.5 Pipe entry (bell-mounded) 0.05 Pipe exit (sudden) pipe bend ( elbow sharp bend) pipe bend (long) 0. Straight manhole on graity sewer (part full) < 0.1 Straight manhole on graity sewer (surcharged) 0.15 Manhole with 30 bend (surcharged) 0.5 Manhole with 60 bend (surcharged) 1.0 Urban Water Chapter 3 Water transport PK, 010 page 14
15 Manning-Strickler formulae Empirical pipe-flow formulae! Velocity 1 kst I R 3 with full pipe R A P r π r R r π D 4 R Hydraulic radius I slope k St Strickler coefficient A circular cross section P wetted perimeter D pipe diameter Urban Water Chapter 3 Water transport PK, 010 page 15
16 Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 3 Water transport 3.1 Basics of hydromechanics 3. Pressurised flow pipe flow 3.3 Steady and uniform free-surface flow 3.4 Dynamic and non-uniform free-surface flow Urban Water Chapter 3 Water transport PK, 010 page 16
17 Open channel flow Normal depth: Equilibrium between friction and fall Friction slope Slope of pipe Hydraulic radius and relation to diameter general R A P for full pipe A D π R P 4 π D D 4 Urban Water Chapter 3 Water transport PK, 010 page 17
18 Manning equation Prerequisite: Normal flow conditions Velocity 1 / 3 1/ R S Flow rate n Q 1 / 3 1/ n A R S Channel material n (m -1/3 s) Glass Cement Concrete Brickwork If k S /D to 0.01 n 0 1/ ks Ackers (1958) Urban Water Chapter 3 Water transport PK, 010 page 18
19 Partially filled pipe Empirically determined λ λ f R f 1/ 4 R Franke (1956) Velocity R f R f 5 / 8 Flow rate Q Q f A A f R R f 5 / 8 Urban Water Chapter 3 Water transport PK, 010 page 19
20 Partially filled pipe 1 0,9 0,8 0,7 A/A f 1 0,9 0,8 0,7 0,6 0,6 Q /Q f h /D 0,5 0,4 0,3 0, R /(D /4) h /D 0,5 0,4 0,3 0, / f 0,1 0, ,1 0, 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1, 1, ,1 0, 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1, R /(D /4), A/A f Q /Q f, resp. / f with λ λ R f R f 1/4 R f R f 5/8 Q Q f A A f R R f 5/8 Urban Water Chapter 3 Water transport PK, 010 page 0
21 Operational k-alue k Op k Op in mm Channel type Normalised manholes Special manholes Transport channel Main collecting channel Brickwork, field concrete No manholes, pressure mains 0.5 Mixture, assumption 1 Urban Water Chapter 3 Water transport PK, 010 page 1
22 Urban Water Chapter 3 Water transport PK, 010 page
23 Critical alues for sediment build-up (pipe half full) DN crit S crit (mm) (m/s) (%o) ,48 0,50 0,56 0,67 0,76 0,84 0,98 1,1 1,4 1,34 1,44 1,54 1,6,7,04 1,51 1,45 1,40 1,37 1,31 1,6 1,4 1,0 1,18 1,16 1,14 Critical elocity (m/s),5 1,5 1 0,5 0 3,5 1,5 1 0, Diameter D (mm) Critical Slope (%o) Urban Water Chapter 3 Water transport PK, 010 page 3
24 Sub- and super-critical flow Froude number F b g A 1/ F gh F < 1 subcritical h > h C Waes down- and upstream F > 1 supercritical h < h C Waes only downstream F 1 critical h h C minimum energy supercritical subcritical Hydraulic jump h C is independent from slope! h > h C h < h C Flat channel Steep channel Urban Water Chapter 3 Water transport PK, 010 page 4
25 Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 3 Water transport 3.1 Basics of hydromechanics 3. Pressurised flow pipe flow 3.3 Steady and uniform free-surface flow 3.4 Dynamic and non-uniform free-surface flow Urban Water Chapter 3 Water transport PK, 010 page 5
26 St. Venant equations Continuity ΔV Q(x) h(t) h(tδt) Q(xΔx) x Δx xδx ΔV Δt Mass conseration Q( x) Q( x Δx) Urban Water Chapter 3 Water transport PK, 010 page 6
27 St. Venant equations: Continuity Mass conseration in differential form V t b dx h t Q x ( ) Q( x dx) dx Q x Diided by b dx h 1 t b Q x Urban Water Chapter 3 Water transport PK, 010 page 7
28 Urban Water Chapter 3 Water transport PK, 010 page 8 dx S P dx S P dx S f S f g dx g x g S W h dx x h h dx S dx g x g dx x h h g h dx S f P St. Venant equations: Momentum equation
29 St. Venant equations: Momentum equation With flow cross section A and flow rate Q Q t x Q A h ga x ( ) ga S f S P 0 ( 1) ( ) ( 3) ( 4) (1) Acceleration in time () Conectie acceleration (3) Source term due to pressure gradient (4) Friction - Fall Numerical procedure to sole equations! Urban Water Chapter 3 Water transport PK, 010 page 9
30 Simplifications of St. Venant equations Momentum equation Continuity Q t x Q A h ga x ga S 1 b Q x h t ( S ) 0 0 f P Normal flow Kinematic wae approximation Diffusie wae approximation Dynamic wae equations (St. Venant equations) Urban Water Chapter 3 Water transport PK, 010 page 30
31 Steady non-uniform flow Gradually aried flow dh dx SP Sf SP S Q b 1 1 F ga3 f singularities: Normal depth h N S h f ( N ) P Critical depth h C F ( ) 1 h C S Urban Water Chapter 3 Water transport PK, 010 page 31
32 Dynamic wae celerity c Wae celerity c ga b 1/ Wae-front propagation elocity λ wae ± ga b 1/ Wae-front propagation downstream and upstream (if flow is subcritical) Backwater effects can be described Urban Water Chapter 3 Water transport PK, 010 page 3
33 Features of dynamic waes Flow is a function of h and h / x Acceleration and deceleration phenomena Diffusion term causes a diminution of wae peak boundary conditions are necessary Q 1 Q > Q 1 Q 3 < Q 1 h 1 h 1 h 1 Urban Water Chapter 3 Water transport PK, 010 page 33
34 Wae propagation h Urban Water Chapter 3 Water transport PK, 010 page 34
35 Velocity of flow and wae front propagation λ wae Urban Water Chapter 3 Water transport PK, 010 page 35
36 Symbols A b Bou c C A D F g h h C h N k S n P p Q Flow cross section channel width at surface Boussinesq number wae celerity Air fraction Diameter Froude number Graity constant Flow depth Critical flow depth Normal flow depth Sand roughness Manning roughness number Wetted perimeter Pressure Flow rate R Hydraulic radius Re Reynolds number S f S P S Pr S W Friction slope Slope of pipe Slope of Pressure line Slope of water table t Time Velocity x Longitudinal coordinate z Vertical coordinate Δh f Friction loss Δl Length of computation element λ Friction factor λ wae ν ρ Wae propagation elocity Kinematic iscosity Density Urban Water Chapter 3 Water transport PK, 010 page 36
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