# GROUNDWATER FLOW NETS Graphical Solutions to the Flow Equations. One family of curves are flow lines Another family of curves are equipotential lines

Save this PDF as:

Size: px
Start display at page:

Download "GROUNDWATER FLOW NETS Graphical Solutions to the Flow Equations. One family of curves are flow lines Another family of curves are equipotential lines"

## Transcription

1 GROUNDWTER FLOW NETS Graphical Solutions to the Flow Equations One family of curves are flow lines nother family of curves are equipotential lines B C D E Boundary Conditions B and DE - constant head BC - atmospheric P - phreatic surface CD - atmospheric P - seepage face E - no-flow Basic ssumptions for Drawing a Flow Net: - material ones are homogeneous - isotropic hydraulic conductivity -fully saturated - flow is steady, laminar, continuous, irrotational - fluid is constant density - Darcy's Law is valid -Drawn parallel to flow Flow into the one between 2 flow lines = flow out of the one 1

2 Rules for drawing flow nets - equipotential lines parallel constant head boundaries - flow lines parallel no-flow boundaries - streamlines are perpendicular to equipotential lines - equipotential lines are perpendicular to no-flow boundaries - the aspect ratio of the shapes formed by intersecting stream and equipotential lines must be constant e.g. if squares are formed, the flow net must be squares throughout (areas near boundaries are eceptions) Each flow tube will represent the same discharage: Q = i Procrastination is common. It is best to "dive in" and begin drawing. Just keep an eraser handy and do not hesitate to revise! Draw a very simple flow net: H 1 H 2 - equipotential lines parallel constant head boundaries - flow lines parallel no-flow boundaries - streamlines are perpendicular to equipotential lines - equipotential lines are perpendicular to no-flow boundaries - Interescting equipotential and flow lines form squares 2

3 Here is a simple net with: 4 stream lines 3 flow tubes n f 6 equipotential lines 5 head drops n d Rate of flow through 1 square: q = i a headloss in is H i = l n since is square w = l H1 H n Total Q per unit width = d d 2 = H n d a = w (1) so for a unit width q = H n d Q = H is total head loss n Hw q = l n f = qnf H Consider an nd application: d sand filter has its base at 0 meters and is 10 meters high. It is the same from top to bottom. plan view, to-scale diagram of it is shown below. There is an impermeable pillar in the center of the filter. Reservoirs on the left and right are separated from the sand by a screen that only crosses a portion of the reservoir wall. The head in the inlet reservoir on the left is 20 m and the outlet reservoir on the right is 12m. Properties of the sand are: 10-3 m/s S=110-3 SY=0.2. Draw and label a flow net. Calculate the discharge through the system using units of meters and seconds. What is the head at the location of the * at the top of the tank? What is the pressure at that location? - equipotential lines parallel constant head boundaries - flow lines parallel no-flow boundaries - streamlines are perpendicular to equipotential lines - equipotential lines are perpendicular to no-flow boundaries - form squares by intersecting stream and equipotential lines 3

4 25m Try this before net class = 0.53m/day Draw the flow net Calculate Q What is the maimum gradient? What are the head and pressure at the *? * 15m We can use the flow net to identify areas where critical gradients may occur and determine the magnitude of the gradient at those locations - equipotential lines parallel constant head boundaries -- flow lines parallel no-flow boundaries -- streamlines are perpendicular to equipotential lines - equipotential lines are perpendicular to no-flow boundaries - form squares by intersecting stream and equipotential lines Stress caused in soil by flow = j = iγ w If flow is upward, stress is resisted by weight of soil If j eceeds submerged weight of soil, soil will be uplifted For uplift to occur j > γ submerged soil = γ t - γ w where: γ t - unit saturated weight of soil γ w - unit weight of water then for uplift to occur: i γ w > (γ t - γ w ) the critical gradient for uplift then is: What is the critical gradient for a soil with 30% porosity and a particle density of 2.65 g/cc (165 lb/ft 3 )? γ t = 0.7 (165 lb/ft 3 ) (62.4 lb/ft 3 ) = (134 lb/ft 3 ) We can use the flow net to identify areas where critical gradients may occur and determine i critical = the 134 magnitude lb/ft of the lb/ft gradient 3 = 1.15at those locations 62.4 lb/ft 3 i critical γ t γ w = γ w 4

5 What is the flu under the sheet pile wall if =2ft/day? Will piping occur? f n Q = qnf = H n d PLN VIEW FLOW NET BY CONTOURING USING FIELD HEDS ND DRWING FLOW LINES PERPENDICULR: can't assume constant or b assuming no inflow from above or below, we can evaluate relative T: Q = V1 = BV2 Δh Δh = BB l lb B B l = = l l l B B B B = wb (b = aquifer thickness) wbbbl = B w blb b wbl T = = b w l T lb l a w b 96 B w a "Irregularities" in "Natural" flow nets varying varying flow thickness recharge/discharge vertical components of flow w Nature's flow nets provide B l =125*200=25000 w clues to l B = 33*100= 3300 T geohydrologic conditions B B B B ~ 8 times T B Is longer the higher narrower transmissivity shape indicates this diagram higher T, at a shorter B? wider shape, low T 5

6 NISOTROPY: How do anisotropic materials influence flownets? Conductivity Ellipsoid: s Flow lines will not meet equipotential right angles, but they will if we transform the domain into an equivalent isotropic section, draw the flow net, and transform it back. For the material above, we would either epand dimensions or compress dimensions To do this we establish revised coordinates In the case where is smaller: stretch ' = or shrink OR ' = ' = ' = Most noticeable is the lack of orthogonality when the net is transformed back Sie of the transformed region depends on whether you choose to shrink or epand but the geometry is the same. To calculate Q or V, work with the transformed sections But use "transformed" ' = 6

7 If the pond elevation is 8m, ground surface is 6m, the drain is at 2m (with 1m diameter, so bottom is at 1.5m and top is at 2.5m), bedrock is at 0m, is 16m/day and 1m/day, what is the flow at the drain? Transform the flow field for this system and draw a flow net. drain pond bedrock surface ' = ' = ' = ' = If you want to know flow direction at a specific point within an anisotropic medium, undertake the following construction on an equipotential line: 1 - Draw an INVERSE ellipse for semi-aes 1 1 and 2 - Draw the direction of the hydraulic gradient through the center of the ellipse and note where it intercepts the ellipse 3 - Draw the tangent to the ellipse at this point 4 - Flow direction is perpendicular to this line try it above for = 16ft / day and = 90ft 4ft / day 100ft 7

8 Toth developed a classic application of the Steady State flow equations for a Vertical 2D section from a stream to a divide His solutions describe flow nets both are methods for solving the flow equations he solved the Laplace Equation 2 2 h h = α boundaries left h lower h (,0) = 0 upper water table ( 0,) = 0 right ( s, ) h h = 0 (, ) = + c = + tan( α) o o o Toth's result: cs 4cs = + h(, ) o a 2 2 π = m 0 cos a = π s ( 2m + 1) cosh ( 2m + 1) 2 o ( 2m + 1) cosh ( 2m + 1) π s π s 8

9 Toth's result for system of differing depth: Discharge Zone Recharge Zone Head decreases with depth downward Head flow increases with depth upward flow Regional Flow (Classic Papers by Freee and Witherspoon): homogeneous & isoptropic with and without hummocks 9

10 Hierarchy of flow systems Local Intermediate Regional Dominance controlled by: Basin Depth Slope of water table Frequency of Hummocks Sie of Hummocks Regional Flow (Classic Papers by Freee and Witherspoon): Layered systems / High at depth

11 Regional Flow (Classic Papers by Freee and Witherspoon): Layered systems / Low at depth 00 0 Regional Flow (Classic Papers by Freee and Witherspoon): Layered systems / High at depth and hummocks

12 Regional Flow (Classic Papers by Freee and Witherspoon): Partial layers and lenses Regional Flow (Classic Papers by Freee and Witherspoon): Layered systems / sloping stratigraphy

13 Regional Flow (Classic Papers by Freee and Witherspoon): nisotropic systems h=10 v=1 h=1 v=10 h=1 v=10 h=10 v=1 bove transformed Constant head in shallow shallow intermediate deep 13

14 Eplore the Flow Net Software at 14

### 2.10 Water Level Maps

.10 Water Level Maps Maps of the water table for an unconfined aquifer or of the potentiometric surface of a confined aquifer are basic tools of hydrogeologic interpretation. These maps are two-dimensional

### Flow of Water in Soil Permeability and Seepage. Water flows through the voids in a soil which are. seepage, since the velocities are very small.

Flow of Water in Soil Permeability and Seepage Water flows through the voids in a soil which are interconnected. t This flow may be called seepage, since the velocities are very small. Water flows from

### Principles of Groundwater Flow. Hsin-yu Shan Department of Civil Engineering National Chiao Tung University

Principles of Groundwater Flow Hsin-yu Shan Department of Civil Engineering National Chiao Tung University Groundwater Flow Forms of energy that ground water possesses Mechanical Thermal Chemical Ground

### CHAPTER: 6 FLOW OF WATER THROUGH SOILS

CHAPTER: 6 FLOW OF WATER THROUGH SOILS CONTENTS: Introduction, hydraulic head and water flow, Darcy s equation, laboratory determination of coefficient of permeability, field determination of coefficient

### Principles of groundwater flow

Principles of groundwater flow Hydraulic head is the elevation to which water will naturally rise in a well (a.k.a. static level). Any well that is not being pumped will do for this, but a well that is

### 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

### HWR 431 / 531 HYDROGEOLOGY LAB SECTION LABORATORY 2 DARCY S LAW

HWR 431 / 531 HYDROGEOLOGY LAB SECTION LABORATORY 2 DARCY S LAW Introduction In 1856, Henry Darcy, a French hydraulic engineer, published a report in which he described a series of experiments he had performed

### LAPLACE'S EQUATION OF CONTINUITY

LAPLACE'S EQUATION OF CONTINUITY y z Steady-State Flow around an impervious Sheet Pile Wall Consider water flow at Point A: v = Discharge Velocity in Direction Figure 5.11. Das FGE (2005). v z = Discharge

### γ [Increase from (1) to (2)] γ (1ft) [Decrease from (2) to (B)]

1. The manometer fluid in the manometer of igure has a specific gravity of 3.46. Pipes A and B both contain water. If the pressure in pipe A is decreased by 1.3 psi and the pressure in pipe B increases

### 5. FLOW OF WATER THROUGH SOIL

5-1 5. FLOW OF WATER THROUGH SOIL 5.1 FLOW OF WATER IN A PIPE The flow of water through a rough open pipe may be expressed by means of the Darcy- Weisbach resistance equation h = f L D v 2 2g (5.1) in

### What is groundwater? unsaturated zone. saturated zone. water table

1 Objectives What are aquifers and aquitards? What is head, and how does it relate to pressure? How is water stored in rock? What is hydraulic conductivity? 2 What is groundwater? unsaturated zone water

### Module 2 Lecture 7 Permeability and Seepage -3 Topics

Module 2 Lecture 7 Permeability and Seepage -3 Topics 1.1.6 Determination of Coefficient of Permeability in the Field Pumping from wells Packer test 1.1.7 Theoretical Solution for Coefficient of Permeability

### FLUID FORCES ON CURVED SURFACES; BUOYANCY

FLUID FORCES ON CURVED SURFCES; BUOYNCY The principles applicable to analysis of pressure-induced forces on planar surfaces are directly applicable to curved surfaces. s before, the total force on the

### 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

### E 490 Fundamentals of Engineering Review. Fluid Mechanics. M. A. Boles, PhD. Department of Mechanical & Aerospace Engineering

E 490 Fundamentals of Engineering Review Fluid Mechanics By M. A. Boles, PhD Department of Mechanical & Aerospace Engineering North Carolina State University Archimedes Principle and Buoyancy 1. A block

CONSTANT HEAD AND FALLING HEAD PERMEABILITY TEST 1 Permeability is a measure of the ease in which water can flow through a soil volume. It is one of the most important geotechnical parameters. However,

### 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

### (Refer Slide Time: 05:33)

Water and Wastewater Engineering Dr. Ligy Philip Department of Civil Engineering Indian Institute of Technology, Madras Sedimentation (Continued) Lecture # 9 Last class we were discussing about sedimentation.

### CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

### CBE 6333, R. Levicky 1. Potential Flow

CBE 6333, R. Levicky Part I. Theoretical Background. Potential Flow Potential Flow. Potential flow is irrotational flow. Irrotational flows are often characterized by negligible viscosity effects. Viscous

### XI / PHYSICS FLUIDS IN MOTION 11/PA

Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

### PERMEABILITY TEST. To determine the coefficient of permeability of a soil using constant head method.

PERMEABILITY TEST A. CONSTANT HEAD OBJECTIVE To determine the coefficient of permeability of a soil using constant head method. need and Scope The knowledge of this property is much useful in solving problems

### Min-218 Fundamentals of Fluid Flow

Excerpt from "Chap 3: Principles of Airflow," Practical Mine Ventilation Engineerg to be Pubished by Intertec Micromedia Publishing Company, Chicago, IL in March 1999. 1. Definition of A Fluid A fluid

### The University of Toledo Soil Mechanics Laboratory

The University of Toledo Soil Mechanics Laboratory Permeability Testing - 1 Constant and Falling Head Tests Introduction In 1856 the French engineer Henri D arcy demonstrated by experiment that it is possible

### 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

DETERMINING TOTAL DYNAMIC HEAD The total dynamic head of a water system must be considered when determining the size of pumping equipment to be installed. It determines the various head losses that the

### Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity

1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood

### Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface

Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface Topographic maps represent the complex curves of earth s surface with contour lines that represent the intersection

### APPENDIX B DESIGN GUIDELINES FOR APPROVED TREATMENT METHODS

APPENDIX B DESIGN GUIDELINES FOR APPROVED TREATMENT METHODS PLANTER BOXES 1. Determine the impervious area contributing flow to the planter box (see Chapter 4.2). 2. Assumption: Typical soil infiltration

### 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

### EN 1997-1 Eurocode 7. Section 10 Hydraulic Failure Section 11 Overall Stability Section 12 Embankments. Trevor L.L. Orr Trinity College Dublin Ireland

EN 1997 1: Sections 10, 11 and 12 Your logo Brussels, 18-20 February 2008 Dissemination of information workshop 1 EN 1997-1 Eurocode 7 Section 10 Hydraulic Failure Section 11 Overall Stability Section

### What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation)

OPEN CHANNEL FLOW 1 3 Question What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation) Typical open channel shapes Figure

### STORMWATER MANAGEMENT CHECKLIST

STORMWATER MANAGEMENT CHECKLIST *This checklist must be completed and part of the Land Disturbing Permit submittal for review if the acreage disturbed is one (1) acre or more: I. SUPPORTING DATA Narrative

### QUANTITATIVE EXERCISES USING THE GROUNDWATER SAND TANK MODEL

QUANTITATIVE EXERCISES USING THE GROUNDWATER SAND TANK MODEL Darcy s Law In 1856 Henri Darcy, a French engineer, discovered a relationship that governs fluid flow through geologic materials. He determined

### ON-LOT SEWAGE DISPOSAL PROGRAM DESIGN OF PRESSURE-DOSED ELEVATED SAND MOUND BED

ON-LOT SEWAGE DISPOSAL PROGRAM DESIGN OF PRESSURE-DOSED ELEVATED SAND MOUND BED INSTRUCTIONS In order to design an elevated sand mound bed using pressure dosing which meets Pennsylvania Department of Environmental

### oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1

Answer, Key Homework 2 David McIntyre 1 This print-out should have 14 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

### Soil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 19 Effective Stress-I I I

Soil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 19 Effective Stress-I I I Welcome to the third lecture on effective stress. In the

### EXPERIMENT 10 CONSTANT HEAD METHOD

EXPERIMENT 10 PERMEABILITY (HYDRAULIC CONDUCTIVITY) TEST CONSTANT HEAD METHOD 106 Purpose: The purpose of this test is to determine the permeability (hydraulic conductivity) of a sandy soil by the constant

### OUTLINE Introduction to Laminar and Turbulent Flow Reynolds Number Laminar Flow

REAL FLUIDS OUTLINE Introduction to Laminar and Turbulent Flow Reynolds Number Laminar Flow Flow in Circular Pipes Hagen Poiseuille Equation Flow between parallel plates REAL FLUIDS Turbulent Flow About

### Viscous Flow in Pipes

Viscous Flow in Pipes Excerpted from supplemental materials of Prof. Kuang-An Chang, Dept. of Civil Engin., Texas A&M Univ., for his spring 2008 course CVEN 311, Fluid Dynamics. (See a related handout

### Foundation Engineering Prof. Mahendra Singh Department of Civil Engineering Indian Institute of Technology, Roorkee

Foundation Engineering Prof. Mahendra Singh Department of Civil Engineering Indian Institute of Technology, Roorkee Module - 03 Lecture - 09 Stability of Slopes Welcome back to the classes of on this Stability

### Module 2. The Science of Surface and Ground Water. Version 2 CE IIT, Kharagpur

Module Te Science of Surface and Ground Water Version CE IIT, Karagpur Lesson 6 Principles of Ground Water Flow Version CE IIT, Karagpur Instructional Objectives On completion of te lesson, te student

### AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same

A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall that

### CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc.

CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc. 1 Centrifugal Pump- Definition Centrifugal Pump can be defined as a mechanical device used to transfer liquid of various types. As

### 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

### Fluid Mechanics. Fluid Statics [3-1] Dr. Mohammad N. Almasri. [3] Fall 2010 Fluid Mechanics Dr. Mohammad N. Almasri [3-1] Fluid Statics

1 Fluid Mechanics Fluid Statics [3-1] Dr. Mohammad N. Almasri Fluid Pressure Fluid pressure is the normal force exerted by the fluid per unit area at some location within the fluid Fluid pressure has the

### Module 5 (Lectures 17 to 19) MAT FOUNDATIONS

Module 5 (Lectures 17 to 19) MAT FOUNDATIONS Topics 17.1 INTRODUCTION Rectangular Combined Footing: Trapezoidal Combined Footings: Cantilever Footing: Mat foundation: 17.2 COMMON TYPES OF MAT FOUNDATIONS

### Laboratory 3 Hydraulic Conductivity of a Porous Media

Laboratory Hydraulic Conductivity of a Porous Media INTRODUCTION Permeability refers to the propensity of a material to allow a gas or fluid to move through its pores or interstices. A material is permeable

### EXAMPLE 1 DESIGN OF CANTILEVERED WALL, GRANULAR SOIL

EXAMPLE DESIGN OF CANTILEVERED WALL, GRANULAR SOIL A sheet pile wall is required to support a 2 excavation. The soil is uniform as shown in the figure. To take into account the friction between the wall

### 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

### Boundary Conditions of the First Kind (Dirichlet Condition)

Groundwater Modeling Boundary Conditions Boundary Conditions of the First Kind (Dirichlet Condition) Known pressure (velocity potential or total heard) head, e.g. constant or varying in time or space.

### Azarian Journal of Agriculture

AJA VOL (3) ISSUE 3, 2016: 58-65 Azarian Journal of Agriculture Research article www.azarianjournals.ir Azarian Journals ISSN:2383-4420 Numerical investigation of underground drain radius, depth and location

### PERC-RITE DRIP DISPERSAL DESIGN GUIDE FOR SEPTIC TANK OR ADVANCED TREATMENT EFFLUENT MAINE

PERC-RITE DRIP DISPERSAL DESIGN GUIDE FOR SEPTIC TANK OR ADVANCED TREATMENT EFFLUENT MAINE This Perc-Rite Design Guide is intended to simplify the design process of a Perc-Rite Drip Dispersal System. This

### Airflow through Mine Openings and Ducts Chapter 5

Airflow through Mine Openings and Ducts Chapter 5 Fundamentals of Airflow Ventilation the application of the principles of fluid mechanics & thermodynamics to the flow of air in underground openings Fluid

### VOLUME AND SURFACE AREAS OF SOLIDS

VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b

VERTICAL STRESS INCREASES IN SOIL Point Loads (P) TYPES OF LOADING Line Loads (q/unit length) Revised 0/015 Figure 6.11. Das FGE (005). Examples: - Posts Figure 6.1. Das FGE (005). Examples: - Railroad

### Open Channel Flow 2F-2. A. Introduction. B. Definitions. Design Manual Chapter 2 - Stormwater 2F - Open Channel Flow

Design Manual Chapter 2 - Stormwater 2F - Open Channel Flow 2F-2 Open Channel Flow A. Introduction The beginning of any channel design or modification is to understand the hydraulics of the stream. The

### STATE OF VERMONT AGENCY OF NATURAL RESOURCES DEPARTMENT OF ENVIRONMENTAL CONSERVATION WASTE MANAGEMENT DIVISION SOLID WASTE MANAGEMENT PROGRAM

STATE OF VERMONT AGENCY OF NATURAL RESOURCES DEPARTMENT OF ENVIRONMENTAL CONSERVATION WASTE MANAGEMENT DIVISION SOLID WASTE MANAGEMENT PROGRAM Solid Waste Management Program Waste Management Division 103

### FOUNDATION DESIGN. Instructional Materials Complementing FEMA 451, Design Examples

FOUNDATION DESIGN Proportioning elements for: Transfer of seismic forces Strength and stiffness Shallow and deep foundations Elastic and plastic analysis Foundation Design 14-1 Load Path and Transfer to

### CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

### Use of arched cables for fixation of empty underground tanks against underground-waterinduced

Journal of Civil Engineering (IEB), 36 () (008) 79-86 Use of arched cables for fixation of empty underground tanks against underground-waterinduced floatation Ala a M. Darwish Department of Building &

### 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

### SL Calculus Practice Problems

Alei - Desert Academ SL Calculus Practice Problems. The point P (, ) lies on the graph of the curve of = sin ( ). Find the gradient of the tangent to the curve at P. Working:... (Total marks). The diagram

### ENSC 283 Introduction and Properties of Fluids

ENSC 283 Introduction and Properties of Fluids Spring 2009 Prepared by: M. Bahrami Mechatronics System Engineering, School of Engineering and Sciences, SFU 1 Pressure Pressure is the (compression) force

### Soil Suction. Total Suction

Soil Suction Total Suction Total soil suction is defined in terms of the free energy or the relative vapor pressure (relative humidity) of the soil moisture. Ψ = v RT ln v w 0ω v u v 0 ( u ) u = partial

### Module 9: Basics of Pumps and Hydraulics Instructor Guide

Module 9: Basics of Pumps and Hydraulics Instructor Guide Activities for Unit 1 Basic Hydraulics Activity 1.1: Convert 45 psi to feet of head. 45 psis x 1 ft. = 103.8 ft 0.433 psi Activity 1.2: Determine

### 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

### 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

### Fluid Mechanics Definitions

Definitions 9-1a1 Fluids Substances in either the liquid or gas phase Cannot support shear Density Mass per unit volume Specific Volume Specific Weight % " = lim g#m ( ' * = +g #V \$0& #V ) Specific Gravity

### CHAPTER 9. Outlet Protection

CHAPTER 9 Outlet Protection General Considerations Not an ABACT, but should be used in all watersheds to prevent erosion due to concentrated discharges For channel or swale, use guidance for pipe with

### APPENDIX G HYDRAULIC GRADE LINE

Storm Drainage 13-G-1 APPENDIX G HYDRAULIC GRADE LINE 1.0 Introduction The hydraulic grade line is used to aid the designer in determining the acceptability of a proposed or evaluation of an existing storm

### Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

### Information sheet on Soakaways in accordance with BRE Digest 365

Information sheet on Soakaways in accordance with BRE Digest 365 CONSTRUCTION DETAILS Maintenance of soakaways has always presented problems, usually in finding them! This is certainly the case with rubble-filled

### Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness

### 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

### 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

### Groundwater flow systems theory: an unexpected outcome of

Groundwater flow systems theory: an unexpected outcome of early cable tool drilling in the Turner Valley oil field K. Udo Weyer WDA Consultants Inc. weyer@wda-consultants.com Introduction The Theory of

### Practice Problems on Bernoulli s Equation. V car. Answer(s): p p p V. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Sep 15

bernoulli_0 A person holds their hand out of a car window while driving through still air at a speed of V car. What is the maximum pressure on the person s hand? V car 0 max car p p p V C. Wassgren, Purdue

### UNDER DRAINAGE AND FILTER DESIGN

UNDER DRAINAGE AND FILTER DESIGN Tailings and HLP Workshop 28 April to 1 May 2010 INTRODUCTION The internal drainage is of crucial importance to the reliability and safety of a tailings dam throughout

### Pipe Flow-Friction Factor Calculations with Excel

Pipe Flow-Friction Factor Calculations with Excel Course No: C03-022 Credit: 3 PDH Harlan H. Bengtson, PhD, P.E. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980

1 Introduction Seepage Exit Gradients Most Soil Mechanics text books present and discuss the concept of seepage exit gradients and state that the exit gradients should not be greater than 1.0 Applying

### Transient Mass Transfer

Lecture T1 Transient Mass Transfer Up to now, we have considered either processes applied to closed systems or processes involving steady-state flows. In this lecture we turn our attention to transient

### ENERGY DISSIPATION CHAPTER 7

CHAPTER 7 ENERGY DISSIPATION 7.1 Overview... 7-1 7.2 Design Criteria... 7-1 7.2.1 General Criteria... 7-1 7.2.2 Erosion Hazards... 7-1 7.2.3 Recommended Dissipators... 7-1 7.3 Riprap Aprons... 7-2 7.3.1

### Flow Loss in Screens: A Fresh Look at Old Correlation. Ramakumar Venkata Naga Bommisetty, Dhanvantri Shankarananda Joshi and Vighneswara Rao Kollati

Journal of Mechanics Engineering and Automation 3 (013) 9-34 D DAVID PUBLISHING Ramakumar Venkata Naga Bommisetty, Dhanvantri Shankarananda Joshi and Vighneswara Rao Kollati Engineering Aerospace, MCOE,

### Chapitre 10. Flow Nets 1

Soil Mechanics Flo Nets page 1 Contents of this chapter : CHAPITRE 10. FLOW NETS...1 10.1 INTRODUCTION...1 10.2 REPRESENTATION OF SOLUTION...2 10.3 SOME GEOMETRIC PROPERTIES OF FLOW NETS...3 10.4 COMMON

### INTRODUCTION TO SOIL MODULI. Jean-Louis BRIAUD 1

INTRODUCTION TO SOIL MODULI By Jean-Louis BRIAUD 1 The modulus of a soil is one of the most difficult soil parameters to estimate because it depends on so many factors. Therefore when one says for example:

### CHAPTER III SITE EXPLORATION

CHAPTER III SITE EXPLORATION Investigational Programs. Field investigations can be divided into two major phases: a surface examination and a subsurface exploration. 1 Surface Examination a. Literature

### When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

### Stream Rehabilitation Concepts, Guidelines and Examples. Objectives. Pierre Y. Julien. Three Laws of Stream Restoration

Stream Rehabilitation Concepts, Guidelines and Examples Pierre Y. Julien Wuhan 2005 Objectives Part I - Stream restoration and rehabilitation: 1. Present and discuss important concepts, laws, criteria

### Higher Mathematics Homework A

Non calcuator section: Higher Mathematics Homework A 1. Find the equation of the perpendicular bisector of the line joining the points A(-3,1) and B(5,-3) 2. Find the equation of the tangent to the circle

### PETE Well Completion Design

PETE 71 Well Completion Design Casing Design Casing Design Why Run Casing? Types of Casing Strings Classification of Casing Wellheads Burst, Collapse and Tension Example Effect of Axial Tension on Collapse

### p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh

IVE1400: n Introduction to Fluid Mechanics Statics : Pressure : Statics r P Sleigh: P..Sleigh@leeds.ac.uk r J Noakes:.J.Noakes@leeds.ac.uk January 008 Module web site: www.efm.leeds.ac.uk/ive/fluidslevel1

### FOOTING DESIGN EXAMPLE

County: Any Design: BRG Date: 10/007 Hwy: Any Ck Dsn: BRG Date: 10/007 FOOTING DESIGN EXAMPLE Design: Based on AASHTO LRFD 007 Specifications, TxDOT LRFD Bridge Design Manual, and TxDOT Project 0-4371

### CLARK COUNTY REGIONAL FLOOD CONTROL DISTRICT HYDROLOGIC CRITERIA AND DRAINAGE DESIGN MANUAL SECTION 1100 ADDITIONAL HYDRAULIC STRUCTURES

CLARK COUNTY REGIONAL FLOOD CONTROL DISTRICT HYDROLOGIC CRITERIA AND DRAINAGE DESIGN MANUAL SECTION 1100 ADDITIONAL HYDRAULIC STRUCTURES TABLE OF CONTENTS Page 1101 INTRODUCTION 1102 1102 CHANNEL DROPS

14.53 THEORETICAL SOIL MECHANICS VERTICAL STRESS INCREASES IN SOILS TYPES OF LOADING Point Loads (P) Line Loads (q/unit length) Figure 6.11. Das FGE (005). Examples: -Posts Figure 6.1. Das FGE (005). Examples:

### Soil Moisture and Groundwater Recharge. Hsin-yu Shan Department of Civil Engineering National Chiao Tung University

Soil Moisture and Groundwater Recharge Hsin-yu Shan Department of Civil Engineering National Chiao Tung University Soil Physics A scientific field that focus on the water in the vadose zone Major concern

### 14.330 SOIL MECHANICS Assignment #4: Soil Permeability.

Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Edward L. Hajduk, D.Eng, PE Lecturer PA105D Tel: (978) 94 2621 Fax: (978) 94 052 e mail: Edward_Hajduk@uml.edu