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CE 3372 Water Systems Design CLOSED CONDUIT HYDRAULICS Review! Difference between an Easement and ROW What is a plat? Explain MUD Explain Bond 3 resources for design Outline Hydraulics/Characteristics Energy Equation Diagram EGL and HGL Head Loss Models Moody Chart Direct Method Hydraulics Definition Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. -Wikipedia Water Characteristics Water moves from higher to lower energy (Path of least resistance) Gravity flow Pumps can be used to increase the energy to move water to a higher level or over a barrier Flow of water has resistance The flow rate (Q) of water moving past a cross section is equal to the area (A) of the cross section multiplied by the velocity (v) Mean Section Velocity In most engineering contexts, the mean section velocity is the ratio of the volumetric discharge and cross sectional area. Q V A The velocity distribution in a section is important in determining frictional losses in a conduit. Flows 1-Dimensional Flow The change of fluid variables (velocity, temp, etc.) in one direction dominates over the change in the other two directions. 2-D and 3-D Change in fluid variables is significant in multiple directions Water is almost always a 3-dimensional flow However, 3D is difficult to quantify and model Most analysis simplifies water to 1-D or 2-D flow Coefficients, model calibration and experience are used to account for simplifying assumptions z y x CONTINUITY CONTINUITY 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. hp = head supplied by a pump ht = head given to a turbine h = mechanical energy converted to thermal L Energy Equation Assumptions Pressure is hydrostatic in both cross sections Pressure changes are due only to elevation Fluid is incompressible Density is constant at the cross section Flow is steady Diagram Diagram Lift Station Suction Side Discharge Side Energy Equation 2 1 Energy Grade Line EGL is a line that represents the elevation of energy head of water flowing in a conduit. It is the sum of the elevation, pressure, and velocity head at a location. Drawn above HGL at a distance equal to the velocity head Hydraulic Grade Line HGL is a line that represents the surface/profile of water flowing in partially full pipe. If pipe is under pressure, flowing full the HGL rises to where a free surface would exist if there were a piezometer installed in the pipeline HGL/EGL Head Loss Darcy-Weisbach Hazen-Williams Chezy-Mannings Darcy-Weisbach Frictional loss (hf) is proportional to Length and Velocity^2 hf is 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 for CIRCULAR conduits Hazen-Williams Frictional loss (hf) proportional to Length, Velocity^(1.85) Loss is inversely proportional to Cross-section area (as hydraulic radius) Loss coefficient (Ch) depends on Pipe material and finish Turbulent flow only (Re>4000) • 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 PERIMET ER 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 Head Loss Major Friction Losses - pipe walls. Occur in all pipes Dependent on pipe and fluid properties Minor Losses - outlets, inlets, expansions, contractions, valves and any other geometrical obstructions in the fluid flow. Mostly caused by disturbances in flow that result in increased turbulence and motion in directions other than the general direction of flow 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 Chart Head loss for given discharge, diameter, material Discharge given head loss, diameter, material Diameter given discharge, head loss, material Direct (Swamee-Jain) Equations An alternative to the Moody chart are regression equations that allow direct computation of discharge, diameter, or friction factor. Head Head – Energy per unit weight of water!! Energy = KE + PE =[ velocity + (elevation + pressure) ] Piezometer