hydraulics of pipelines -...

Hydraulics of pipelines

K 141 HYAE Hydraulics of pipelines 1

Application of Bernoulli equation BE

continuity equation CE

Zg

v

g

ph

g

v

g

ph

22

2

222

2

111

Z – loss head (losses):

friction losses Zt (in distance L)

local losses Zm

mt ZZZ

BE 1 - 2

CE 1 - 2

221121 SvSvQQ


FRICTION LOSSES

uniform flow D = const, v = const

iE = hydraulic slope (friction slope) = slope of EL

Zt = Zt (v, D, L, character of walls of pipeline)


Equilibrium of forces in elementary volume EV

dsOSpSdpp 0

S

O

ds

dp0

for circle pipeline D: D

4

4

D

D

S

O

4

DS,DO

2

2

D

4

ds

dp 0


Darcy-Weisbach equation

2

v

D

1

D

4v

8D

4

ds

dpi

220

uniform flow: gZpL

Z

Lg

pELPL

t

t

g2

v

D

LZ

2

t

(for ds = L, dp = p)

g2

v

D

1

L

Zi

2

tE

Expression of 0 under turbulent flow

2

00

f

v2

1volumeunitinenergykinetic

sshearstresf

202

0f v

8v

8f4

coefficient of friction loss = f (Re, /D) ν

vDRe

friction coefficient:


iE = a vb friction slope

b = 1 LF

1 < b < 2 TF

transit z.

b = 2 quadratic zone

iE

vk Rek = 2320

vm vk v

LP - laminar flow

TP - turbulent flow


Effect of dimensions of projections on flow in close vicinity to

pipeline wall

turbulent flow

laminar flow


FRICTION FACTOR

Moody diagram 1 Laminar flow

Poiseuille

2 Region of transition

3 Smooth pipes

4 Turbulent flow Colebrook - White - transitional zone

2

0,25

3,71 Dlog

0,2568

0,11Re D

1 2,512log

3,71DRe

64

Re

0,25

0,3164

Re

3 4 5 Altshul

Nikuradse Δ

D

λ

200Re

5 Rough turbulent quadratic

zone

Blasius


Notes:

- tap water T = 12°C = 1,24.10-6 m2s-1

- hydraulic roughness = 0,01 mm 1 mm

- recommended velocity for water pipeline 0,5 1,5 ms-1

tables


LOCAL LOSSES IN PIPELINES

loss coefficient i

INLET (common, curved, streamlined, suction basket,

backflow valve, grid, …)

v = 0,5 0,05 0,2 2 20

TAB

Total losses = friction losses + local losses

g2

vZ

2

imi

2g

v

D

LλZ

2j

ij

jjmt ZZ


CHANGE OF DIRECTION (bend, knee pipe, segment knee pipe)

BRANCHING,

CONNECTION

CHANGE OF PROFILE (sudden x continuous,

enlargement x thinning)

MEASURING DEVICE (pipe flow meters)

OUTLET

6 -10°

u = 0 large reservoir

u= 1

D

Δα,,

D

rfζ s

s

δ,

D

Dfζ

2

1z

α,

Q

Q,

Q

Q,

D

D,

D

Dfζ

1

3

1

2

3

2

3

1o


slide valve valve

CLOSURES (valves, backflow valves, taps, slide valves)

openningtype,fζu

ball tap


HYDRAULIC CALCULATIONS OF PIPELINES

3 kinds of equations:

geometry and roughness of pipe,

discharge

- Bernoulli equation elevations and pressure relations,

boundary conditions

calculation: Q, v, D, L, H, p, Z

- continuity equation

- equation of losses


2 2A A B Bp v p v

H Zg 2g g 2g

2g

vζ

D

LλZZZ

2

imt

BE

CE jj2211 SvSvSvQ

equation of losses


EL PL

Note:

so called „hydraulically long pipeline“

02g

αvZ

2g

αv 2

t

2

ttm ZZZ Z


• open and large reservoirs

• outlet from pipe to open space

BE: H = Z

... total head loss

BR:

exit loss

no exit loss

pB = 0

pA = pB = 0 (overpressures)

vA = vB = 0

Z2g

αvH

2


UNDERPRESSURES IN PIPELINES

always to check!

|pva|max (6 8).104 Pa

(6 8) m w. col. va

max

p

g

underpressures cavitation

• places with high elevation siphon tube

(top above upper reservoir level)

BE 0-1:

10

1

101

Z

sh,

Zh

2g

αvs

ρg

p

ρg

p

pp0,v0,h

2g

αv

ρg

p

2g

αv

ρg

ph

2

1a1

a000

2

11

2

000

0

1

2RL

s

SZ0-1

EL

PL

maxva sρg

p

max

for


Description of system: lower reservoir suction pipe SP pump Č delivery pipe VP upper reservoir (event. outlet to open space)

Solved problems : - determination of Q, D - checking of underpressure in SP - determination of input power of Č

Types of losses:

SP:

Zs friction, suction basket,

backflow valve, knee pipe, bends

VP:

Zv friction, closures, knee pipe,

bends

PIPELINE – PUMP SYSTEM


g2

v

g

pp

g

p2

sČava

Sgsva ZHH

pA

BE: lower reservoir - Č

s

2

sČgS

a Zg2

v

g

pH

g

p

for open large reservoir

0v,0pp ApA aAp

practically Hva < (6 8) m w. col.

determination of Q, D - basic equations (BE, CE)

checking of underpressure in SP


geodetic gradient:

total head:

g2

v

g2

v

g

p

g

p2

A

2

BAB

VSgd ZZHH

Z gVSgd HZZHH

gvgsg HHH

For open large reservoirs

0vv,pp BA aBAp

Input power [W]

efficacy: … practically up to 0,9

dρgQHη

1P

determination of necessary input power


V

A

Branched net

Closed loop

PIPELINE SYSTEMS

- branched

- close loop

- combined

V - distribution

reservoir


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)

• ...

hydraulics of pipelines -...

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