1. CE 3372 Water Systems Design
Closed Conduit Hydraulics-I

2. Flow in Closed Conduits
Diagram
Energy Equation
Head Loss Models
Pipe loss
Fitting loss
Moody Chart Problems
Direct Method (Jain equations)
Branched Systems
Looped System

3. Diagram

4. Diagram
Suction Side
Lift Station
Discharge Side

5. Mean Section Velocity
In most engineering contexts, the mean section velocity is the ratio of the volumetric discharge and cross sectional area.
The velocity distribution in a section is important in determining frictional losses in a conduit.

6. Energy Equation
The energy equation relates the total dynamic head at two points in a system, accounting for frictional losses and any added head from a pump.

7. Energy Equation 2 1

8. Head Loss Models
Darcy-Weisbach
Hazen-Williams
Chezy-Mannings

9. Darcy-Weisbach Frictional loss proportional to
Length, Velocity^2
Inversely proportional to
Cross sectional area
Loss coefficient depends on
Reynolds number (fluid and flow properties)
Roughness height (pipe material properties)

10. Darcy-Weisbach Frictional loss proportional to
Length, Velocity^2
Inversely proportional to
Cross sectional area
Loss coefficient depends on
Reynolds number (fluid and flow properties)
Roughness height (pipe material properties)

11. Darcy-Weisbach DW Head Loss Equation
DW Equation, Discharge Form, CIRCULAR conduits

12. Hazen-Williams Frictional loss proportional to
Length, Velocity^(1.8)
Inversely proportional to
Cross section area (as hydraulic radius)
Loss coefficient depends on
Pipe material and finish
WATER ONLY!

13. Hazen-Williams
HW Head Loss
Discharge Form

14. Hydraulic Radius
HW is often presented as a velocity equation using the hydraulic radius
The hydraulic radius is the ratio of cross section flow area to wetted perimeter

15. Hydraulic Radius For circular pipe, full flow (no free surface) AREA D
PERIMETER D

16. Chezy-Manning Frictional loss proportional to
Length, Velocity^2
Inversely proportional to
Cross section area (as hydraulic radius)
Loss coefficient depends on
Material, finish

17. Chezy-Manning
CM Head Loss
Discharge form replaces V with Q/A

18. Fitting (Minor) Losses
Fittings, joints, elbows, inlets, outlets cause additional head loss.
Called “minor” loss not because of magnitude, but because they occur over short distances.
Typical loss model is

19. Fitting (Minor) Losses
The loss coefficients are tabulated for different kinds of fittings

20. Moody Chart
Moody-Stanton chart is a tool to estimate the friction factor in the DW head loss model
Used for the pipe loss component of friction

21. Examples Three “classical” examples using Moody Char
Head loss for given discharge, diameter, material
Discharge given head loss, diameter, material
Diameter given discharge, head loss, material

22. Direct (Jain) Equations
An alternative to the Moody chart are regression equations that allow direct computation of discharge, diameter, or friction factor.

23. Branched System Distribution networks are multi-path pipelines
One topological structure is branching

24. Branched System Node Links Inflow = Outflow Energy is unique value
Head loss along line

25. Branched System
Head loss in each pipe
Common head at the node

26. Branched System
Continuity at the node

27. Branched System 4 Equations, 4 unknowns Non-linear so solve by
Newton-Raphson/Quasi-Linearization
Quadratic in unknown, so usually can find solution in just a few iterations

28. Looped System
Looped system is extension of branching where one or more pipes rejoin at a different node.

29. Looped System Nodes: Links Inflow = Outflow Energy Unique
Head loss along pipe
Head loss in any loop is zero
LOOP

30. Examples
Branched System
Loop System

31. Hydraulic Grade Line
Hydraulic grade line is a plot along a conduit profile of the sum of elevation and pressure head at a location.
It is where a free surface would exist if there were a piezometer installed in the pipeline

32. Energy Grade Line
Hydraulic grade line is a plot along a conduit profile of the sum of elevation, pressure, and velocity head at a location.

33. HGL/EGL