Water Pumps and Pumping Systems

8/10/2019 Water Pumps and Pumping Systems

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Water Pumps andWater Pumps andPumping SystemsPumping Systems

ByBy

Dr. MohaDr. Mohammmedmed HaggagHaggag

Lecture 2Lecture 2


2/46

Applications of the Darcy-Weisbach Equ.

Type I: To Determine Head LossGiven (d, v or Q, material)

Direct application

Type II: To Determine Velocity or Flow Rate

Given (d, hf, material)

Since V or (Q) is not known, Re and f can not bedetermined directly.

Iterative application

Type III: To Determine DiameterGiven (Q, limit of hf)

Since V or (Q) is not known, Re and f can not be

determined directly.Iterative application


3/46

In addition to the continuous head loss along thepipe length due to friction, local head lossesoccur at changes in pipe section, bends, valves

and fittings.

Head loss due to

outlet, inlet, bends, elbows, valves, pipe sizechanges

Can be disregarded in long pipes

But significant for short lengths (< 50 m)

Most minor losses can not be obtainedanalytically, so they must be measured

Head Loss: Minor Losses


4/46

Equivalent Length Technique

A fictions length of pipe is estimated that will cause thesame pressure drop as any fitting or change in pipe

cross section. This length is added to the actual pipelength

Proportional to Kinetic energy technique

The loss is considered proportional to kinetic energyhead given by the following formula



5/46



6/46

Flow expansions have high losses

Kinetic energy decreases across expansion

Kinetic energy ________ and _________

energy

Examples

________________________________

____________________________________

Losses can be minimized by gradualtransitions


potential thermal

Hydraulic jump

Vena contracta


7/46

Apply in direction of flow

Neglect surface shear

Divide by (A2)

Head Loss due to Sudden Expansion:

Conservation of Momentum

Pressure is applied over all ofsection 1.

Momentum is transferred overarea corresponding toupstream pipe diameter.V1 is velocity upstream.

sspp FFFWMM +++=+21

21

1 2

xx ppxx FF

2121 +=+

1

2

11 AVM x = 22

22 AVM x =

22212

2

21

2

1 ApApAVAV =+

g

AVV

pp 2

12

1

2

2

21

=

AA11AA22

xx


8/46

Head Loss due to Sudden Expansion:

Conservation of Energy

1 2

l

tp

hg

Vzpg

Vzp +++=++22

2

22

2

2

2

11

1

1

lhg

VVpp

+

=

2

2

1

2

221

g

VVpph l

2

2

2

2

121 +

=

z1 = z2

What isp1

- p2

?


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Energy

Head Loss due to

Sudden Expansion

g

VVpph

l 2

2

2

2

121 +

=

g

AVV

pp 2

12

1

2

2

21

=

1

2

2

1

V

V

A

A

=

g

VV

g

V

VVV

h l 2

2

2

2

11

22

1

2

2

+

= g

VVVV

h l 2

2 21212

2 +

=

( )

g

VVh

l 2

2

21=

2

2

1

2

1 12

=

A

A

g

Vh l

2

2

11

=

A

AK

Momentum

Mass


10/46

Contraction

V1 V2

EGL

HGL

vena contracta

g

VKh

cc2

22=

losses are reduced with a gradual contraction

Expansion!!!


11/46

Entrance Losses

Losses can bereduced byaccelerating the

flow gradually andeliminating thevena contracta

Ke 0.5

Ke 1.0

Ke 0.04

he=Ke V

2

2g

reentrant


12/46

Head Loss in Valves

Function of valve typeand valve position

The complex flow paththrough valves oftenresults in high head loss

What is the maximumvalue that K

vcan have?

_____

hv=KvV2

2g

How can K be greater than 1?


13/46

Minor/Local Losses


14/46

Questions

What is the headloss when a pipeenters a

reservoir?

Draw the EGL

and HGL

V

gV2

2

EGLHGL

2

2

1

1

= A

A

K


15/46

Can the Darcy-Weisbach equation andMoody Diagram be used for fluids otherthan water? _____

Does a perfectly smooth pipe have head loss?

_____

Is it possible to decrease the head loss in a

pipe by installing a smooth liner? ______

Questions

Yes

Yes

Yes


16/46

D=40 cmL=1000 m

D=20 cmL=500 m

valve100 m

Find the discharge, Q.What additional information do you need?Apply energy equationHow could you get a quick estimate? _________________Or spreadsheet solution: find head loss as function of Q.

lh

g

Vz

p

g

Vz

p+++=++

22

2

22

2

2

2

11

1

1

cs1

cs2

2

21 0 02

l

Vm h

g= +


17/46

Quiz

In the rough pipe law region if the flow rate is

doubled (be as specific as possible)What happens to the major head loss?

What happens to the minor head loss?

Why do contractions have energy loss?


18/46

Can you draw TEL and HGL?

hi

hfhe

V2/2g

Hs

Hs=hi+hf+he


19/46

Hs=hi+hf+he

Thus

Static

head

Inlet head

loss

Friction head

loss

Exit head

loss

LossesHs =


20/46

71

Hs=hi+hf+he

Can you get the required d to passa given flow in the system?

g

v

Keg

v

d

Lf

g

v

KiHs 22

.

2

222

++=

g

v

d

LfKHs

n

i 2)

.(

2

1

+= =


21/46

72

Q

d

))4/.(2

).

(22

2

1

mindg

Q

d

lfkH

n

i

ors

+= =

g

v

d

LfKHs

n

i 2

).

(2

1

+= =

Q(eq. 2)fRnV=Q/AAd

Required d

Can you get the required d to

pass a given flow in the system?


22/46

73

What if

d > available pipe

diameters

in the market


23/46

74

In this case,

One could think of usinga pump


24/46

75


Hp=Hs+hi+hfs+hfd+he

HpHs


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76

Can you get now Hp?

Hp=Hs+hi+hfs+hfd+he

g

v

d

Lf

d

LfKHH

d

dd

s

ssn

i

sp2

)..

(2

1

+++= =


26/46

77


HpHs


27/46

TEL Concept

For the shown Transmission Line Profile, Draw the TELand HGL

For the shown Transmission Line Profile, Draw the TELand HGL

What if we used amore powerful

pump?

Note also that:2- TEL Slope becomes steeper

as:

Q gets Bigger;D gets Smaller;

Pipe gets Rougher.

Note also that:2- TEL Slope becomes steeper

as:

Q gets Bigger;D gets Smaller;

Pipe gets Rougher.


28/46

Answer the Following

Identify the flow direction for the given pipe:

PA =62 psi

PA =48 psi

ZA = 100 m

ZB = 112 m


29/46

Q

Answer the Following

For the given TEL of the

shown transmission line:


30/46

81

Determination of Pumping Head

Calculation of Hp,A numerical Example


31/46

a) Calculate the required pumping head

b) Electric motor power (t =0.78)c) Monthly and annual cost of workingelectrical power if:

- Daily working hours = 12 hrs

- Cost of 1kw-hour=0.18 L.E.82

Calculation of Hreq & Electric Power

Example

(11.40)

(20.50)

60o, r/d=2

Q=100 l/s d= 300 mm L = 4.8 km

G.Steel pipe


32/46

83

g

v

d

Lf

KHH

n

isp

2)

.

(

2

1++= =

mg

V

smAA

QV

mA

10211197.02

/415.11.0

07065.04

)3.0.(

2

22

=

===

==

Hs=20.5-11.4 =9.1 m

Pipe material Galvanized S. = 0.15 mm /d = 0.0005


33/46

84

5

6102.4

10011.1

3.0415428.1.x

x

xdVRn ===

From Moody Diagram get f

f 0.0165


34/46

85

Determination of Local Losses

KiType of local losses

Inlet

Exit

BendValves

Others

Ki

1.0

0.21x30.25+3

1.0

5.88


35/46

86

g

v

d

Lf

KHH

n

isp 2)

.

(

2

1++= =

mH

H

p

p

6.37)6001.0448.27(1.9

1021119.0*)3.0

4800*0165.088.5(1.9

=++=

++=


36/46

87

Electricenergy

Mechanicalenergy

Water

energyMotor Pump

Efficiencies

mpt

t

m

p

x

PHE

PHWPHE

PHMPHM

PHW

=

=

=

=

..

....

..

..

..


37/46

88

Calculation of EHP Cost

WHP =75

.. pHQ =1000 kg/m3,

Q = 0.1 m3/s,

Hp=37.6m

WHP = 49.48

EHP= 49.48/0.78 = 63.44

EMP = EHPx0.746=48KWatt

Monthly cost of E.P.=E.M.PxTxCost

Monthly cost of E.P.=48x12(hrs)x30(day)x0.18

= 3100 L.E.

Annual Cost of E.P.= 3100x12(month)=37000 L.E.

(t =0.78)


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89

Any Questions?


39/46

90

How to get f?

Moody Diagram (Chart)

dV.

d

0.025

0.02

0.0180.016

0.014

0.012

0.010

0.008

0.006

0.005

0.004

0.0030.0025

0.002

103

104

105

107

106

108

Friction Coefficient

Reynolds Number

Roughness Ratio

(k/d)

0.01

0.001

0.0001

0.00001

0.00004

0.0002

0.0006

0.002

0.004

0.006

0.02

0.04

0.06

4/f


40/46

91

RoughnessHeight (mm)

Pipe Material

0.003PVC

0.03Glass fiber ReinforcedPlastic (GRP)

0.15Galvanized Steel

0.25Cast Iron

1.00Reinforced Concrete


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92

Inlet losses

Ki = 0.5 Ki = 1.0


42/46

93

Exit losses

Ke = 1.0

Bend/Elbow losses


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Bend/Elbow losses

o, r/d

Bendr

o

Elbow

4321.51 r/d

0.080.080.090.10.1122.5

0.150.150.160.170.1945

0.190.20.210.220.2560

0.260.260.270.290.3390

0.350.350.350.360.41135

0.420.420.420.430.48180

907560453022.5

1.510.70.40.20.17Kelbow


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95

Valve LossesPartially OpenFully Open

Kgate = 0.25Gate Valve

Kcheck = 3

Check valve

(Non Return Valve)

Check valve Gate valve

Radial Flow Centrifugal Pump


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96

Radial Flow Centrifugal Pump

Settings

Suction level

Delivery level

Suction pipe, ls

Delivery pipe, ld

hs

Axial Flow Propeller Pump


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Axial Flow Propeller Pump

Settings

Delivery level

Delivery pipe, ld

Motor

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