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Conduits
• Gravity conduits
Open channel
Tunnel
Flumes
Aqueducts
• Pressure conduits
Pipelines
Pressure conduits
Pressure aqueducts
1
INTRODUCTION
Awater pipe isany pipe or tube designed to transport treated
drinking water/potable water to consumers/building.
 Theydiffer according tosizes:-
1) Large diameter mainpipes, whichsupply entire towns
2) Smaller branch linesthat supply a street or group of
buildings,
3) Smalldiameter pipes located within individual buildings
DIFFERENTTYPES
• CAST IRON (CI) PIPES
• STEEL PIPES
• GALVANIZED IRON (GI) PIPES
• COPPER PIPES
• PLASTIC OR POLYTHENE OR
PVC PIPES
• ASBESTOS CEMENT (AC) PIPES
• CONCRETE PIPES
• POLYPROPYLENE(PPR) PIPES
GAL
V
ANIZEDIRONPIPES
• THIS TYPE OF PIPE IS USED FOR
WATER SUPPLY WORK INSIDE
THE BUILDING. THESE PIPES
ARE WROUGHT STEEL PIPES
PROVIDED WITH ZINC COATING.
• APPLICATION AREAS:
• WATER & SEWERAGE.
• FIRE FIGHTING INSTALLATIONS.
• PLUMBING SYSTEMS.
GALVANIZEDIRONPIPES
 Advantages :-
 Low installation and
maintenance cost
 Long life
 Toughness
 Anti-rust pipes
 Useful for large construction
projects-durable and large
diameter
• Disadvantages :-
• Heavy to handle.
• Develops blockages.
• Difficult to repair.
GAL
V
ANIZEDIRONPIPES
Screwed joints Grooved Joints
Welded Joints
Flanged Joints
GAL
V
ANIZEDIRONPIPES
PVC/PLASTIC/POL
YTHENE PIPES
• These Pipes Are Being Used Increasingly
These Days For Supply Of Cold Water
In External And Internal Plumbing Work.
• There Are 3 Common Types Of Plastic Pipes
Are Available In Market, As Given Below.
• Unplasticized Pvc (UPVC) Or Rigid
Pipes For Use With Cold Water
• Plasticized PVC Pipes Which Are Plasticized
With The Addition Of Rubber. It Has Lower
Strength And Lower Working Temperature
Than UPVC Pipes.
• Which Can Withstand (Chlorinated Pvc
(CPVC) Pipes) Higher Temperatures Upto
1200 (Used To Carry Hot Water).
PVC/PLASTIC/POLYTHENE PIPES
• ADVANTAGES :-
1. DURABLE AND
USABLE.
2. CORROSION
RESISTANT.
3. INSULATION.
• DISADVANTAGES :-
1. HEAT
CONSTRAINTS.
2. COST.
3. WEIGHT.
PVC/PLASTIC/POLYTHENE PIPES
Solvent Cementing Heat Fusion
PVC/PLASTIC/POLYTHENE PIPES
A
V
AILABLEFITTINGS:-
STEELPIPES
• Steel Pipes Are Comparatively Expensive.
• But They Are The Strongest And Most Durable Of All Water
Supply Pipes.
• They Can Withstand High Water Pressure, Come In
Convenient (Longer) Lengths Than Most Other Pipes And
Thus Incur Lower Installation/Transportation Costs. They Can
Also Be Easily Welded.
SOURCE:http://www.slideshare.net/M
anishPandey63/ppt-on-water-
distribution-system-by-manish-pandey
ADV
ANT
AGESOFSTEELPIPES
• Lighter
• Cheaper
• Easier to construct and transport
Source:
https://www.google.com/#tbm=
isch&q=steel+pipes+specificatio
n+sizes&imgrc=88ZUm-
ZhD0RPeM%3A
DISADV
ANT
AGESOFSTEELPIPES
• THERMAL CONDUCTIVITY IS VERY POOR
• IT IS VERY DIFFICULT TO FABRICATE AND SINCE IT IS
NOT THAT MUCH MALLEABLE AS COMPARED TO OTHER
METALS THEREFORE IT IS DIFFICULT IN CASE OF
REPAIR OR RE WORK BEING DONE.
Source:
https://www.google.com/#tb
m=isch&q=steel+pipes+specif
ication+sizes&imgrc=88ZUm-
ZhD0RPeM%3A
USESOFSTEELPIPES
• WATER MAINS
• SEWERAGE SYSTEMS. INDUSTRIAL WATER LINES
• PLANT PIPING.
• DEEP TUBE-WELLS
• CASING PIPES
• PIPE LINES FOR NATURAL GAS
Source:
https://www.google.co
m/#tbm=isch&q=steel
+pipes+specification+s
izes&imgrc=88ZUm-
ZhD0RPeM%3A
PRP PIPES
• The PPR Pipe Is One Of The Latest Pipes Resulting From
European Advanced Technology Of Gods. Its Raw Materials, A
Propylene Random Copolymer
• Featured By Excellent Cleanness, Cost Effectiveness,
Applicability And Advantage In Safety, It Is Considered As The
Optimal Pipe Material For Cold And Hot Water System, Water
Purifying Engineering, Underground Heating System For
Wooden Floor, Chemical Pipe Works
Https://Www.Google.Com/#Q=ppr
+p
Ipes+specification+sizes&tbm=isch
PPRPIPESANDITSINST
ALLA
TION
• PPR pipe is known of polypropylene pipe.
• It is used in most home improvement projects a water
supply pipeline.
http://www.hengxing-
group.com/faq/products-
knowledge/What-is-the-PPR-
• SOUR
C
E:HTTP://WW W.123R
F
.COM/PHOT
O_7606230_
VECTOR-COLLECTION-OF-DETAILED-CONSTRUCTION-
PIECES-PIPES-FITTINGS-GA
TE-V
AL
VE-FAUCET-ELLS.HTML
IRON PIPES
Theycomein various shapessuchasL-
shape,T-shape,I-shape etc.
IRONPIPESADVANTAGESANDDISADVANTAGES
• Cast Iron Pipe Is The Preferred Choice For Handling High
Pressures And Loads Of Water.
• However, These Pipes Are Very Heavy And It Requires
Specific Means Of Transportation.
• They Are Cheaper In Cost, It Has High Resistance To
Corrosion, It Is Highly Durable.
• It Is Also Not Advisable To Use Cast Iron Pipes In
Inaccessible Places
MANUF
ACTURING METHODS
• Horizontally cast (MC ware pipes)
• Vertical cast (pit cast in sand moulds)
• Centrifugally cast in sand lines moulds spun type
• Centrifugally cast in water cooled metal moulds
Nowadays horizontally cast C.I. pipes are no longer used.
Centrifugally cast pipes posses fine-grained dense structure and
uniform thickness and therefore they are widely used.
CUTTING METHODS FOR CAST IRON
• CUTTING CAST IRON SOIL PIPE WITHA SNAP CUTTER
JOINING METHODS FOR CAST IRON
THREETYPES:-
• CompressionGaskets
• HublessJoints
• CaulkedJoints
COPPER PIPES
• But because of steel’s tendency to
corrode over time, copper pipes have
superseded galvanized steel as the
metal of choice during the last 70
years.
COPPERPIPES
ADVANTAGES
• Copper isa naturally corrosion-resistant metal.
• Durable metal (capable of withstanding 1,000 psi of pressure),copper isalso
lightweight.
• Easierto extend over long stretcheswithout supports.
DISADV
ANTAGE
• Copper pipes also encounter problems from water acidity, sothey are not
good to install for plumbing systemsthat draw water from a well.
• Costsmorethan plastic.
• Copper isflexible asfar asmetalsgo, but plastic pipes canbend to fit into
almostany space necessary.
CONCRETEPIPE
Steel reinforced concretepipe (SRCP)hasa product life of 100 years
Applications:
• Transverse culverts
• Stormwater drainage
• Pressure and irrigation
• Pipejacking and micro-tunneling
CONCRETEPIPES
Advantages of the reinforced concrete pipes are as follows:
•Suitable for conveying all types of water;
•Easy to install and with flexible joints;
•Because of the smooth inner surface, there are small friction losses;
•They are water tight and durable, even with cracks in the inner and outer
coating layers
The Disadvantages of reinforced concrete pipes are as follows:
•It is necessary to conduct detailed studies regarding the pipe fittings, based on
the specific project requirements;
•They are heavy, with this feature being reflected in their transportation and
installation costs;
•They require special care in its manufacturing, transportation and installation;
LOADS ON BURIEDPIPES
WEIGHTONMATERIAL
Correct Width Wider Trench
= MORE SEVERE LOAD
Pipe Laying Sequence
 The pipe laying sequence is normally conducted facing upstream,
with the spigot end facing down-stream.
 The spigot ends are pushed into the socket end.
Progress
Push home
ASBESTOS-CEMENT PIPES
These pipes have been in use throughout the world since 1913. They
are made of a mixture of 82-90% cement and 10-18% asbestos fibers.
ASBESTOS-CEMENT PIPES
The advantages of asbestos pipes are as follows:
• They are resistant to wear and corrosion, thereby being
useful in situations involving corrosive water or soil;
• They have smooth internal surfaces, resulting in low friction
losses;
• They are easy to install and maintain;
• The major raw material (cement) required for their
manufacture are Asbestos,Silica and Cement.
ASBESTOS-CEMENT PIPES
The disadvantages of asbestos pipes are as follows:
•The asbestos material used in manufacturing the pipes represent a
carcinogenic health hazard when used to transport water for
human consumption.
•The pipes have a low resistance to vibrations from vehicular
traffic passing over them;
•They have a low resistance to shocks,
Jointing and testing of pipes
Types of joints:
1. Socket and Spigot joint
2. Flanged joint
3. Mechanical joint called dresser coupling
4. Flexible joint
5. Expansion joint
• Cast iron pipes are being jointed by a “socket and spigot (stopper) joint”
• This joint is till today used very large scale.
• It is to made in such a way that one of their end is enlarged, whereas other
end is normal. The enlarged end is called as “spigot”.
Socket and Spigot joint
Socket and Spigot joint – cont.,
• The Spigot is fitted into socket (hole or opening or hollow).
• A few strands (elements or components) of jute (Rough fiber made from
the stems of a tropical Old World plant) are wrapped (enfolded or
enveloped or covered) around the spigot before inserting it into the
socket.
• The remaining space filled with “molten lead”.
Flanged joint
• It is used for pumping stations, filter plants, and at other locations, where
it may be occasionally (infrequently) disjoint the pipe.
• The flanges are fitted at end of C.I pipes.
• Those two flanges are brought together, keeping a rubber washer (called
gasket) in b/w them, so as to make them water tight.
Flanged joint – cont.,
• Also they are fixed by nuts and bolts.
• These joints are strong but rigid, and cannot be used where deflection or
vibrations are expected.
• These are expansive and mostly used for indoor works.
Mechanical joint
• These type of joint is used to plain ends of cast iron pipes.
• A special type of metallic collar is then fitted and tightened.
• An iron ring and a gasket are slipped over abutting (adjoining or
neighboring) ends of the pipes.
• The joints are strong and rigid, they can withstand vibrations also used to
bridges or below bridges in hangers.
Flexible joint
• Flexible joints are used where large scale flexibilities are required.
• The pipes are laid rivers with uneven beds, large scale settlements may
break the ordinary types of joint.
• Similarly laying pipes on curves, they provided must be flexible,
otherwise they may be break.
• Socket is spherical; the spigot, can be moved to get the desired deflection
and nuts tightened over gland ring.
Expansion joint
• Expansion joints are provided at suitable intervals in the pipe line, so as
counteract the thermal stresses produced due to temperature variations.
• For providing expansion joints in C.I pipes, the socket end is cast flanged
and spigot end is plain.
• The Socket end is connected rigidly to an annular ring which can slide
freely over the spigot end.
• All the time, annular ring, maintains the gaskets in position, thus keeping
water tight.
Corrosion of metal pipes
Fe2+ +2 OH- = Fe(OH)2
Fe(OH)2 + dissolved oxygen = Fe(OH)3
EFFECTS OF PIPE CORROSION
CORROSION CONTROL
• Protective coatings
• Selecting proper pipe materials
• Quality of water
• Cathodic protection
CORROSION CONTROL
• Protective coatings
• Selecting proper pipe materials
• Quality of water
• Cathodic protection
Laying of pipes
Preparing a detailed map showing the alignment
of pipelines
Locating the proposed alignment of the pipeline
on the ground
Location of pipes with respect to ground surface
during laying.
Excavation of trench
Side protection of trench
Bottoming of trench
Lowering of pipes into trench
Jointing of pipes
Backfilling of trenches
Anchoring of pipes
Disinfection of pipes
Testing the pipelines
Hydraulics of flow
Darcy weisbach formula
HL=
𝑓′𝐿𝑉2
2𝑔𝑑
Mannings formula
HL =
𝑛2𝑉2𝐿
𝑅4/3
Hazen William formula
𝑉 = 0.85𝐶𝐻𝑅0.63
𝑆0.54
pipes.pptx
pipes.pptx
pipes.pptx

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pipes.pptx

  • 1. Conduits • Gravity conduits Open channel Tunnel Flumes Aqueducts • Pressure conduits Pipelines Pressure conduits Pressure aqueducts 1
  • 2. INTRODUCTION Awater pipe isany pipe or tube designed to transport treated drinking water/potable water to consumers/building.  Theydiffer according tosizes:- 1) Large diameter mainpipes, whichsupply entire towns 2) Smaller branch linesthat supply a street or group of buildings, 3) Smalldiameter pipes located within individual buildings
  • 3. DIFFERENTTYPES • CAST IRON (CI) PIPES • STEEL PIPES • GALVANIZED IRON (GI) PIPES • COPPER PIPES • PLASTIC OR POLYTHENE OR PVC PIPES • ASBESTOS CEMENT (AC) PIPES • CONCRETE PIPES • POLYPROPYLENE(PPR) PIPES
  • 4. GAL V ANIZEDIRONPIPES • THIS TYPE OF PIPE IS USED FOR WATER SUPPLY WORK INSIDE THE BUILDING. THESE PIPES ARE WROUGHT STEEL PIPES PROVIDED WITH ZINC COATING. • APPLICATION AREAS: • WATER & SEWERAGE. • FIRE FIGHTING INSTALLATIONS. • PLUMBING SYSTEMS.
  • 5. GALVANIZEDIRONPIPES  Advantages :-  Low installation and maintenance cost  Long life  Toughness  Anti-rust pipes  Useful for large construction projects-durable and large diameter • Disadvantages :- • Heavy to handle. • Develops blockages. • Difficult to repair.
  • 6. GAL V ANIZEDIRONPIPES Screwed joints Grooved Joints Welded Joints Flanged Joints
  • 8. PVC/PLASTIC/POL YTHENE PIPES • These Pipes Are Being Used Increasingly These Days For Supply Of Cold Water In External And Internal Plumbing Work. • There Are 3 Common Types Of Plastic Pipes Are Available In Market, As Given Below. • Unplasticized Pvc (UPVC) Or Rigid Pipes For Use With Cold Water • Plasticized PVC Pipes Which Are Plasticized With The Addition Of Rubber. It Has Lower Strength And Lower Working Temperature Than UPVC Pipes. • Which Can Withstand (Chlorinated Pvc (CPVC) Pipes) Higher Temperatures Upto 1200 (Used To Carry Hot Water).
  • 9. PVC/PLASTIC/POLYTHENE PIPES • ADVANTAGES :- 1. DURABLE AND USABLE. 2. CORROSION RESISTANT. 3. INSULATION. • DISADVANTAGES :- 1. HEAT CONSTRAINTS. 2. COST. 3. WEIGHT.
  • 12. STEELPIPES • Steel Pipes Are Comparatively Expensive. • But They Are The Strongest And Most Durable Of All Water Supply Pipes. • They Can Withstand High Water Pressure, Come In Convenient (Longer) Lengths Than Most Other Pipes And Thus Incur Lower Installation/Transportation Costs. They Can Also Be Easily Welded. SOURCE:http://www.slideshare.net/M anishPandey63/ppt-on-water- distribution-system-by-manish-pandey
  • 13. ADV ANT AGESOFSTEELPIPES • Lighter • Cheaper • Easier to construct and transport Source: https://www.google.com/#tbm= isch&q=steel+pipes+specificatio n+sizes&imgrc=88ZUm- ZhD0RPeM%3A
  • 14. DISADV ANT AGESOFSTEELPIPES • THERMAL CONDUCTIVITY IS VERY POOR • IT IS VERY DIFFICULT TO FABRICATE AND SINCE IT IS NOT THAT MUCH MALLEABLE AS COMPARED TO OTHER METALS THEREFORE IT IS DIFFICULT IN CASE OF REPAIR OR RE WORK BEING DONE. Source: https://www.google.com/#tb m=isch&q=steel+pipes+specif ication+sizes&imgrc=88ZUm- ZhD0RPeM%3A
  • 15. USESOFSTEELPIPES • WATER MAINS • SEWERAGE SYSTEMS. INDUSTRIAL WATER LINES • PLANT PIPING. • DEEP TUBE-WELLS • CASING PIPES • PIPE LINES FOR NATURAL GAS Source: https://www.google.co m/#tbm=isch&q=steel +pipes+specification+s izes&imgrc=88ZUm- ZhD0RPeM%3A
  • 16. PRP PIPES • The PPR Pipe Is One Of The Latest Pipes Resulting From European Advanced Technology Of Gods. Its Raw Materials, A Propylene Random Copolymer • Featured By Excellent Cleanness, Cost Effectiveness, Applicability And Advantage In Safety, It Is Considered As The Optimal Pipe Material For Cold And Hot Water System, Water Purifying Engineering, Underground Heating System For Wooden Floor, Chemical Pipe Works Https://Www.Google.Com/#Q=ppr +p Ipes+specification+sizes&tbm=isch
  • 17. PPRPIPESANDITSINST ALLA TION • PPR pipe is known of polypropylene pipe. • It is used in most home improvement projects a water supply pipeline. http://www.hengxing- group.com/faq/products- knowledge/What-is-the-PPR-
  • 19. IRONPIPESADVANTAGESANDDISADVANTAGES • Cast Iron Pipe Is The Preferred Choice For Handling High Pressures And Loads Of Water. • However, These Pipes Are Very Heavy And It Requires Specific Means Of Transportation. • They Are Cheaper In Cost, It Has High Resistance To Corrosion, It Is Highly Durable. • It Is Also Not Advisable To Use Cast Iron Pipes In Inaccessible Places
  • 20. MANUF ACTURING METHODS • Horizontally cast (MC ware pipes) • Vertical cast (pit cast in sand moulds) • Centrifugally cast in sand lines moulds spun type • Centrifugally cast in water cooled metal moulds Nowadays horizontally cast C.I. pipes are no longer used. Centrifugally cast pipes posses fine-grained dense structure and uniform thickness and therefore they are widely used.
  • 21. CUTTING METHODS FOR CAST IRON • CUTTING CAST IRON SOIL PIPE WITHA SNAP CUTTER
  • 22. JOINING METHODS FOR CAST IRON THREETYPES:- • CompressionGaskets • HublessJoints • CaulkedJoints
  • 23. COPPER PIPES • But because of steel’s tendency to corrode over time, copper pipes have superseded galvanized steel as the metal of choice during the last 70 years.
  • 24. COPPERPIPES ADVANTAGES • Copper isa naturally corrosion-resistant metal. • Durable metal (capable of withstanding 1,000 psi of pressure),copper isalso lightweight. • Easierto extend over long stretcheswithout supports. DISADV ANTAGE • Copper pipes also encounter problems from water acidity, sothey are not good to install for plumbing systemsthat draw water from a well. • Costsmorethan plastic. • Copper isflexible asfar asmetalsgo, but plastic pipes canbend to fit into almostany space necessary.
  • 25. CONCRETEPIPE Steel reinforced concretepipe (SRCP)hasa product life of 100 years Applications: • Transverse culverts • Stormwater drainage • Pressure and irrigation • Pipejacking and micro-tunneling
  • 26. CONCRETEPIPES Advantages of the reinforced concrete pipes are as follows: •Suitable for conveying all types of water; •Easy to install and with flexible joints; •Because of the smooth inner surface, there are small friction losses; •They are water tight and durable, even with cracks in the inner and outer coating layers The Disadvantages of reinforced concrete pipes are as follows: •It is necessary to conduct detailed studies regarding the pipe fittings, based on the specific project requirements; •They are heavy, with this feature being reflected in their transportation and installation costs; •They require special care in its manufacturing, transportation and installation;
  • 27. LOADS ON BURIEDPIPES WEIGHTONMATERIAL Correct Width Wider Trench = MORE SEVERE LOAD
  • 28. Pipe Laying Sequence  The pipe laying sequence is normally conducted facing upstream, with the spigot end facing down-stream.  The spigot ends are pushed into the socket end. Progress Push home
  • 29. ASBESTOS-CEMENT PIPES These pipes have been in use throughout the world since 1913. They are made of a mixture of 82-90% cement and 10-18% asbestos fibers.
  • 30. ASBESTOS-CEMENT PIPES The advantages of asbestos pipes are as follows: • They are resistant to wear and corrosion, thereby being useful in situations involving corrosive water or soil; • They have smooth internal surfaces, resulting in low friction losses; • They are easy to install and maintain; • The major raw material (cement) required for their manufacture are Asbestos,Silica and Cement.
  • 31. ASBESTOS-CEMENT PIPES The disadvantages of asbestos pipes are as follows: •The asbestos material used in manufacturing the pipes represent a carcinogenic health hazard when used to transport water for human consumption. •The pipes have a low resistance to vibrations from vehicular traffic passing over them; •They have a low resistance to shocks,
  • 32. Jointing and testing of pipes Types of joints: 1. Socket and Spigot joint 2. Flanged joint 3. Mechanical joint called dresser coupling 4. Flexible joint 5. Expansion joint
  • 33. • Cast iron pipes are being jointed by a “socket and spigot (stopper) joint” • This joint is till today used very large scale. • It is to made in such a way that one of their end is enlarged, whereas other end is normal. The enlarged end is called as “spigot”. Socket and Spigot joint
  • 34. Socket and Spigot joint – cont., • The Spigot is fitted into socket (hole or opening or hollow). • A few strands (elements or components) of jute (Rough fiber made from the stems of a tropical Old World plant) are wrapped (enfolded or enveloped or covered) around the spigot before inserting it into the socket. • The remaining space filled with “molten lead”.
  • 35. Flanged joint • It is used for pumping stations, filter plants, and at other locations, where it may be occasionally (infrequently) disjoint the pipe. • The flanges are fitted at end of C.I pipes. • Those two flanges are brought together, keeping a rubber washer (called gasket) in b/w them, so as to make them water tight.
  • 36. Flanged joint – cont., • Also they are fixed by nuts and bolts. • These joints are strong but rigid, and cannot be used where deflection or vibrations are expected. • These are expansive and mostly used for indoor works.
  • 37. Mechanical joint • These type of joint is used to plain ends of cast iron pipes. • A special type of metallic collar is then fitted and tightened. • An iron ring and a gasket are slipped over abutting (adjoining or neighboring) ends of the pipes. • The joints are strong and rigid, they can withstand vibrations also used to bridges or below bridges in hangers.
  • 38. Flexible joint • Flexible joints are used where large scale flexibilities are required. • The pipes are laid rivers with uneven beds, large scale settlements may break the ordinary types of joint. • Similarly laying pipes on curves, they provided must be flexible, otherwise they may be break. • Socket is spherical; the spigot, can be moved to get the desired deflection and nuts tightened over gland ring.
  • 39. Expansion joint • Expansion joints are provided at suitable intervals in the pipe line, so as counteract the thermal stresses produced due to temperature variations. • For providing expansion joints in C.I pipes, the socket end is cast flanged and spigot end is plain. • The Socket end is connected rigidly to an annular ring which can slide freely over the spigot end. • All the time, annular ring, maintains the gaskets in position, thus keeping water tight.
  • 40. Corrosion of metal pipes Fe2+ +2 OH- = Fe(OH)2 Fe(OH)2 + dissolved oxygen = Fe(OH)3 EFFECTS OF PIPE CORROSION CORROSION CONTROL • Protective coatings • Selecting proper pipe materials • Quality of water • Cathodic protection
  • 41. CORROSION CONTROL • Protective coatings • Selecting proper pipe materials • Quality of water • Cathodic protection
  • 42. Laying of pipes Preparing a detailed map showing the alignment of pipelines Locating the proposed alignment of the pipeline on the ground Location of pipes with respect to ground surface during laying. Excavation of trench Side protection of trench Bottoming of trench Lowering of pipes into trench Jointing of pipes Backfilling of trenches Anchoring of pipes
  • 43.
  • 44.
  • 46. Hydraulics of flow Darcy weisbach formula HL= 𝑓′𝐿𝑉2 2𝑔𝑑 Mannings formula HL = 𝑛2𝑉2𝐿 𝑅4/3 Hazen William formula 𝑉 = 0.85𝐶𝐻𝑅0.63 𝑆0.54