Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Closed Conduit Flow CEE 332

Design Project Introduction ä How many drinking water treatment plants are located in Ithaca? ä How did Cornell obtain water when Fall Creek was contaminated by a diesel fuel spill? ä What are the advantages/disadvantages of the various treatment plants? ä How many drinking water treatment plants are located in Ithaca? ä How did Cornell obtain water when Fall Creek was contaminated by a diesel fuel spill? ä What are the advantages/disadvantages of the various treatment plants?

Economics of Plant Location ä What is the elevation of Cayuga Lake? 382 feet (116.4 m) ä Elevation of dam on Fall Creek where Cornell gets its water? 856 feet (260.9 m) ä How much does it cost to lift 1 m 3 of water from Cayuga Lake to the Cornell Water Treatment Plant? ä What is the elevation of Cayuga Lake? 382 feet (116.4 m) ä Elevation of dam on Fall Creek where Cornell gets its water? 856 feet (260.9 m) ä How much does it cost to lift 1 m 3 of water from Cayuga Lake to the Cornell Water Treatment Plant?

Economic Advantage of Altitude Work = N*m

Cost of Water from Bolton Point

Integration of Water Supply Systems ä How would you operate the local plants to minimize cost?

Limitation of Cornell Water Treatment Plant ä The Plant has a treatment capacity of 3.0 to 3.6 million gallons per day (MGD) ä Under normal operating conditions, the raw water from the upstream intake flows by gravity through a 16-inch diameter pipe to the treatment chambers at the Filter Plant ä At approximately 2 MGD it is necessary to turn on the supplemental pump ä The Plant has a treatment capacity of 3.0 to 3.6 million gallons per day (MGD) ä Under normal operating conditions, the raw water from the upstream intake flows by gravity through a 16-inch diameter pipe to the treatment chambers at the Filter Plant ä At approximately 2 MGD it is necessary to turn on the supplemental pump

Design Project Gravity feed Raw Water Pump Station Fall Creek Filter Plant Clear Well Finished Water Pump Station Ground Tanks Johnson Museum PRV State Pump Station Low Pressure Distribution Grid High Pressure Distribution Grid Elevated Tank

How could I get more water through the gravity pipe? ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä ä

Theory? ä How would you Quantify your Alternatives? ä Why isn’t there a simple equation? ä How would you Quantify your Alternatives? ä Why isn’t there a simple equation?

Closed Conduit Flow ä Energy equation ä EGL and HGL ä Head loss ä major losses ä minor losses ä Non circular conduits ä Energy equation ä EGL and HGL ä Head loss ä major losses ä minor losses ä Non circular conduits 

Conservation of Energy ä Kinetic, potential, and thermal energy hL =hL = hL =hL = h p = ht =ht = ht =ht = head supplied by a pump head given to a turbine head loss between sections 1 and 2 Cross section 2 is ____________ from cross section 1! downstream

Energy Equation Assumptions ä Pressure is _________ in both cross sections ä pressure changes are due to elevation only ä section is drawn perpendicular to the streamlines (otherwise the _______ energy term is incorrect) ä Constant ________at the cross section ä _______ flow ä Pressure is _________ in both cross sections ä pressure changes are due to elevation only ä section is drawn perpendicular to the streamlines (otherwise the _______ energy term is incorrect) ä Constant ________at the cross section ä _______ flow hydrostatic density Steady kinetic

EGL (or TEL) and HGL ä The energy grade line must always slope ___________ (in direction of flow) unless energy is added (pump) ä The decrease in total energy represents the head loss or energy dissipation per unit weight ä EGL and HGL are coincident and lie at the free surface for water at rest (reservoir) ä If the HGL falls below the point in the system for which it is plotted, the local pressures are _____ ____ __________ ______ ä The energy grade line must always slope ___________ (in direction of flow) unless energy is added (pump) ä The decrease in total energy represents the head loss or energy dissipation per unit weight ä EGL and HGL are coincident and lie at the free surface for water at rest (reservoir) ä If the HGL falls below the point in the system for which it is plotted, the local pressures are _____ ____ __________ ______ velocity head velocity head elevation head (w.r.t. datum) elevation head (w.r.t. datum) pressure head (w.r.t. reference pressure) pressure head (w.r.t. reference pressure) downward lower than reference pressure

Energy equation z = 0 pump Energy Grade Line Hydraulic G L velocity head pressure head elevation datum z static head

Bernoulli Equation Assumption ä _________ (viscosity can’t be a significant parameter!) ä Along a __________ ä ______ flow ä Constant ________ ä _________ (viscosity can’t be a significant parameter!) ä Along a __________ ä ______ flow ä Constant ________ density Steady streamline Frictionless

Pipe Flow: Review ä We have the control volume energy equation for pipe flow. ä We need to be able to predict the head loss term. ä How do we predict head loss? __________ _______. ä We have the control volume energy equation for pipe flow. ä We need to be able to predict the head loss term. ä How do we predict head loss? __________ _______. dimensional analysis

Pipe Flow Energy Losses Horizontal pipe Dimensional Analysis Darcy-Weisbach equation

Friction Factor : Major losses ä Laminar flow ä Hagen-Poiseuille ä Turbulent (Smooth, Transition, Rough) ä Colebrook Formula ä Moody diagram ä Swamee-Jain ä Laminar flow ä Hagen-Poiseuille ä Turbulent (Smooth, Transition, Rough) ä Colebrook Formula ä Moody diagram ä Swamee-Jain

Laminar Flow Friction Factor Slope of ___ on log-log plot Hagen-Poiseuille Darcy-Weisbach

Turbulent Pipe Flow Head Loss ä ___________ to the length of the pipe ä ___________ to the square of the velocity (almost) ä ________ with surface roughness ä Is a function of density and viscosity ä Is __________ of pressure ä ___________ to the length of the pipe ä ___________ to the square of the velocity (almost) ä ________ with surface roughness ä Is a function of density and viscosity ä Is __________ of pressure Proportional Increases independent

Smooth, Transition, Rough Turbulent Flow ä Hydraulically smooth pipe law (von Karman, 1930) ä Rough pipe law (von Karman, 1930) ä Transition function for both smooth and rough pipe laws (Colebrook) ä Hydraulically smooth pipe law (von Karman, 1930) ä Rough pipe law (von Karman, 1930) ä Transition function for both smooth and rough pipe laws (Colebrook) (used to draw the Moody diagram)

Moody Diagram E+031E+041E+051E+061E+071E+08 Re friction factor laminar smooth

Swamee-Jain ä 1976 ä limitations   /D < 2 x ä Re >3 x 10 3 ä less than 3% deviation from results obtained with Moody diagram ä easy to program for computer or calculator use ä 1976 ä limitations   /D < 2 x ä Re >3 x 10 3 ä less than 3% deviation from results obtained with Moody diagram ä easy to program for computer or calculator use no f Each equation has two terms. Why?

Pipe roughness pipe material pipe roughness   (mm) glass, drawn brass, copper commercial steel or wrought iron asphalted cast iron 0.12 galvanized iron 0.15 cast iron 0.26 concrete rivet steel corrugated metal 45 PVC 0.12

Solution Techniques l find head loss given (D, type of pipe, Q) l find flow rate given (head, D, L, type of pipe) l find pipe size given (head, type of pipe,L, Q)

Exponential Friction Formulas ä Commonly used in commercial and industrial settings ä Only applicable over _____ __ ____ collected ä Hazen-Williams exponential friction formula ä Commonly used in commercial and industrial settings ä Only applicable over _____ __ ____ collected ä Hazen-Williams exponential friction formula C = Hazen-Williams coefficient range of data

Head loss: Hazen-Williams Coefficient CCondition 150PVC 140Extremely smooth, straight pipes; asbestos cement 130Very smooth pipes; concrete; new cast iron 120Wood stave; new welded steel 110Vitrified clay; new riveted steel 100Cast iron after years of use 95Riveted steel after years of use 60-80Old pipes in bad condition CCondition 150PVC 140Extremely smooth, straight pipes; asbestos cement 130Very smooth pipes; concrete; new cast iron 120Wood stave; new welded steel 110Vitrified clay; new riveted steel 100Cast iron after years of use 95Riveted steel after years of use 60-80Old pipes in bad condition

Hazen-Williams vs Darcy-Weisbach ä Both equations are empirical ä Darcy-Weisbach is rationally based, dimensionally correct, and ________. ä Hazen-Williams can be considered valid only over the range of gathered data. ä Hazen-Williams can’t be extended to other fluids without further experimentation. ä Both equations are empirical ä Darcy-Weisbach is rationally based, dimensionally correct, and ________. ä Hazen-Williams can be considered valid only over the range of gathered data. ä Hazen-Williams can’t be extended to other fluids without further experimentation. preferred EGL

Head Loss: Minor Losses ä Head loss due to outlet, inlet, bends, elbows, valves, pipe size changes ä Losses due to expansions are greater than losses due to contractions ä Losses can be minimized by gradual transitions ä Head loss due to outlet, inlet, bends, elbows, valves, pipe size changes ä Losses due to expansions are greater than losses due to contractions ä Losses can be minimized by gradual transitions

Minor Losses ä Most minor losses can not be obtained analytically, so they must be measured ä Minor losses are often expressed as a loss coefficient, K, times the velocity head. ä Most minor losses can not be obtained analytically, so they must be measured ä Minor losses are often expressed as a loss coefficient, K, times the velocity head. High Re

Head Loss due to Sudden Expansion: Conservation of Energy 1 2 z 1 = z 2 What is p 1 - p 2 ?

Head Loss due to Sudden Expansion: Conservation of Momentum Pressure is applied over all of section 1. Momentum is transferred over area corresponding to upstream pipe diameter. V 1 is velocity upstream. Pressure is applied over all of section 1. Momentum is transferred over area corresponding to upstream pipe diameter. V 1 is velocity upstream. 1 2 A1A1A1A1 A2A2A2A2 x Apply in direction of flow Neglect surface shear Divide by (A 2  )

Head Loss due to Sudden Expansion Energy Momentum Mass

Contraction V1V1 V2V2 EGL HGL vena contracta ä losses are reduced with a gradual contraction

Entrance Losses ä Losses can be reduced by accelerating the flow gradually and eliminating the vena contracta

Head Loss in Bends ä Head loss is a function of the ratio of the bend radius to the pipe diameter (R/D) ä Velocity distribution returns to normal far downstream ä Head loss from a series of bends is not the number of bends times the loss through a single bend ä Head loss is a function of the ratio of the bend radius to the pipe diameter (R/D) ä Velocity distribution returns to normal far downstream ä Head loss from a series of bends is not the number of bends times the loss through a single bend High pressure Low pressure Possible separation from wall D R R

Head Loss in Valves ä Function of valve type and valve position ä The complex flow path through valves often results in high head loss ä What is the maximum value that K v can have? ä Function of valve type and valve position ä The complex flow path through valves often results in high head loss ä What is the maximum value that K v can have?

Questions ä What is the head loss when a pipe enters a reservoir? ä Draw the EGL and HGL ä What is the head loss when a pipe enters a reservoir? ä Draw the EGL and HGL V EGL HGL

Questions ä Can the Darcy-Weisbach equation and Moody Diagram be used for fluids other than water? _____ Yes No Yes What about the Hazen-Williams equation? ___ Do smooth pipes have head loss? _____ Is it possible to decrease the head loss in a pipe by installing a smooth liner? ______

Example D=40 cm L=1000 m D=40 cm L=1000 m D=20 cm L=500 m D=20 cm L=500 m valve 100 m Find the discharge, Q. What additional information do you need? Find the discharge, Q. What additional information do you need?

Non-Circular Conduits: Hydraulic Radius Concept ä A is cross sectional area ä P is wetted perimeter ä R h is the “Hydraulic Radius” (Area/Perimeter) ä Don’t confuse with radius! ä A is cross sectional area ä P is wetted perimeter ä R h is the “Hydraulic Radius” (Area/Perimeter) ä Don’t confuse with radius! For a pipe We can use Moody diagram or Swamee Jain with D = 4R!

What is a mgd? ä Million Gallons per Day