Hydraulics of pipelines

Hydraulics of pipelines

K 4 HYAE Hydraulics of pipelines Application of Bernoulli equation BE continuity equation CE g g p h g g p h loss head (losses): friction losses t (in distance L) local losses m t m BE - CE - S S Q Q

FRICTION LOSSES uniform flow = const, = const i E = hydraulic slope (friction slope) = slope of EL t = t (,, L, character of walls of pipeline) K 4 HYAE Hydraulics of pipelines

Equilibrium of forces in elementary olume EV p dp S p S 0 O ds dp ds 0 O S for circle pipeline : O O, S 4 S 4 4 dp ds 0 4 K 4 HYAE Hydraulics of pipelines 3

arcy-weisbach equation i Expression of 0 under turbulent flow friction coefficient: dp ds 0 4 4 8 uniform flow: (for ds = L, dp = p) f f kinetic shearstres s energy in unit 8 0 4 ff 0 8 coefficient of friction loss PL EL 0 olume = f (Re, /) p g L 0 t L Re ν p t g t L g i E L t g K 4 HYAE Hydraulics of pipelines 4

friction slope i E = a b i E b = LF < b < TF transit z. b = quadratic zone k Re k = 30 k m LP - laminar flow TP - turbulent flow K 4 HYAE Hydraulics of pipelines 5

Effect of dimensions of projections on flow in close icinity to pipeline wall laminar flow turbulent flow K 4 HYAE Hydraulics of pipelines 6

Moody diagram FRICTION FACTOR Laminar flow Poiseuille 64 Re Region of transition 3 Smooth pipes Blasius 0,364 0,5 Re,5 4 Turbulent flow Colebrook - White log - transitional zone 3,7 Re 0,5 68 3 4 5 Altshul 0, Re 5 Rough turbulent quadratic 00 0,5 Re Nikuradse zone λ Δ 3,7 log K 4 HYAE Hydraulics of pipelines 7

Notes: - tap water T = C =,4.0-6 m s - - hydraulic roughness = 0,0 mm mm tables - recommended elocity for water pipeline 0,5,5 ms - K 4 HYAE Hydraulics of pipelines 8

LOCAL LOSSES IN PIPELINES mi i g loss coefficient i TAB Total losses = friction losses + local losses t m L j λ j i j g INLET (common, cured, streamlined, suction basket, backflow ale, grid, ) = 0,5 0,05 0, 0 j K 4 HYAE Hydraulics of pipelines 9

K 4 HYAE Hydraulics of pipelines 0 CHANGE OF IRECTION (bend, knee pipe, segment knee pipe) BRANCHING, CONNECTION CHANGE OF PROFILE (sudden x continuous, enlargement x thinning) MEASURING EVICE (pipe flow meters) OUTLET 6-0 u = 0 large reseroir u = Δ,α, r f ζ s s δ, f ζ z α, Q Q, Q Q,, f ζ 3 3 3 o

CLOSURES (ales, backflow ales, taps, slide ales) ζ u f type, openning slide ale ale ball tap K 4 HYAE Hydraulics of pipelines

HYRAULIC CALCULATIONS OF PIPELINES 3 kinds of equations: - Bernoulli equation eleations and pressure relations, boundary conditions - continuity equation - equation of losses geometry and roughness of pipe, discharge calculation: Q,,, L, H, p, K 4 HYAE Hydraulics of pipelines

BE A A B B p p H g g g g CE Q equation of losses S S j Sj t m λ ζi L g K 4 HYAE Hydraulics of pipelines 3

Note: so called hydraulically long pipeline m t t α g t α g 0 EL PL K 4 HYAE Hydraulics of pipelines 4

open and large reseroirs p A = p B = 0 (oerpressures) A = B = 0 BE: H =... total head loss exit loss outlet from pipe to open space p B = 0 BR: H α g no exit loss K 4 HYAE Hydraulics of pipelines 5

0 UNERPRESSURES IN PIPELINES p a max (6 8).0 4 Pa p a g max places with high eleation s S 0- (6 8) m w. col. EL PL RL underpressures caitation always to check! siphon tube (top aboe upper reseroir leel) BE 0-: h 0 h 0 p0 ρg 0, α0 g 0 p ρg for 0, h p 0 p ρg p pa s ρg pa ρg max a, h α g s α g s max 0 0 K 4 HYAE Hydraulics of pipelines 6

PIPELINE PUMP SYSTEM escription of system: lower reseroir suction pipe SP pump Č deliery pipe VP upper reseroir (eent. outlet to open space) Types of losses: SP: s friction, suction basket, backflow ale, knee pipe, bends VP: friction, closures, knee pipe, bends Soled problems : - determination of Q, - checking of underpressure in SP - determination of input power of Č K 4 HYAE Hydraulics of pipelines 7

p A determination of Q, - basic equations (BE, CE) for open large reseroir p A p a BE: lower reseroir - Č pa H g gs p 0, 0 checking of underpressure in SP pa pč g s g A s H a pa g p a p g Č H gs S s g practically H a < (6 8) m w. col. K 4 HYAE Hydraulics of pipelines 8

determination of necessary input power geodetic gradient: total head: H d H g S V H g H gs H g pb pa B g g g A g For open large reseroirs p A p B p a, A B 0 H d H g S V H g Input power P ρgqh d η [W] efficacy: practically up to 0,9 K 4 HYAE Hydraulics of pipelines 9

PIPELINE SYSTEMS - branched - close loop - combined Closed loop V Branched net A V - distribution reseroir K 4 HYAE Hydraulics of pipelines 0

WATER HAMMER quick manipulation with closure, pump starting or failure rapid change of pressure (water hammer), in particular at long pipelines protection against water hammer: sufficiently slow manipulation with closures air chambers, surge chambers (equilibrating towers)... K 4 HYAE Hydraulics of pipelines