# Mathematics and Computation of Sediment Transport in Open Channels

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Mathematics and Computation of Sediment Transport in Open Channels Junping Wang Division of Mathematical Sciences National Science Foundation May 26, 2010

2 Sediment Transport and Life One major problem to people living downstream of Mount St. Helens is the high sedimentation rates resulting from stream erosion of the volcanic deposits. Streams are continuously downcutting channels, eroding their banks, and eating away at the avalanche and lahar deposits. This material is eventually transported downstream and deposited on the streambeds, decreasing the carrying capacity of the channels and increasing the chances of floods. USGS Photo by Lyn Topinka, February 22, 1982

3 Mathematical Models for Sediment Transport The computer/mathematical simulation of open channels includes the following major components: Flow calculation (coupled surface and subsurface fluid flow) Saint-Vernant equations Darcy flow Interface conditions that link the two systems Sediment calculation Sediment transport (math and computation) Bed change Bed material sorting

4 Components in Math Simulation

5 Surface Flow Model Conservative form of the Saint-Venant equations: where E = U t U = + F = S, h hu hv hu hu 2 +gh 2 /2 huv ; F = [E,G]; ; G = hv huv hv 2 +gh 2 /2

6 Saint-Venant Equations (cont d) S = 0 gh(s 0x S fx ) gh(s 0y S fy ) Force due to the change of bottom slop: (S 0x,S 0y ) = and friction (Manning s formula) S fx = n2 u u 2 +v 2 K 2 nh 4/3 +(R f I n ) ( f x, f y ), 1 u v ; S fy = n2 v u 2 +v 2 Knh 2 4/3 where n is the Manning s roughness coefficient..

7 Subsurface Flow The Darcy s law for one-dimensional, unsteady, vertical flow is given by ( ) h(θ) q = K(θ) +1. z The positive z-direction points upward. The mass conservation: θ t + q = 0, where θ is the volumetric water content. A 3D porous media flow model should be employed for a more accurate simulation of the subsurface flow.

8 Boundary and Initial Conditions: Surface Flow Boundary conditions on lateral sides are wall condition (fix boundary) free flow (moving boundary) given data (such as flow rate) at inflow boundary Initial condition for flux. Water depth and velocity are expected to satisfy the Manning s formula: S 0x = n2 u u 2 +v 2 Kn 2 ; S 0y = n2 v u 2 +v 2 h4/3 Kn 2h4/3

9 Surface and Subsurface Coupling Continuity of velocity in normal component: u n 1 +q n 2 = 0, I n is the infiltration rate which appears in the surface flow, as well as in the subsurface flow as a boundary condition at the bed z = z b (x,y,t). Force continuity: ρn t 1 σ(u,p) n 1 = s, where s is the pressure of the subsurface flow on the interface. Water depth is h(t,x,y) = z t z b so that s = ρgh(t,x,y).

10 The Green-Ampt Formula The model comes from mass conservation and the Darcy s law: ( ) h(t,z) q(t,z) = K +1, z b L(t) < z < z b, z θ t + q(t,z) = 0, z b L(t) < z < z b. z Dirichlet boundary at two ends: h(t,z b ) = h 0 (t) (surface water depth) h(t,z b L(t)) = ψ (capilarity) Neumann at the wet (moving) front L(t) θ = q(t,z w ). t

11 The Green-Ampt Formula with Uncertainty Solving the equation gives an ODE for the moving wet front: L (t) = ( (ψ +h 0 (t))l 1 (t)+1 ) K/ θ. Big uncertainty on Manning s coefficient n Hydraulic conductivity K Suction head ψ

12 Numerics for Surface Flow Integrate the governing equation over the control volume K gives U K t dx + Fdx = Sdx. K K Apply the divergence theorem one obtains U t dx + F nds = Sdx. K K With U K = 1 K K U K t K = Udx, one arrives at K K F nds + Sdx. K

13 Numerics for Surface Flow The boundary integrals involve the normal component of the flux variable which has to be determined. Suppose that there is already a way to determine these boundary fluxes. Then the numerical scheme can be written as U K = t K 3 i=1 F i n i l i + t Sdx. K K The boundary flux can be approximated by approximating the corresponding Riemann problem.

14 Modeling of Sediment Transport

15 Classification of Grain Classes The range of transport material, say between 0.002mm and 1048mm, is divided into N grain classes or bins that contain adjacent, nonoverlaping portions of the grain size spectrum. The default grain classes are based on a standard log base 2 scale where the upper bound of each class is twice the upper bound of the adjacent, but smaller class. All the particles in each grain class are presented by a single and representative grain size. We use the geometric mean of the grain class (the square root of the product of the upper and lower bounds) to represent the grain size for each bin.

16 Classification of Grain Classes For example, for the transport material ranging between smm and Smm, the grain class j contains particles of size between s2 j 1 mm to s2 j mm. The geometric mean of class j grains would be d j = s2 j 1/2. With s = 210 3, we see that the grain size d 1 = 0.002mm and grain size d 20 = 1048mm. In other words, the sediment material is divided into 20 grain classes for the ranges under consideration.

17 Sediment Transport in Suspended Zone For each grain class j, let C j be the average concentration for class size j in the suspended region. (hc j ) t + (huc j) x + (hvc j) y = Φ s,j, where the source/sink term Φ s,j is given by Φ s,j = ω β ( βp ) b,j q b,j C j, 6.11U k sj q b,j : bed-load transport capacity pb,j : portion of the size class j in the mixing layer

18 Sediment Transport in Suspended Zone β: a parameter given by: with β = 1 ( ) a z h h a h a a ( ) h z z dz ω z = κ κ = 0.4, U 2 +V2, U : shear velocity which will be discussed in coming Sections. z

19 Sediment Transport for Bed Load Bed load transport equation: (θ j (1 ε j )) t + (p j q b,j ) = 0, where ε j is the porosity of bed load for size class j. θ j : thickness of the mixing layer for size class j as a result of the bed-load (rolling of sediments along the river bed).

20 Sediment Transport for Total Bed Material Load The total bed material load simulation contains two components: the accumulation/dispersion of sediment from/to the suspended region the transport of sediments along the river bed. The first component comes from the suspended load: (1 ε) z b,j t = Φ s,j, where ε is the porosity of the bed material. The second component comes from the bed load. The combined version gives (z j (1 ε j )) t + (p j q t,j ) = Φ s,j.

21 Bed Material Sorting Update the bed elevation at time level t n+1 as follows: N z b (x,y,t n+1 ) = z b (x,y,t n )+ δ j (x,y,t n+1 ). How can we update the material gradation function p j? Amount of size class j sediment at time level t n+1 is given by j=1 A j = p j (t n )(z b (t n ) z ne )+ δ j (t n+1 ), and the total amount of sediment at time level t n+1 is N A = z b (x,y,t n ) z ne (x,y)+ δ j (x,y,t n+1 ). j=1 Thus, the material gradation at time level t n+1 is p j (x,y,t n+1 ) = A j A = p j(t n )(z b (t n ) z ne )+ δ j (t n+1 ) z b (t n ) z ne + N δ j=1 j (t n+1 ).

22 Bed-load Formulas Non-dimensional form: Φ B = Kalinske-Frijlink formula q B d (s 1)gd. q B = 2d 50 τb ρ exp ( 0.27(s 1)d50 ρg τ b Meyer-Peter formula: Φ B = 8(θ θ c ) 3/2, where θ : effective Shields parameter given by θ = τ b : effective shear stress θ c : critical Shields parameter ), τ b ρ(s 1)gd

23 Bed-load Formulas Einstein-Brown formula: Φ B = 40K(θ ) 3, where K = ν 2 (s 1)gd50 3 d ν. (s 1)g

24 Shields diagram Figure: Shields diagram that defines the critical value θ c as a function of the Reynolds number.

### ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts

ME 305 Fluid Mechanics I Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey csert@metu.edu.tr

### Open channel flow Basic principle

Open channel flow Basic principle INTRODUCTION Flow in rivers, irrigation canals, drainage ditches and aqueducts are some examples for open channel flow. These flows occur with a free surface and the pressure

### Hydraulics Prof. A. K. Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati. Module No. # 02 Uniform Flow Lecture No.

Hydraulics Prof. A. K. Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati Module No. # 02 Uniform Flow Lecture No. # 04 Computation of Uniform Flow (Part 02) Welcome to this

### Appendix 4-C. Open Channel Theory

4-C-1 Appendix 4-C Open Channel Theory 4-C-2 Appendix 4.C - Table of Contents 4.C.1 Open Channel Flow Theory 4-C-3 4.C.2 Concepts 4-C-3 4.C.2.1 Specific Energy 4-C-3 4.C.2.2 Velocity Distribution Coefficient

### Comparison of CFD models for multiphase flow evolution in bridge scour processes

Comparison of CFD models for multiphase flow evolution in bridge scour processes A. Bayón-Barrachina, D. Valero, F.J. Vallès Morán, P. A. López-Jiménez Dept. of Hydraulic and Environmental Engineering

### CHAPTER 9 CHANNELS APPENDIX A. Hydraulic Design Equations for Open Channel Flow

CHAPTER 9 CHANNELS APPENDIX A Hydraulic Design Equations for Open Channel Flow SEPTEMBER 2009 CHAPTER 9 APPENDIX A Hydraulic Design Equations for Open Channel Flow Introduction The Equations presented

### CIVE2400 Fluid Mechanics Section 2: Open Channel Hydraulics

CIVE400 Fluid Mechanics Section : Open Channel Hydraulics. Open Channel Hydraulics.... Definition and differences between pipe flow and open channel flow.... Types of flow.... Properties of open channels...

### ALL GROUND-WATER HYDROLOGY WORK IS MODELING. A Model is a representation of a system.

ALL GROUND-WATER HYDROLOGY WORK IS MODELING A Model is a representation of a system. Modeling begins when one formulates a concept of a hydrologic system, continues with application of, for example, Darcy's

### Fraternity & Sorority Academic Report Spring 2016

Fraternity & Sorority Academic Report Organization Overall GPA Triangle 17-17 1 Delta Chi 88 12 100 2 Alpha Epsilon Pi 77 3 80 3 Alpha Delta Chi 28 4 32 4 Alpha Delta Pi 190-190 4 Phi Gamma Delta 85 3

### Basic Equations, Boundary Conditions and Dimensionless Parameters

Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

### 1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

### Fraternity & Sorority Academic Report Fall 2015

Fraternity & Sorority Academic Report Organization Lambda Upsilon Lambda 1-1 1 Delta Chi 77 19 96 2 Alpha Delta Chi 30 1 31 3 Alpha Delta Pi 134 62 196 4 Alpha Sigma Phi 37 13 50 5 Sigma Alpha Epsilon

### BOTTOM SHEAR STRESS AND BED LOAD SEDIMENT TRANSPORT FORMULA FOR MODELING THE MORPHOLOGICAL CHANGE IN THE CANAL WATER INTAKE

BOTTOM SHEAR STRESS AND BED LOAD SEDIMENT TRANSPORT FORMULA FOR MODELING THE MORPHOLOGICAL CHANGE IN THE CANAL WATER INTAKE Made Mustika Wijaya, Suntoyo and Happy Ayu Damerianne Department of Ocean Engineering,

### Topic 8: Open Channel Flow

3.1 Course Number: CE 365K Course Title: Hydraulic Engineering Design Course Instructor: R.J. Charbeneau Subject: Open Channel Hydraulics Topics Covered: 8. Open Channel Flow and Manning Equation 9. Energy,

### Calculating resistance to flow in open channels

Alternative Hydraulics Paper 2, 5 April 2010 Calculating resistance to flow in open channels http://johndfenton.com/alternative-hydraulics.html johndfenton@gmail.com Abstract The Darcy-Weisbach formulation

### 2.0 BASIC CONCEPTS OF OPEN CHANNEL FLOW MEASUREMENT

2.0 BASIC CONCEPTS OF OPEN CHANNEL FLOW MEASUREMENT Open channel flow is defined as flow in any channel where the liquid flows with a free surface. Open channel flow is not under pressure; gravity is the

### M6a: Open Channel Flow (Manning s Equation, Partially Flowing Pipes, and Specific Energy)

M6a: Open Channel Flow (, Partially Flowing Pipes, and Specific Energy) Steady Non-Uniform Flow in an Open Channel Robert Pitt University of Alabama and Shirley Clark Penn State - Harrisburg Continuity

### FILTRATION. Water Treatment Course

FILTRATION Course, Zerihun Alemayehu FILTRATION Filtration involves the removal of suspended and colloidal particles from the water by passing it through a layer or bed of a porous granular material, such

### Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

### Environmental Data Management Programs

Hydrologic Engineering Centre (HEC) Software CD Collection of programs, developed by the U.S. Army Corps of Engineers Environmental Data Management Programs Name: HEC-DSS Package Purpose: Data Storage

### Period #16: Soil Compressibility and Consolidation (II)

Period #16: Soil Compressibility and Consolidation (II) A. Review and Motivation (1) Review: In most soils, changes in total volume are associated with reductions in void volume. The volume change of the

### Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

### Chapter 8: Flow in Pipes

Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks

### ENV5056 Numerical Modeling of Flow and Contaminant Transport in Rivers. Equations. Asst. Prof. Dr. Orhan GÜNDÜZ

ENV5056 Numerical Modeling of Flow and Contaminant Transport in Rivers Derivation of Flow Equations Asst. Prof. Dr. Orhan GÜNDÜZ General 3-D equations of incompressible fluid flow Navier-Stokes Equations

### Lecture Notes - Sediment Transport The Sediment Problem. 1. The Difference Between τ c and τ r. 2. The Different Applications of Critical Shear Stress

Lecture Notes - Sediment Transport The Sediment Problem At the end of the first lecture, we noted that our steep, nonlinear transport model depended on τ*, which is the ratio of the bed shear stress τ

### Chapter 9. Steady Flow in Open channels

Chapter 9 Steady Flow in Open channels Objectives Be able to define uniform open channel flow Solve uniform open channel flow using the Manning Equation 9.1 Uniform Flow in Open Channel Open-channel flows

### Floodplain Hydraulics! Hydrology and Floodplain Analysis Dr. Philip Bedient

Floodplain Hydraulics! Hydrology and Floodplain Analysis Dr. Philip Bedient Open Channel Flow 1. Uniform flow - Manning s Eqn in a prismatic channel - Q, V, y, A, P, B, S and roughness are all constant

### NUMERICAL ANALYSIS OF OPEN CHANNEL STEADY GRADUALLY VARIED FLOW USING THE SIMPLIFIED SAINT-VENANT EQUATIONS

TASK QUARTERLY 15 No 3 4, 317 328 NUMERICAL ANALYSIS OF OPEN CHANNEL STEADY GRADUALLY VARIED FLOW USING THE SIMPLIFIED SAINT-VENANT EQUATIONS WOJCIECH ARTICHOWICZ Department of Hydraulic Engineering, Faculty

### Simulating Sedimentation Model in Balarood Dam Reservoir Using CCHE2D Software

Bulletin of Environment, Pharmacology and Life Sciences Bull. Env. Pharmacol. Life Sci., Vol 4 [1] December 2014: 67-72 2014 Academy for Environment and Life Sciences, India Online ISSN 2277-1808 Journal

### 1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #2: Aquifers, Porosity, and Darcy s Law. Lake (Exposed Water Table)

1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #2: Aquifers, Porosity, and Darcy s Law Precipitation Infiltration Lake (Exposed Water Table) River Water table Saturated zone - Aquifer

### SEDIMENT TRANSPORT CAPACITY OF PRESSURE FLOW AT BRIDGES

SDIMNT TRANSORT CAACITY OF RSSUR FLOW AT BRIDGS Martin N.R. Jaeggi Consulting river engineer, Bergholzweg 22, 8123 bmatingen, Switzerland phone +41 44 980 36 26, fax +41 44 980 36 30, e-mail: jaeggi@rivers.ch

### Energy dissipation downstream of dams established in alluvial beds

Energy dissipation downstream of dams established in alluvial beds A. Sá Lopes, M.F. Proença & R. Maia Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto

### Hydraulic losses in pipes

Hydraulic losses in pipes Henryk Kudela Contents 1 Viscous flows in pipes 1 1.1 Moody Chart.................................... 2 1.2 Types of Fluid Flow Problems........................... 5 1.3 Minor

### CHAPTER II UNIFORM FLOW AND ITS FORMULAS MODULE 1. This experiment was designed to observe the characteristics of uniform flow in

CHAPTER II UNIFORM FLOW AND ITS FORMULAS MODULE 1 2.1 Introduction and Objective This experiment was designed to observe the characteristics of uniform flow in the teaching flume and to utilize the common

### PRINCIPLES OF SEDIMENT TRANSPORT RIVERS, ESTUARIES AND COASTAL SEAS. PART I: Edition 1993

PRINCIPLES OF SEDIMENT TRANSPORT IN RIVERS, ESTUARIES AND COASTAL SEAS PART I: Edition 1993 by Leo C. van Rijn Department of Physical Geography C.1 Other publications: Principles of Fluid Flow and Surface

### ME19b. SOLUTIONS. Feb. 11, 2010. Due Feb. 18

ME19b. SOLTIONS. Feb. 11, 21. Due Feb. 18 PROBLEM B14 Consider the long thin racing boats used in competitive rowing events. Assume that the major component of resistance to motion is the skin friction

### Chapter 13 OPEN-CHANNEL FLOW

Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Lecture slides by Mehmet Kanoglu Copyright The McGraw-Hill Companies, Inc. Permission required

### University of Maryland Fraternity & Sorority Life Spring 2015 Academic Report

University of Maryland Fraternity & Sorority Life Academic Report Academic and Population Statistics Population: # of Students: # of New Members: Avg. Size: Avg. GPA: % of the Undergraduate Population

### OPEN-CHANNEL FLOW. Free surface. P atm

OPEN-CHANNEL FLOW Open-channel flow is a flow of liquid (basically water) in a conduit with a free surface. That is a surface on which pressure is equal to local atmospheric pressure. P atm Free surface

### L r = L m /L p. L r = L p /L m

NOTE: In the set of lectures 19/20 I defined the length ratio as L r = L m /L p The textbook by Finnermore & Franzini defines it as L r = L p /L m To avoid confusion let's keep the textbook definition,

### Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics

Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.

### Catchment Scale Processes and River Restoration. Dr Jenny Mant Jenny@therrc.co.uk. The River Restoration Centre therrc.co.uk

Catchment Scale Processes and River Restoration Dr Jenny Mant Jenny@therrc.co.uk The River Restoration Centre therrc.co.uk 3 Main Catchment Elements Hydrology Energy associated with the flow of water affects

### Pressure drop in pipes...

Pressure drop in pipes... PRESSURE DROP CALCULATIONS Pressure drop or head loss, occurs in all piping systems because of elevation changes, turbulence caused by abrupt changes in direction, and friction

### Chapter 10. Open- Channel Flow

Updated: Sept 3 2013 Created by Dr. İsmail HALTAŞ Created: Sept 3 2013 Chapter 10 Open- Channel Flow based on Fundamentals of Fluid Mechanics 6th EdiAon By Munson 2009* *some of the Figures and Tables

### Hydraulics Laboratory Experiment Report

Hydraulics Laboratory Experiment Report Name: Ahmed Essam Mansour Section: "1", Monday 2-5 pm Title: Flow in open channel Date: 13 November-2006 Objectives: Calculate the Chezy and Manning coefficients

### ANALYSIS OF OPEN-CHANNEL VELOCITY MEASUREMENTS COLLECTED WITH AN ACOUSTIC DOPPLER CURRENT PROFILER

Reprint from RIVERTECH 96 Proceedings from the1st International Conference On New/Emerging Concepts for Rivers Organized by the International Water Resources Association Held September 22-26, 1996, Chicago,

### Urban Hydraulics. 2.1 Basic Fluid Mechanics

Urban Hydraulics Learning objectives: After completing this section, the student should understand basic concepts of fluid flow and how to analyze conduit flows and free surface flows. They should be able

### Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

### Experiment 3 Pipe Friction

EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A cross-sectional

### INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

### Lecture 11 Boundary Layers and Separation. Applied Computational Fluid Dynamics

Lecture 11 Boundary Layers and Separation Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Overview Drag. The boundary-layer

### MIKE 21 FLOW MODEL HINTS AND RECOMMENDATIONS IN APPLICATIONS WITH SIGNIFICANT FLOODING AND DRYING

1 MIKE 21 FLOW MODEL HINTS AND RECOMMENDATIONS IN APPLICATIONS WITH SIGNIFICANT FLOODING AND DRYING This note is intended as a general guideline to setting up a standard MIKE 21 model for applications

### Emergency Spillways (Sediment basins)

Emergency Spillways (Sediment basins) DRAINAGE CONTROL TECHNIQUE Low Gradient Velocity Control Short-Term Steep Gradient Channel Lining Medium-Long Term Outlet Control Soil Treatment Permanent [1] [1]

### Scour and Scour Protection

Design of Maritime Structures Scour and Scour Protection Steven A. Hughes, PhD, PE Coastal and Hydraulics Laboratory US Army Engineer Research and Development Center Waterways Experiment Station 3909 Halls

### Index-Velocity Rating Development (Calibration) for H-ADCP Real-Time Discharge Monitoring in Open Channels

Index-Velocity Rating Development (Calibration) for H-ADCP Real-Time Discharge Monitoring in Open Channels Hening Huang Teledyne RD Instruments, Inc., 14020 Stowe Drive, Poway, CA. 92064, USA (Tel: 858-842-2600,

### Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary

### Experiment (13): Flow channel

Introduction: An open channel is a duct in which the liquid flows with a free surface exposed to atmospheric pressure. Along the length of the duct, the pressure at the surface is therefore constant and

### The value of the wastewater flow used for sewer design is the daily peak flow. This can be estimated as follows:

This Section presents the theory of simplified sewer design. Firstly, in Section 2.1, the peak daily wastewater flow in the length of sewer being designed is described. Section 2.2 presents the trigonometric

### Civil Engineering Hydraulics Open Channel Flow. Adult: Where s your costume? What are you supposed to be?

Civil Engineering Hydraulics Calvin: Trick or treat! Adult: Where s your costume? What are you supposed to be? Calvin: I m yet another resource-consuming kid in an overpopulated planet, raised to an alarming

### CITY UTILITIES DESIGN STANDARDS MANUAL

CITY UTILITIES DESIGN STANDARDS MANUAL Book 2 (SW) SW9 June 2015 SW9.01 Purpose This Chapter provides information for the design of open channels for the conveyance of stormwater in the City of Fort Wayne.

### Open Channel Flow. M. Siavashi. School of Mechanical Engineering Iran University of Science and Technology

M. Siavashi School of Mechanical Engineering Iran University of Science and Technology W ebpage: webpages.iust.ac.ir/msiavashi Email: msiavashi@iust.ac.ir Landline: +98 21 77240391 Fall 2013 Introduction

### Basic Principles of Channel Design

United States Department of Agriculture Natural Resources Conservation Service Stream Restoration Design Chapter 7 Basic Principles of Channel Design Issued August 2007 Cover photo: Where modification

### Package rivr. October 16, 2015

Type Package Package rivr October 16, 2015 Title Steady and Unsteady Open-Channel Flow Computation Version 1.1 Date 2015-10-15 Author Michael C Koohafkan [aut, cre] Maintainer Michael C Koohafkan

### Effect of Aspect Ratio on Laminar Natural Convection in Partially Heated Enclosure

Universal Journal of Mechanical Engineering (1): 8-33, 014 DOI: 10.13189/ujme.014.00104 http://www.hrpub.org Effect of Aspect Ratio on Laminar Natural Convection in Partially Heated Enclosure Alireza Falahat

### Abaqus/CFD Sample Problems. Abaqus 6.10

Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel

### For Water to Move a driving force is needed

RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND

### USSD Workshop on Dam Break Analysis Applied to Tailings Dams

USSD Workshop on Dam Break Analysis Applied to Tailings Dams Antecedents Newtonian / non-newtonian flows Available models that allow the simulation of non- Newtonian flows (tailings) Other models used

### 7.2.4 Seismic velocity, attenuation and rock properties

7.2.4 Seismic velocity, attenuation and rock properties Rock properties that affect seismic velocity Porosity Lithification Pressure Fluid saturation Velocity in unconsolidated near surface soils (the

### Module 7: Hydraulic Design of Sewers and Storm Water Drains. Lecture 7 : Hydraulic Design of Sewers and Storm Water Drains

1 P age Module 7: Hydraulic Design of Sewers and Storm Water Drains Lecture 7 : Hydraulic Design of Sewers and Storm Water Drains 2 P age 7.1 General Consideration Generally, sewers are laid at steeper

### CE 3500 Fluid Mechanics / Fall 2014 / City College of New York

1 Drag Coefficient The force ( F ) of the wind blowing against a building is given by F=C D ρu 2 A/2, where U is the wind speed, ρ is density of the air, A the cross-sectional area of the building, and

### Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

### HEC-RAS. River Analysis System. Applications Guide. Version 4.1 January 2010. US Army Corps of Engineers Hydrologic Engineering Center CPD-70

US Army Corps of Engineers Hydrologic Engineering Center HEC-RAS HEC-RAS River Analysis System Applications Guide Version 4.1 January 2010 Approved for Public Release. Distribution Unlimited CPD-70 REPORT

### Performance Estimation of Water Thermal Energy Storage Tank by Using Simplified Simulation

Performance Estimation of Water Thermal Energy Storage Tank by Using Simplified Simulation M. Kubota, K. Sagara, T. Yamanaka, H. Kotani Division of Global Architecture, Graduate School of Engineering,

### The Hydrologic Engineering Center Training Course on

The Hydrologic Engineering Center Training Course on SEDIMENT TRANSPORT ANALYSIS WITH HEC-RAS Davis, California Course Objectives This course is intended to prepare engineers to perform studies using various

### WEPP MODEL APPLICATIONS FOR EVALUATIONS OF BEST MANAGEMENT PRACTICES

WEPP MODEL APPLICATIONS FOR EVALUATIONS OF BEST MANAGEMENT PRACTICES D.C. FLANAGAN 1, W.J. ELLIOT 2, J.R. FRANKENBERGER 3, C. HUANG 4 1 USDA-Agricultural Research Service, National Soil Erosion Research

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### Background Why Evaluate the Physical Characteristics of a Stream? Pebble Count Method

Background Why Evaluate the Physical Characteristics of a Stream? A stream is the carpenter of its own edifice Stream channels and floodplains are constantly adjusting to the amount of water and sediment

### 4.3 Results... 27 4.3.1 Drained Conditions... 27 4.3.2 Undrained Conditions... 28 4.4 References... 30 4.5 Data Files... 30 5 Undrained Analysis of

Table of Contents 1 One Dimensional Compression of a Finite Layer... 3 1.1 Problem Description... 3 1.1.1 Uniform Mesh... 3 1.1.2 Graded Mesh... 5 1.2 Analytical Solution... 6 1.3 Results... 6 1.3.1 Uniform

### Lecture 22 Example Culvert Design Much of the following is based on the USBR technical publication Design of Small Canal Structures (1978)

Lecture 22 Example Culvert Design Much of the following is based on the USBR technical publication Design of Small Canal Structures (1978) I. An Example Culvert Design Design a concrete culvert using the

### Investigation of Effect of Changes in Dimension and Hydraulic of Stepped Spillways for Maximization Energy Dissipation

World Applied Sciences Journal 8 (): 6-67, 0 ISSN 88-495 IDOSI Publications, 0 DOI: 0.589/idosi.wasj.0.8.0.49 Investigation of Effect of Changes in Dimension and Hydraulic of Stepped Spillways for Maximization

### Commercial CFD Software Modelling

Commercial CFD Software Modelling Dr. Nor Azwadi bin Che Sidik Faculty of Mechanical Engineering Universiti Teknologi Malaysia INSPIRING CREATIVE AND INNOVATIVE MINDS 1 CFD Modeling CFD modeling can be

### Laminar to Turbulent Transition in Cylindrical Pipes

Course I: Fluid Mechanics & Energy Conversion Laminar to Turbulent Transition in Cylindrical Pipes By, Sai Sandeep Tallam IIT Roorkee Mentors: Dr- Ing. Buelent Unsal Ms. Mina Nishi Indo German Winter Academy

### Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any

Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass

### Hydraulic Jumps and Non-uniform Open Channel Flow, Course #507. Presented by: PDH Enterprises, LLC PO Box 942 Morrisville, NC 27560 www.pdhsite.

Hydraulic Jumps and Non-uniform Open Channel Flow, Course #507 Presented by: PDH Enterprises, LLC PO Box 942 Morrisville, NC 27560 www.pdhsite.com Many examples of open channel flow can be approximated

### SIMULATION OF SEDIMENT TRANSPORT AND CHANNEL MORPHOLOGY CHANGE IN LARGE RIVER SYSTEMS. Stephen H. Scott 1 and Yafei Jia 2

US-CHINA WORKSHOP ON ADVANCED COMPUTATIONAL MODELLING IN HYDROSCIENCE & ENGINEERING September 19-21, Oxford, Mississippi, USA SIMULATION OF SEDIMENT TRANSPORT AND CHANNEL MORPHOLOGY CHANGE IN LARGE RIVER

### Program COLANY Stone Columns Settlement Analysis. User Manual

User Manual 1 CONTENTS SYNOPSIS 3 1. INTRODUCTION 4 2. PROBLEM DEFINITION 4 2.1 Material Properties 2.2 Dimensions 2.3 Units 6 7 7 3. EXAMPLE PROBLEM 8 3.1 Description 3.2 Hand Calculation 8 8 4. COLANY

### Solutions to Homework 10

Solutions to Homework 1 Section 7., exercise # 1 (b,d): (b) Compute the value of R f dv, where f(x, y) = y/x and R = [1, 3] [, 4]. Solution: Since f is continuous over R, f is integrable over R. Let x

### LECTURE 6: Fluid Sheets

LECTURE 6: Fluid Sheets The dynamics of high-speed fluid sheets was first considered by Savart after his early work on electromagnetism with Biot, and was subsequently examined in a series of papers by

### Part 654 Stream Restoration Design National Engineering Handbook

United States Department of Agriculture Natural Resources Conservation Service Stream Restoration Design Chapter 6 Issued August 007 Cover photo: Stream hydraulics focus on bankfull frequencies, velocities,

### College of the Holy Cross, Spring 2009 Math 373, Partial Differential Equations Midterm 1 Practice Questions

College of the Holy Cross, Spring 29 Math 373, Partial Differential Equations Midterm 1 Practice Questions 1. (a) Find a solution of u x + u y + u = xy. Hint: Try a polynomial of degree 2. Solution. Use

### On the Determination of the Stable Bed Slope of a Channel Using Mathematical Model

On the Determination of the Stable Bed Slope of a Channel Using Mathematical Model František Křovák Department of Land Use and Improvement, Faculty of Forestry and Environment, Czech University of Life

### MATLAB AS A PROTOTYPING TOOL FOR HYDRONIC NETWORKS BALANCING

MATLAB AS A PROTOTYPING TOOL FOR HYDRONIC NETWORKS BALANCING J. Pekař, P. Trnka, V. Havlena* Abstract The objective of this note is to describe the prototyping stage of development of a system that is

### CHAPTER 5 OPEN-CHANNEL FLOW

CHAPTER 5 OPEN-CHANNEL FLOW 1. INTRODUCTION 1 Open-channel flows are those that are not entirely included within rigid boundaries; a part of the flow is in contract with nothing at all, just empty space

### HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS

HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS P.R.Hatwar 1, Bhojraj N. Kale 2 1, 2 Department of Mechanical Engineering Dr. Babasaheb Ambedkar College of Engineering & Research,

### HEAT TRANSFER CODES FOR STUDENTS IN JAVA

Proceedings of the 5th ASME/JSME Thermal Engineering Joint Conference March 15-19, 1999, San Diego, California AJTE99-6229 HEAT TRANSFER CODES FOR STUDENTS IN JAVA W.J. Devenport,* J.A. Schetz** and Yu.

### CHAPTER 2 HYDRAULICS OF SEWERS

CHAPTER 2 HYDRAULICS OF SEWERS SANITARY SEWERS The hydraulic design procedure for sewers requires: 1. Determination of Sewer System Type 2. Determination of Design Flow 3. Selection of Pipe Size 4. Determination

### Open Channel Flow Measurement Weirs and Flumes

Open Channel Flow Measurement Weirs and Flumes by Harlan H. Bengtson, PhD, P.E. 1. Introduction Your Course Title Here Measuring the flow rate of water in an open channel typically involves some type of