- Chemical Resistance
- Safety Data Sheets (SDS)
- Material Properties
- PRO Systems
- PE Pressure Pipe
- PE Pipe Selection
- MAOP for PE Pipes
- Temperature Influences
- E-Modulus
- Selection of Wall Thickness for Special Applications
- Hydraulic Design for PE Pipes
- Surge and Fatigue
- Celerity
- Slurry Flow
- Pneumatic Flow
- Expansion and Contraction
- External Pressure Resistance
- Allowable Bending Radius
- Thrust Block Support
- Conductivity, Vibration and Heat Sources
- Polyethylene Jointing
- Handling and Storage
- Trench Preparation for Buried Pipes
- Relining and Sliplining
- Pipeline Detection
- Above Ground Installation
- Accommodation of Thermal Movement by Deflection Legs
- Service Connections for PE Pipes
- Concrete Encasement
- Fire Rating
- Testing and Commissioning

- PVC Pressure Pipe
- PVC Pressure Pipe Standards
- Pressure Considerations
- PVC Temperature Considerations
- Mine Subsidence
- Buckling
- Water Hammer
- Thrust Support
- Air and Scour Valves
- Soil and Traffic Loads
- Bending Loads
- PVC Pipe Jointing
- Jointing Components with Ductile Iron Flanged Joints
- Service Connections for PVC Pipe
- PVC Pipe Handling and Storage
- Below Ground Installation
- Above Ground Installation for PVC Pipe
- Testing and Commissioning for PVC Pressure Pipe
- Detecting Buried Pipes

- FLUFF – Friction Loss in Uniform Fluid Flow
- Technical Notes

# Hydraulic Design for PE Pipes

Vinidex Polyethylene (PE) pipes offer advantages to the designer due to the smooth internal bores which are maintained over the working lifetime of the pipelines. The surface energy characteristics of PE inhibit the build up of deposits on the internal pipe surfaces thereby retaining the maximum bore dimensions and flow capacities.

The flow charts presented in this section relate the combinations of pipe diameters, flow velocities and head loss with discharge of water in PE pipelines. These charts have been developed for the flow of water through the pipes. Where fluids other than water are being considered, the charts may not be applicable due to the flow properties of these different fluids. In these cases the advice of Vinidex engineers should be obtained.

There are a number of flow formulae in common use which have either a theoretical or empirical background. However, only the Hazen-Williams and Colebrook-White formulae are considered in this section.

## Hazen Williams

The original Hazen-Williams formula was published in 1920 in the form:

where:

*C*_{1} = Hazen-Williams roughness coefficient

*r* = hydraulic radius (ft)

*s* = hydraulic gradient

The variations inherent with diameter changes are accounted for by the introduction of the coefficient *C*_{2} so that

Adoption of a Hazen-Williams roughness coefficient of 155 results in the following relationship for discharge in Vinidex PE pipes:

where

*Q* = discharge (litres/second)

*D* = internal diameter (mm)

*H* = head loss (metres/100 metres length of pipe)

Flow charts for pipe systems using the Hazen – Williams formula have been in operation in Australia for over 30 years.

The charts calculate the volumes of water transmitted through pipelines of various materials, and have been proven in practical installations.

## Colebrook – White

The development from first principles of the Darcy-Weisbach formula results in the expression

where

and

*f* = Darcy friction factor

*H* = head loss due to friction (m)

*D* = pipe internal diameter (m)

*L* = pipe length (metres)

*V* = flow velocity (m/s)

*g* = gravitational acceleration (9.81 m/s^{2})

*Re* = Reynolds Number

This is valid for the laminar flow region (R 2000), however, as most pipe applications are likely to operate in the transition zone between smooth and full turbulence, the transition function developed by Colebrook-White is necessary to establish the relationship between f and R.

where

*k* = Colebrook-White roughness coefficient (m)

The appropriate value for PE pipes is *k* = 0.003 x 10^{-3} m = 0.003 mm

This value provides for the range of pipe diameters, and water flow velocities encountered in normal pipe installations.

## Flow Variations

The flow charts presented for PE pipes are based on a number of assumptions, and variations to these standard conditions may require evaluation as to the effect on discharge.

### Water Temperature

The charts are based on a water temperature of 20°C. A water temperature increase above this value, results in a decrease in viscosity of the water, with a corresponding increase in discharge (or reduced head loss) through the pipeline.

An allowance of approximately 1% increase in the water discharge must be made for each 3°C increase in temperature above 20°C. Similarly, a decrease of approximately 1% in discharge occurs for each 3°C step below 20°C water temperature.

### Pipe Dimensions

The flow charts presented in this section are based on mean pipe dimensions of Series 1 pipes made to AS/NZS 4130 PE pipes for Pressure applications.

### Surface Roughness

The roughness coefficients adopted for Vinidex PE pipes result from experimental programs performed in Europe and the USA, and follow the recommendations laid down in Australian Standard AS2200 – Design Charts for Water Supply and Sewerage.

## Head Loss in Fittings

Wherever a change to pipe cross section, or a change in the direction of flow occurs in a pipeline, energy is lost and this must be accounted for in the hydraulic design. Under normal circumstances involving long pipelines these head losses are small in relation to the head losses due to pipe wall friction. However, geometry and inlet/exit condition head losses may be significant in short pipe runs or in complex installations where a large number of fittings are included in the design.

The general relationship for head losses in fittings may be expressed as:

where

*H* = head loss (m)

*V* = velocity of flow (m/s)

*K* = head loss coefficient

*g* = gravitational acceleration (9.81 m/s2)

The value of the head loss coefficient K is dependent on the particular geometry of each fitting, and values for specific cases are listed in the Table below. The total head loss in the pipeline network is then obtained by adding together the calculations performed for each fitting in the system, the head loss in the pipes, and any other design head losses.

#### Resistance coefficients for valves, fittings and changes in cross section

#### Worked Example

What is the head loss occurring in a 250mm equal tee with the flow in the main pipeline at a flow velocity of 2 m/s?

where

*K* = 0.35 (see Table)

*V* = 2 m/s

*g* = 9.81 m/s

If the total system contains 15 tees under the same conditions, then the total head loss in the fittings is 15 x 0.07 = 1.05 metres

## Flow Charts

### Flow Chart Worked Examples

#### Example 1 – Gravity Main

#### Gravity flow example

A flow of water of 32 litres/second is required to flow from a storage tank located on a hill 50 metres above an outlet. The tank is located 4.5 km away from the outlet. Hence the information available is :

*Q*= 32 l/s- Head available = 50 metres
- Length of pipeline = 4500 metres
- Minimum PN rating of pipe available to withstand the 50 m static head is PN 6.3.
- Head loss per 100 m length of pipe is :

Use Table 4.1 to select the SDR rating of PN6.3 class pipes in both PE 80, and PE 100 materials.

##### PE 80 Material Option

PE 80 PN6.3 pipe is SDR 21. Use the SDR 21 flow chart, read intersection of discharge line at 32 l/s and head loss line at 1.11m/100m of pipe. Select the next largest pipe size. This results in a DN 200 mm pipe diameter.

##### PE 100 Material Option

PE 100 PN6.3 pipe is SDR 26.Use the SDR26 flow chart, read the intersection of discharge line at 32 l/s and head loss line at 1.11m/100m of pipe. Select the next largest pipe size. This results in a DN180 mm pipe diameter.

Hence for this application, there are two options available, either :

- DN 200 PE 80 PN 6.3 or
- DN 180 PE 100 PN 6.3

#### Example 2 – Pumped Main

#### Pumped flow example

A line is required to provide 20 litres/second of water from a dam to a high level storage tank located 5000 metres away. The tank has a maximum water elevation of 100 m and the minimum water elevation in the dam is 70 m. The maximum flow velocity is required to be limited to 1.0 metres/second to minimise water hammer effects.

The maximum head required at the pump = static head + pipe friction head + fittings form loss

##### 1. Static head

= 100 – 70 = 30 m

##### 2. Pipe friction head

Considering the data available, start with a PN 6.3 class pipe.

PE 80 Option

A PE80 PN6.3 pipe is SDR 21. Use the SDR 21 flow chart, find the intersection of the discharge line at 20 l/s and the velocity line at 1 m/s. Select the corresponding or next largest size of pipe. Where the discharge line intersects the selected pipe size, trace across to find the head loss per 100m length of pipe. This gives a value of 0.5m/100m. Calculate the total friction head loss in the Pipe.

0.5/100 x 5000 = 25m

Then from the flow chart, estimate the velocity of flow This gives 1 m/s.

##### 3. Fittings head loss

From the figure, identify the type and number of different fittings used in the pipeline. Select the appropriate form factor K for each fitting type from the resistance coefficients Table, Then:

Fitting | From Factor K |
Head loss m |

Foot valve | 15.0 | 15 x 0.05 = 0.75 |

Gate valve | 0.2 | 2 x 0.2 x 0.05 = 0.02 |

Reflux valve | 2.5 | 2.5 x 0.05 = 0.125 |

90° elbow | 1.1 | 4 x 1.1 x 0.05 = 0.220 |

45° elbow | 0.35 | 2 x 0.35 x 0.05 = 0.035 |

Square outlet | 1.0 | 1.0 x 0.05=0.050 |

Total fittings head loss | 1.2 |

##### 4. Total pumping head

= 30 + 25 + 1.2 = 56.2m, allow 57m.

Note: This example does not make any provision for surge allowance in pressure class selection

## Part Full Flow

Non pressure pipes are designed to run full under anticipated peak flow conditions. However, for a considerable period the pipes run at less than full flow conditions and in these circumstances they act as open channels with a free fluid to air surface.

In these instances consideration must be given to maintaining a minimum transport velocity to prevent deposition of solids and blockage of the pipeline. For pipes flowing part full, the most usual self cleansing velocity adopted for sewers is 0.6 metres/second.

#### Example 3. Determine flow velocity and discharge under part full flow conditions

Given gravity conditions:

Pipe DN 200 PE80 PN6.3

Mean Pipe ID 180 mm

Gradient 1 in 100

Depth of flow 80 mm

Problem:Find flow and velocity

Solution:

Proportional Depth = Depth of flow / Pipe ID

From the Figure below for Part Full Flow, for a proportional depth of 0.44, the proportional discharge is 0.4 and the proportional velocity if 0.95.

Refer to the Vinidex PE pipe flow chart for the SDR 21 pipe. For a gradient of 1 in 100 full flow is 39 l/s and the velocity is 1.6 m/s.

Then, for part full flow Discharge = 0.4 x 39 = 15.6 l/s

Velocity = 0.95 x 1.6 = 1.52 m/s