CE 3372 Water Systems Design Closed Conduit Hydraulics-I

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

Diagram

Diagram Suction Side Lift Station Discharge Side

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.

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.

Energy Equation 2 1

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

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)

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)

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

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!

Hazen-Williams HW Head Loss Discharge Form

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

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

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

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

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

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

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

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

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

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

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

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

Branched System Continuity at the node

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

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

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

Examples Branched System Loop System

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

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.

HGL/EGL