SlideShare a Scribd company logo
Hardycross Method 
Muhammad Nouman 
UET,Peshawar,Pakistan
Hardy Cross Method:- 
• To analyze a given distribution system to determine the pressure and flow available in any section of the 
system and to suggest improvement if needed a number of methods are used like Equivalent pipe, Circle 
method, method of section and Hardy-cross method. Hardy-cross method is a popular method. According 
to this method the sum of the loss of head for a closed network / loop is equal to zero. Also the sum of 
inflow at a node / joint is equal to the out flow i.e. Σinflow = Σoutflow or total head loss = 0 
Assumption:- 
Sum of the inflow at a node/point is equal to outflow. Σinflow = Σoutflow; Σtotal flow = 0 
Algebraic sum of the head losses in a closed loop is equal to zero. Σhead losses = 0 
Clockwise flows are positive. Counter clockwise flows are negative. 
• Derivation:- 
According to Hazen William Equation H= 10.68 (Q/C) 1.85 (L / d)4.87 
H= KQ1.85 where K = (10.68L)/(C1.85*d4.87) 
For any pipe in a closed loop 
Q = Q+ Δ where Q = actual flow; Q= assumed flow and Δ = required flow correction 
1 1 H= KQx (i) x is an exponent whose value is generally 1.85 
From (i) H = K(Q+ Δ)x By Binomial theorm = K[Qx + (xQx-1Δ)/1! + {x(x-1)Qx-2Δ2}/2! + ……..] 
1 1 
1 
As Δ is very small as compared to Q, we can neglect Δ2 etc. Therefore, H = KQ1 
x + KxQ1 
x-1Δ (ii) 
For a closed loop Σ H = 0 => Σ Qx = 0 => Σ k Q1 
x = - ΔΣ x Q1 
x-1) => Δ = - Σ k Q1 
x / (Σ x Q1 
x-1)
As H = K*Q x 
Σ KQ1 
x/ Q1 = H/Q 1 
Therefore, Δ = - Σ H/ [x* Σ (H)/ Q1] 
Above equation is used in Hardy Cross Method 
Procedure : (i) Assume the diameter of each pipe in the loop. 
(ii) Assume the flow in the pipe such that sum of the inflow = sum of the outflow at any junction or node 
( V = V1 + V2 or Q = Q1 + Q2 ) 
(iii) Compute the head losses in each pipe by Hazen William Equation H = 10.68 * (Q/C)1.85 * L/D4.87 
(iv) Taking clock wise flow as positive and anti clock wise as negative. 
(v) Find sum of the ratio of head loss and discharge in each pipe without regard of sign Σ ( H/Q1 ) 
(vi) Find the correction for each loop from Δ = - Σ H/ [x* Σ (H)/ Q1] and apply it to all pipes. 
(vii) Repeat the procedure with corrected values of flow and continue till the correction become very small
Example 2: For the branching pipe system shown below: At B and C, a 
minimum pressure of 5 m. At A, maximum pressure required is 46 m and the 
minimum is 36 m. Select a suitable diameter for AB and BC. 
0.15 l/s 
219 m A 
2.9 m3/h 2.4 m3/h C (219 m, 
700m 
0.5m3/h 
825 m 
B 189 m 
Public water main 
Example
Solution: Computation Table 
Pipe 
Sect. 
Flow 
(m3/h 
) 
Lengt 
h (m) 
Pipe 
Dia 
mm 
Head 
Loss 
(m/10 
0 m 
Flow 
Vel 
m/s 
Head 
Loss 
(m) 
Elev. 
of 
hydr. 
Grade 
(m) 
Groun 
d level 
elev 
(m) 
Press 
Head 
(m) 
Rem. 
AB 2.9 700 32 3.3 0.85 23 A 
260 
B 
237 
189 46 O.K 
BC 0.5 825 19 1.6 0.5 13 B 
237 
C 
224 
219 5 Just 
O.K
Example 
Example: Obtain the flow rates in the network shown below. 
90 l/s 
A 55 600 m B 
45 
254 mm 
35 600 m 
254 mm 
600 m C C 
152 mm 15 
15 60l/s 
66600 600 m 
E 600 m 5 D 152 mm 
152 mm 
10 
+ve 
600 
152 mm 
ABDE is one loop above and BCD is the second loop. 
Note that the clockwise water flows are positive while the anti-clockwise ones are negative. 
Positive and negative flows give rise to positive and negative head losses respectively
Solution 
Circuit Pipe L (m) D (m) Q (m3/s) hf (m) hf/Q Q 
AB 600 0.254 + 0.055 2.72 49.45 
I BD 600 0.152 + 0.01 1.42 142 
DE 600 0.152 - 0.005 - 0.39 78 0.008 
EA 600 0.152 - 0.035 -14.42 412 
Total - 10.67 681.45 
BC 600 0.254 + 0.045 1.88 41.8 
II CD 600 0.152 - 0.015 - 3.01 200.67 0.004 
DB 600 0.152 - 0.010 - 1.42 142 
Total - 2.55 384.47 
Sample Calculation: Using the Hazen Williams Equation in Step 2 : 
hf for pipe AB = 10.67 x 135 – 1.85 x 0.254 -4.87 x 0.055 1.85 x 600 = 2.72

More Related Content

What's hot

Highway Drainage (Highway Engineering)
Highway Drainage (Highway Engineering)Highway Drainage (Highway Engineering)
Highway Drainage (Highway Engineering)
Kiranmoy Samanta
 
Class 8 Triaxial Test ( Geotechnical Engineering )
Class 8    Triaxial Test ( Geotechnical Engineering )Class 8    Triaxial Test ( Geotechnical Engineering )
Class 8 Triaxial Test ( Geotechnical Engineering )
Hossam Shafiq I
 
Notches and weir
Notches and weirNotches and weir
Notches and weir
Aditya Mistry
 
Estimation of storm sewage
Estimation of storm sewageEstimation of storm sewage
Estimation of storm sewage
sidrarashiddar
 
Spillways & energy dissipator
Spillways & energy dissipatorSpillways & energy dissipator
Spillways & energy dissipator
SAGAR RAUT
 
Water supply appurtenances
Water supply appurtenancesWater supply appurtenances
Water supply appurtenances
Ajay B.K
 
Hydraulics of water Distribution System
 Hydraulics of water Distribution System Hydraulics of water Distribution System
Hydraulics of water Distribution System
UET Lahore | University of Engineering and Technology
 
Open Channel VS Pipe Flow
Open Channel VS Pipe FlowOpen Channel VS Pipe Flow
Open Channel VS Pipe Flow
Fatma Abdalla
 
Dry weather flow
Dry weather flowDry weather flow
Dry weather flow
Ghanashyam Prajapati
 
Hydraulic design of sewer
Hydraulic design of sewerHydraulic design of sewer
Hydraulic design of sewer
Bibhabasu Mohanty
 
Methods of boring ppt
Methods of boring  pptMethods of boring  ppt
Methods of boring ppt
Rakesh Ahirwar
 
Chapter 7 spillway and energy dissipators
Chapter 7 spillway and energy dissipatorsChapter 7 spillway and energy dissipators
Chapter 7 spillway and energy dissipators
Mohsin Siddique
 
Gravity Dam
Gravity DamGravity Dam
(Part ii)- open channels
(Part ii)- open channels(Part ii)- open channels
(Part ii)- open channels
Mohsin Siddique
 
design of weirs
design of weirsdesign of weirs
design of weirs
SANJEEV Wazir
 
Standard Penetration Test
Standard Penetration TestStandard Penetration Test
Standard Penetration Test
Abdur Rahman Quadri
 
Lecture notes 04
Lecture notes 04Lecture notes 04
Lecture notes 04
Yakup Kocaman
 
Cross section of the canal, balancing depth and canal fsl
Cross section of the canal, balancing depth  and canal fslCross section of the canal, balancing depth  and canal fsl
Cross section of the canal, balancing depth and canal fsl
Aditya Mistry
 
Field control of compaction and compaction Equipment
Field control of compaction and compaction EquipmentField control of compaction and compaction Equipment
Field control of compaction and compaction Equipment
aishgup
 
Design of sewers
Design of sewersDesign of sewers
Design of sewers
AnkitTurambekar
 

What's hot (20)

Highway Drainage (Highway Engineering)
Highway Drainage (Highway Engineering)Highway Drainage (Highway Engineering)
Highway Drainage (Highway Engineering)
 
Class 8 Triaxial Test ( Geotechnical Engineering )
Class 8    Triaxial Test ( Geotechnical Engineering )Class 8    Triaxial Test ( Geotechnical Engineering )
Class 8 Triaxial Test ( Geotechnical Engineering )
 
Notches and weir
Notches and weirNotches and weir
Notches and weir
 
Estimation of storm sewage
Estimation of storm sewageEstimation of storm sewage
Estimation of storm sewage
 
Spillways & energy dissipator
Spillways & energy dissipatorSpillways & energy dissipator
Spillways & energy dissipator
 
Water supply appurtenances
Water supply appurtenancesWater supply appurtenances
Water supply appurtenances
 
Hydraulics of water Distribution System
 Hydraulics of water Distribution System Hydraulics of water Distribution System
Hydraulics of water Distribution System
 
Open Channel VS Pipe Flow
Open Channel VS Pipe FlowOpen Channel VS Pipe Flow
Open Channel VS Pipe Flow
 
Dry weather flow
Dry weather flowDry weather flow
Dry weather flow
 
Hydraulic design of sewer
Hydraulic design of sewerHydraulic design of sewer
Hydraulic design of sewer
 
Methods of boring ppt
Methods of boring  pptMethods of boring  ppt
Methods of boring ppt
 
Chapter 7 spillway and energy dissipators
Chapter 7 spillway and energy dissipatorsChapter 7 spillway and energy dissipators
Chapter 7 spillway and energy dissipators
 
Gravity Dam
Gravity DamGravity Dam
Gravity Dam
 
(Part ii)- open channels
(Part ii)- open channels(Part ii)- open channels
(Part ii)- open channels
 
design of weirs
design of weirsdesign of weirs
design of weirs
 
Standard Penetration Test
Standard Penetration TestStandard Penetration Test
Standard Penetration Test
 
Lecture notes 04
Lecture notes 04Lecture notes 04
Lecture notes 04
 
Cross section of the canal, balancing depth and canal fsl
Cross section of the canal, balancing depth  and canal fslCross section of the canal, balancing depth  and canal fsl
Cross section of the canal, balancing depth and canal fsl
 
Field control of compaction and compaction Equipment
Field control of compaction and compaction EquipmentField control of compaction and compaction Equipment
Field control of compaction and compaction Equipment
 
Design of sewers
Design of sewersDesign of sewers
Design of sewers
 

Similar to Hardycross method

Ejercicio Redes Malladas
Ejercicio Redes MalladasEjercicio Redes Malladas
Ejercicio Redes Malladas
UbaldoJGarca
 
Hydraulics of structures
Hydraulics of structuresHydraulics of structures
Hydraulics of structures
Zagazig University
 
Ejercicio Red Ramificada
Ejercicio Red RamificadaEjercicio Red Ramificada
Ejercicio Red Ramificada
UbaldoJGarca
 
Section 7 multistage separation processes
Section 7   multistage separation processesSection 7   multistage separation processes
Section 7 multistage separation processes
Amal Magdy
 
2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf
2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf
2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf
Bhargãv Pâtel
 
3.1 hydraulics
3.1  hydraulics3.1  hydraulics
3.1 hydraulics
Muhammad Usman
 
14.pdf
14.pdf14.pdf
friction loss along a pipe
friction loss along a pipefriction loss along a pipe
friction loss along a pipe
Saif al-din ali
 
Design of Lined Channels.pptx
Design of Lined Channels.pptxDesign of Lined Channels.pptx
Design of Lined Channels.pptx
Tahseensanai
 
Unit6 energy loss in pipelines
Unit6   energy loss in pipelinesUnit6   energy loss in pipelines
Unit6 energy loss in pipelines
Malaysia
 
S3 Minor Losses Presentation
S3 Minor Losses PresentationS3 Minor Losses Presentation
S3 Minor Losses Presentation
no suhaila
 
pipe lines lec 5.pdf
pipe lines lec 5.pdfpipe lines lec 5.pdf
pipe lines lec 5.pdf
amirashraf61
 
Momentum equation.pdf
 Momentum equation.pdf Momentum equation.pdf
Momentum equation.pdf
Dr. Ezzat Elsayed Gomaa
 
pipe lines lec 1.pptx
pipe lines lec 1.pptxpipe lines lec 1.pptx
pipe lines lec 1.pptx
amirashraf61
 
Odemba ECE2304 Hydraulics1Lab
Odemba ECE2304 Hydraulics1LabOdemba ECE2304 Hydraulics1Lab
Odemba ECE2304 Hydraulics1Lab
Walumasi Odemba
 
Basic Theory & Formulae Training Module
Basic Theory & Formulae Training ModuleBasic Theory & Formulae Training Module
Basic Theory & Formulae Training Module
CookLegacyTraining
 
Pipe sizing
Pipe sizingPipe sizing
Pipe sizing
Ajay Kumar Sharma
 
1 FLO-2D Updates and Enhancements 2019.pptx
1 FLO-2D Updates and Enhancements 2019.pptx1 FLO-2D Updates and Enhancements 2019.pptx
1 FLO-2D Updates and Enhancements 2019.pptx
Jorge Atau
 
Problema 5
Problema 5Problema 5
Problema 5
yeisyynojos
 
UNIT-II FMM
UNIT-II FMMUNIT-II FMM
UNIT-II FMM
Aravind Ra
 

Similar to Hardycross method (20)

Ejercicio Redes Malladas
Ejercicio Redes MalladasEjercicio Redes Malladas
Ejercicio Redes Malladas
 
Hydraulics of structures
Hydraulics of structuresHydraulics of structures
Hydraulics of structures
 
Ejercicio Red Ramificada
Ejercicio Red RamificadaEjercicio Red Ramificada
Ejercicio Red Ramificada
 
Section 7 multistage separation processes
Section 7   multistage separation processesSection 7   multistage separation processes
Section 7 multistage separation processes
 
2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf
2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf
2A- Hydraulics, Water Distribution and WW Collection_AC_W2022 (1).pdf
 
3.1 hydraulics
3.1  hydraulics3.1  hydraulics
3.1 hydraulics
 
14.pdf
14.pdf14.pdf
14.pdf
 
friction loss along a pipe
friction loss along a pipefriction loss along a pipe
friction loss along a pipe
 
Design of Lined Channels.pptx
Design of Lined Channels.pptxDesign of Lined Channels.pptx
Design of Lined Channels.pptx
 
Unit6 energy loss in pipelines
Unit6   energy loss in pipelinesUnit6   energy loss in pipelines
Unit6 energy loss in pipelines
 
S3 Minor Losses Presentation
S3 Minor Losses PresentationS3 Minor Losses Presentation
S3 Minor Losses Presentation
 
pipe lines lec 5.pdf
pipe lines lec 5.pdfpipe lines lec 5.pdf
pipe lines lec 5.pdf
 
Momentum equation.pdf
 Momentum equation.pdf Momentum equation.pdf
Momentum equation.pdf
 
pipe lines lec 1.pptx
pipe lines lec 1.pptxpipe lines lec 1.pptx
pipe lines lec 1.pptx
 
Odemba ECE2304 Hydraulics1Lab
Odemba ECE2304 Hydraulics1LabOdemba ECE2304 Hydraulics1Lab
Odemba ECE2304 Hydraulics1Lab
 
Basic Theory & Formulae Training Module
Basic Theory & Formulae Training ModuleBasic Theory & Formulae Training Module
Basic Theory & Formulae Training Module
 
Pipe sizing
Pipe sizingPipe sizing
Pipe sizing
 
1 FLO-2D Updates and Enhancements 2019.pptx
1 FLO-2D Updates and Enhancements 2019.pptx1 FLO-2D Updates and Enhancements 2019.pptx
1 FLO-2D Updates and Enhancements 2019.pptx
 
Problema 5
Problema 5Problema 5
Problema 5
 
UNIT-II FMM
UNIT-II FMMUNIT-II FMM
UNIT-II FMM
 

More from Muhammad Nouman

Water properties pressure_flocculation coagulation
Water properties pressure_flocculation coagulationWater properties pressure_flocculation coagulation
Water properties pressure_flocculation coagulation
Muhammad Nouman
 
Water treatment
Water treatmentWater treatment
Water treatment
Muhammad Nouman
 
Water pollutants
Water pollutantsWater pollutants
Water pollutants
Muhammad Nouman
 
Water distribution
Water distributionWater distribution
Water distribution
Muhammad Nouman
 
Sources of water
Sources of waterSources of water
Sources of water
Muhammad Nouman
 
Point source and non point source pollution
Point source and non point source pollutionPoint source and non point source pollution
Point source and non point source pollution
Muhammad Nouman
 
Natural purification in streams and rivers
Natural purification in streams and riversNatural purification in streams and rivers
Natural purification in streams and rivers
Muhammad Nouman
 
Ce 401 introduction to environmental engineering
Ce 401 introduction to environmental engineeringCe 401 introduction to environmental engineering
Ce 401 introduction to environmental engineering
Muhammad Nouman
 

More from Muhammad Nouman (8)

Water properties pressure_flocculation coagulation
Water properties pressure_flocculation coagulationWater properties pressure_flocculation coagulation
Water properties pressure_flocculation coagulation
 
Water treatment
Water treatmentWater treatment
Water treatment
 
Water pollutants
Water pollutantsWater pollutants
Water pollutants
 
Water distribution
Water distributionWater distribution
Water distribution
 
Sources of water
Sources of waterSources of water
Sources of water
 
Point source and non point source pollution
Point source and non point source pollutionPoint source and non point source pollution
Point source and non point source pollution
 
Natural purification in streams and rivers
Natural purification in streams and riversNatural purification in streams and rivers
Natural purification in streams and rivers
 
Ce 401 introduction to environmental engineering
Ce 401 introduction to environmental engineeringCe 401 introduction to environmental engineering
Ce 401 introduction to environmental engineering
 

Recently uploaded

Null Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAMNull Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAM
Divyanshu
 
Object Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOADObject Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOAD
PreethaV16
 
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
ijseajournal
 
AN INTRODUCTION OF AI & SEARCHING TECHIQUES
AN INTRODUCTION OF AI & SEARCHING TECHIQUESAN INTRODUCTION OF AI & SEARCHING TECHIQUES
AN INTRODUCTION OF AI & SEARCHING TECHIQUES
drshikhapandey2022
 
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
MadhavJungKarki
 
Supermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdfSupermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdf
Kamal Acharya
 
Blood finder application project report (1).pdf
Blood finder application project report (1).pdfBlood finder application project report (1).pdf
Blood finder application project report (1).pdf
Kamal Acharya
 
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
upoux
 
Levelised Cost of Hydrogen (LCOH) Calculator Manual
Levelised Cost of Hydrogen  (LCOH) Calculator ManualLevelised Cost of Hydrogen  (LCOH) Calculator Manual
Levelised Cost of Hydrogen (LCOH) Calculator Manual
Massimo Talia
 
SCALING OF MOS CIRCUITS m .pptx
SCALING OF MOS CIRCUITS m                 .pptxSCALING OF MOS CIRCUITS m                 .pptx
SCALING OF MOS CIRCUITS m .pptx
harshapolam10
 
一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理
一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理
一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理
sydezfe
 
Determination of Equivalent Circuit parameters and performance characteristic...
Determination of Equivalent Circuit parameters and performance characteristic...Determination of Equivalent Circuit parameters and performance characteristic...
Determination of Equivalent Circuit parameters and performance characteristic...
pvpriya2
 
Assistant Engineer (Chemical) Interview Questions.pdf
Assistant Engineer (Chemical) Interview Questions.pdfAssistant Engineer (Chemical) Interview Questions.pdf
Assistant Engineer (Chemical) Interview Questions.pdf
Seetal Daas
 
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Transcat
 
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
SENTIMENT ANALYSIS ON PPT AND Project template_.pptxSENTIMENT ANALYSIS ON PPT AND Project template_.pptx
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
b0754201
 
Height and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdfHeight and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdf
q30122000
 
Open Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surfaceOpen Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surface
Indrajeet sahu
 
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
ydzowc
 
Ericsson LTE Throughput Troubleshooting Techniques.ppt
Ericsson LTE Throughput Troubleshooting Techniques.pptEricsson LTE Throughput Troubleshooting Techniques.ppt
Ericsson LTE Throughput Troubleshooting Techniques.ppt
wafawafa52
 
Digital Twins Computer Networking Paper Presentation.pptx
Digital Twins Computer Networking Paper Presentation.pptxDigital Twins Computer Networking Paper Presentation.pptx
Digital Twins Computer Networking Paper Presentation.pptx
aryanpankaj78
 

Recently uploaded (20)

Null Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAMNull Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAM
 
Object Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOADObject Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOAD
 
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
 
AN INTRODUCTION OF AI & SEARCHING TECHIQUES
AN INTRODUCTION OF AI & SEARCHING TECHIQUESAN INTRODUCTION OF AI & SEARCHING TECHIQUES
AN INTRODUCTION OF AI & SEARCHING TECHIQUES
 
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
 
Supermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdfSupermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdf
 
Blood finder application project report (1).pdf
Blood finder application project report (1).pdfBlood finder application project report (1).pdf
Blood finder application project report (1).pdf
 
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
 
Levelised Cost of Hydrogen (LCOH) Calculator Manual
Levelised Cost of Hydrogen  (LCOH) Calculator ManualLevelised Cost of Hydrogen  (LCOH) Calculator Manual
Levelised Cost of Hydrogen (LCOH) Calculator Manual
 
SCALING OF MOS CIRCUITS m .pptx
SCALING OF MOS CIRCUITS m                 .pptxSCALING OF MOS CIRCUITS m                 .pptx
SCALING OF MOS CIRCUITS m .pptx
 
一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理
一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理
一比一原版(uoft毕业证书)加拿大多伦多大学毕业证如何办理
 
Determination of Equivalent Circuit parameters and performance characteristic...
Determination of Equivalent Circuit parameters and performance characteristic...Determination of Equivalent Circuit parameters and performance characteristic...
Determination of Equivalent Circuit parameters and performance characteristic...
 
Assistant Engineer (Chemical) Interview Questions.pdf
Assistant Engineer (Chemical) Interview Questions.pdfAssistant Engineer (Chemical) Interview Questions.pdf
Assistant Engineer (Chemical) Interview Questions.pdf
 
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
 
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
SENTIMENT ANALYSIS ON PPT AND Project template_.pptxSENTIMENT ANALYSIS ON PPT AND Project template_.pptx
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
 
Height and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdfHeight and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdf
 
Open Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surfaceOpen Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surface
 
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
 
Ericsson LTE Throughput Troubleshooting Techniques.ppt
Ericsson LTE Throughput Troubleshooting Techniques.pptEricsson LTE Throughput Troubleshooting Techniques.ppt
Ericsson LTE Throughput Troubleshooting Techniques.ppt
 
Digital Twins Computer Networking Paper Presentation.pptx
Digital Twins Computer Networking Paper Presentation.pptxDigital Twins Computer Networking Paper Presentation.pptx
Digital Twins Computer Networking Paper Presentation.pptx
 

Hardycross method

  • 1. Hardycross Method Muhammad Nouman UET,Peshawar,Pakistan
  • 2. Hardy Cross Method:- • To analyze a given distribution system to determine the pressure and flow available in any section of the system and to suggest improvement if needed a number of methods are used like Equivalent pipe, Circle method, method of section and Hardy-cross method. Hardy-cross method is a popular method. According to this method the sum of the loss of head for a closed network / loop is equal to zero. Also the sum of inflow at a node / joint is equal to the out flow i.e. Σinflow = Σoutflow or total head loss = 0 Assumption:- Sum of the inflow at a node/point is equal to outflow. Σinflow = Σoutflow; Σtotal flow = 0 Algebraic sum of the head losses in a closed loop is equal to zero. Σhead losses = 0 Clockwise flows are positive. Counter clockwise flows are negative. • Derivation:- According to Hazen William Equation H= 10.68 (Q/C) 1.85 (L / d)4.87 H= KQ1.85 where K = (10.68L)/(C1.85*d4.87) For any pipe in a closed loop Q = Q+ Δ where Q = actual flow; Q= assumed flow and Δ = required flow correction 1 1 H= KQx (i) x is an exponent whose value is generally 1.85 From (i) H = K(Q+ Δ)x By Binomial theorm = K[Qx + (xQx-1Δ)/1! + {x(x-1)Qx-2Δ2}/2! + ……..] 1 1 1 As Δ is very small as compared to Q, we can neglect Δ2 etc. Therefore, H = KQ1 x + KxQ1 x-1Δ (ii) For a closed loop Σ H = 0 => Σ Qx = 0 => Σ k Q1 x = - ΔΣ x Q1 x-1) => Δ = - Σ k Q1 x / (Σ x Q1 x-1)
  • 3. As H = K*Q x Σ KQ1 x/ Q1 = H/Q 1 Therefore, Δ = - Σ H/ [x* Σ (H)/ Q1] Above equation is used in Hardy Cross Method Procedure : (i) Assume the diameter of each pipe in the loop. (ii) Assume the flow in the pipe such that sum of the inflow = sum of the outflow at any junction or node ( V = V1 + V2 or Q = Q1 + Q2 ) (iii) Compute the head losses in each pipe by Hazen William Equation H = 10.68 * (Q/C)1.85 * L/D4.87 (iv) Taking clock wise flow as positive and anti clock wise as negative. (v) Find sum of the ratio of head loss and discharge in each pipe without regard of sign Σ ( H/Q1 ) (vi) Find the correction for each loop from Δ = - Σ H/ [x* Σ (H)/ Q1] and apply it to all pipes. (vii) Repeat the procedure with corrected values of flow and continue till the correction become very small
  • 4. Example 2: For the branching pipe system shown below: At B and C, a minimum pressure of 5 m. At A, maximum pressure required is 46 m and the minimum is 36 m. Select a suitable diameter for AB and BC. 0.15 l/s 219 m A 2.9 m3/h 2.4 m3/h C (219 m, 700m 0.5m3/h 825 m B 189 m Public water main Example
  • 5. Solution: Computation Table Pipe Sect. Flow (m3/h ) Lengt h (m) Pipe Dia mm Head Loss (m/10 0 m Flow Vel m/s Head Loss (m) Elev. of hydr. Grade (m) Groun d level elev (m) Press Head (m) Rem. AB 2.9 700 32 3.3 0.85 23 A 260 B 237 189 46 O.K BC 0.5 825 19 1.6 0.5 13 B 237 C 224 219 5 Just O.K
  • 6. Example Example: Obtain the flow rates in the network shown below. 90 l/s A 55 600 m B 45 254 mm 35 600 m 254 mm 600 m C C 152 mm 15 15 60l/s 66600 600 m E 600 m 5 D 152 mm 152 mm 10 +ve 600 152 mm ABDE is one loop above and BCD is the second loop. Note that the clockwise water flows are positive while the anti-clockwise ones are negative. Positive and negative flows give rise to positive and negative head losses respectively
  • 7. Solution Circuit Pipe L (m) D (m) Q (m3/s) hf (m) hf/Q Q AB 600 0.254 + 0.055 2.72 49.45 I BD 600 0.152 + 0.01 1.42 142 DE 600 0.152 - 0.005 - 0.39 78 0.008 EA 600 0.152 - 0.035 -14.42 412 Total - 10.67 681.45 BC 600 0.254 + 0.045 1.88 41.8 II CD 600 0.152 - 0.015 - 3.01 200.67 0.004 DB 600 0.152 - 0.010 - 1.42 142 Total - 2.55 384.47 Sample Calculation: Using the Hazen Williams Equation in Step 2 : hf for pipe AB = 10.67 x 135 – 1.85 x 0.254 -4.87 x 0.055 1.85 x 600 = 2.72