HEC-RAS. River Analysis System systém pre analýzu prúdenia vody v riekach

Size: px
Start display at page:

Download "HEC-RAS. River Analysis System systém pre analýzu prúdenia vody v riekach"

Transcription

1 HEC-RAS River Aalysis System systém pre aalýzu prúdeia vody v riekach HEC Hydraulic Egieerig Corporatio združeie ižiierov pracujúcich v hydraulike Cross Sectio Subdivisio or Coveyace Calculatio Rozdeleie priečeho proilu pre výpočet modulu prietoku = K. S = A. v = AC.. R. S R / 6 C = Chezy velocity coeiciet Maig expressio. / K = A R or SI uits.486 Chézyho rýchlostý súčiiteľ Maigov tvar pre SI jedotky / K = A. R or Eglish uits pre aglické (US ) jedotky K i i A i coveyace or subdivisio modul prietoku pre časť proilu Maig s roughess coeiciet or subdivisio Maigov súčiiteľ treia pre časť proilu low area or subdivisio prietočá plocha pre časť proilu

2 R i hydraulic radius or subdivisio (area/wetted perimeter) hydraulický polomer pre časť proilu c = N i= P i P / i / c / a N a P i i i= = a=, /, P c P P i i composite equivalet coeiciet o roughess ekvivaletý súčiiteľ treia pre zložeý proil wetted perimeter o etire mai chael omočeý obvod pre celý hlavý kaál wetted perimeter o subdivisio i omočeý obvod pre časť proilu i coeiciet o roughess or subdivisio i súčiiteľ drsosti pre časť proilu i Equatio or Basic Water Surace Proiles Rovica pre eergetickú bilaciu riečeho prúdeia Beroulli equatio Beruliho rovica p α. v + g. h + ρ g = cost Datum Chael Bottom Water Surace Eergy Grade Lie zrovávacia hladia do kaála vodá hladia sklo čiary eergie

3 αv αv Y + Z + = Y + Z + + g g h e Y Z V α g h e depth o water at cross sectio hĺbka vody v proile elevatio o the mai chael iverts kóta da hlavého kaála average velocities priemerá proilová rýchlosť velocity weightig coeiciet Coriolis coeiciet koeiciet vyjadrujúci erovomeré rozložeie rýchlosti vody v proile gravitatio acceleratio koštata gravitačého zrýchleia eergy head loss straty a eergetickej výške h e = L. S α V V C α + g g L discharge weighted reach legth modiikovaá vzdialeosť medzi dvoma proilmi a základe rozdeleia prietoku

4 S C represetative rictio slope betwee sectios charakteristický sklo čiary eergie medzi dvoma proilmi expasio or cotractio loss coeiciet koeiciet strát v dôsledku rozšíreia alebo zúžeia prietočého proilu L = Llob lob + Lchch + L rob rob L lob, L ch, L rob cross sectio reach legths speciied or low i the let overbak, mai chael ad right overbak vzdialeosť prislúchajúcich častí proilov ľavej iudácie, hlavého kaála a pravej iudácie lob, ch, rob arithmetic average o the lows betwee sectio aritmetický priemer prietokov medzi prislúchajúcimi časťami proilov Evaluatio o the Mea Kietic Eergy Head Rovica pre výpočet stredej hodoty kietickej hladiy

5 V + V g α = g + V g α = A V + A V A.V α = A v. da AV. Critical depth Determiatio Určeie kritickej hĺbky Eergy Head or a cross sectio Čiara eergie pre priečy proil H αv = WS + g H WS αv g total eergy head celková hladia eergie water surace elevatio kóta hladiy velocity head rýchlostá výška

6 Supercritical Flow Superkritické prúdeie bystrié prúdeie F x = ma P P + W x F = ρδv x P W x F ρ ΔV x hydrostatic pressure orce sila spôsobeá hydraulickým tlakom orce due to the weight o water sila spôsobeá tiažou vody orce due to exteral rictio losses sila v dôsledku vokajšieho treia discharge Prietok desity o water hustota vody chage i velocity zmea v rýchlosti P = γay cos θ γay

7 γ A Y uit weight o water merá tiaž vody wetted area o the cross sectio prietočá plocha v proile depth measured rom the water surace to the cetroid o A hĺbka meraá od vodej hladiy po ťažisko plochy A W x A + A = γ Lsiθ γ A + A LS 0 L S 0 distace betwee cross sectios vzdialeosť medzi priečymi proilmi Slope o the chael sklo da kaála F = τ PL = γ RS A + A PL = γ S L R average hydraulic radius priemerý hydraulický polomer S slope o the eergy grade lie rictio slope sklo čiary eergie γ ma = g ( β V β ) V β mometum coeiciet koeiciet erovomerého rozdeleia mometu v proile Speciic Force SF Špeciická sila SF sa zachováva β A + A + AY + ga L β SF = + AY. ga β ( S ) 0 S = + A Y ga

Computer Applications in Hydraulic Engineering

Computer Applications in Hydraulic Engineering Computer Applications in Hydraulic Engineering www.haestad.com Academic CD Aplikácie výpočtovej techniky v hydraulike pre inžinierov Flow Master General Flow Characteristic Všeobecná charakteristika prúdenia

More information

UNIFORM FLOW. U x. U t

UNIFORM FLOW. U x. U t UNIFORM FLOW if : 1) there are o appreciable variatios i the chael geometry (width, slope, roughess/grai size), for a certai legth of a river reach ) flow discharge does ot vary the, UNIFORM FLOW coditios

More information

4.1 Introduction. 4. Uniform Flow and its Computations

4.1 Introduction. 4. Uniform Flow and its Computations 4. Uiform Flow ad its Computatios 4. Itroductio A flow is said to be uiform if its properties remai costat with respect to distace. As metioed i chapter oe of the hadout, the term ope chael flow i ope

More information

Free Surface Hydrodynamics

Free Surface Hydrodynamics Water Sciece ad Egieerig Free Surface Hydrodyamics y A part of Module : Hydraulics ad Hydrology Water Sciece ad Egieerig Dr. Shreedhar Maskey Seior Lecturer UNESCO-IHE Istitute for Water Educatio S. Maskey

More information

Notes on the GSW function gsw_geostrophic_velocity (geo_strf,long,lat,p)

Notes on the GSW function gsw_geostrophic_velocity (geo_strf,long,lat,p) Notes o gsw_geostrophic_velocity Notes o the GSW fuctio gsw_geostrophic_velocity (geo_strf,log,lat,p) Notes made 7 th October 2, ad updated 8 th April 2. This fuctio gsw_geostrophic_velocity(geo_strf,log,lat,p)

More information

Module 3d: Flow in Pipes Manning s Equation

Module 3d: Flow in Pipes Manning s Equation Module d: Flow i Pipes Maig's Equatio for velocity ad flow applicable to both pipe (closed-coduit) flow ad ope chael flow. Robert Pitt Uiversity of Alabama ad hirley Clark Pe tate - Harrisburg It is typically

More information

LECTURE 9: Open channel flow: Uniform flow, best hydraulic sections, energy principles, Froude number

LECTURE 9: Open channel flow: Uniform flow, best hydraulic sections, energy principles, Froude number LECTURE 9: Open channel flow: Uniform flow, best hydraulic sections, energy principles, Froude number Assist. Prof. Neslihan SEMERCİ Marmara University Department of Environmental Engineering Open channel

More information

Mechanical Vibrations

Mechanical Vibrations Mechaical Vibratios Cotets Itroductio Free Vibratios o Particles. Siple Haroic Motio Siple Pedulu (Approxiate Solutio) Siple Pedulu (Exact Solutio) Saple Proble 9. Free Vibratios o Rigid Bodies Saple Proble

More information

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Mechanical Vibrations. Seventh Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Mechanical Vibrations. Seventh Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr. Seveth Editio CHAPTER 9 VECTOR MECHANICS FOR ENGINEERS: DYNAMICS Ferdiad P. Beer E. Russell Johsto, Jr. Mechaical Vibratios Lecture Notes: J. Walt Oler Texas Tech Uiversity 003 The McGraw-Hill Copaies,

More information

Design Data 16. Partial Flow Conditions For Culverts. x S o Q F = C 1 = (3) A F V F Q = x A x R2/3 x S o n 1/2 (2) 1 DD 16 (07/09)

Design Data 16. Partial Flow Conditions For Culverts. x S o Q F = C 1 = (3) A F V F Q = x A x R2/3 x S o n 1/2 (2) 1 DD 16 (07/09) Desig Data 16 Partial Flow Coditios For Culverts Sewers, both saitary ad storm, are desiged to carry a peak flow based o aticipated lad developmet. The hydraulic capacity of sewers or culverts costructed

More information

Presented by: Civil Engineering Academy

Presented by: Civil Engineering Academy Presented by: Civil Engineering Academy Open-Channel Flow Uniform Flow (See CERM Ch. 19) Characterized by constant depth volume, and cross section. It can be steady or unsteady Non-uniform Flow *Not on

More information

UNIFORM FLOW CRITICAL FLOW GRADUALLY VARIED FLOW

UNIFORM FLOW CRITICAL FLOW GRADUALLY VARIED FLOW UNIFORM FLOW CRITICAL FLOW GRADUALLY VARIED FLOW Derivation of uniform flow equation Dimensional analysis Computation of normal depth UNIFORM FLOW 1. Uniform flow is the flow condition obtained from a

More information

Determination of Manning s Flow Resistance Coefficient for Rivers in Malaysia

Determination of Manning s Flow Resistance Coefficient for Rivers in Malaysia Determiatio of Maig s Flow Resistace Coefficiet for Rivers i Malaysia AHMAD BAKRI ABDUL GHAFFAR, Research Studet, School of Civil Egieerig, Uiversiti Sais Malaysia, Egieerig Campus, Seri Ampaga, 143 Nibog

More information

: ) 9) 6 PM, 6 PM

: ) 9) 6 PM, 6 PM Physics 101 Sectio 3 Mar. 1 st : Ch. 7-9 review Ch. 10 Aoucemets: Test# (Ch. 7-9) will be at 6 PM, March 3 (6) Lockett) Study sessio Moday eveig at 6:00PM at Nicholso 130 Class Website: http://www.phys.lsu.edu/classes/sprig010/phys101-3/

More information

Channel design. riprap-lined channels

Channel design. riprap-lined channels Chael desig Vegetatio ad cobbles are used to cotrol erosio, dissipate eergy ad provide a evirometally sustaiable way to desig differet size chaels riprap-lied chaels Smooth chaels i circular coduits: PVC

More information

Section 7. Gaussian Reduction

Section 7. Gaussian Reduction 7- Sectio 7 Gaussia eductio Paraxial aytrace Equatios eractio occurs at a iterace betwee two optical spaces. The traser distace t' allows the ray height y' to be determied at ay plae withi a optical space

More information

Hydraulics Part: Open Channel Flow

Hydraulics Part: Open Channel Flow Hydraulics Part: Open Channel Flow Tutorial solutions -by Dr. K.N. Dulal Uniform flow 1. Show that discharge through a channel with steady flow is given by where A 1 and A 2 are the sectional areas of

More information

Section 1.1. Calculus: Areas And Tangents. Difference Equations to Differential Equations

Section 1.1. Calculus: Areas And Tangents. Difference Equations to Differential Equations Differece Equatios to Differetial Equatios Sectio. Calculus: Areas Ad Tagets The study of calculus begis with questios about chage. What happes to the velocity of a swigig pedulum as its positio chages?

More information

a b c d e f g h Supplementary Information

a b c d e f g h Supplementary Information Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;

More information

Wind Energy Explained, 2 nd Edition Errata

Wind Energy Explained, 2 nd Edition Errata Wid Eergy Explaied, d Editio Errata This summarizes the ko errata i Wid Eergy Explaied, d Editio. The errata ere origially compiled o July 6, 0. Where possible, the chage or locatio of the chage is oted

More information

MIDTERM 2 CALCULUS 2. Monday, October 22, 5:15 PM to 6:45 PM. Name PRACTICE EXAM

MIDTERM 2 CALCULUS 2. Monday, October 22, 5:15 PM to 6:45 PM. Name PRACTICE EXAM MIDTERM 2 CALCULUS 2 MATH 23 FALL 218 Moday, October 22, 5:15 PM to 6:45 PM. Name PRACTICE EXAM Please aswer all of the questios, ad show your work. You must explai your aswers to get credit. You will

More information

Mathematical Description of Discrete-Time Signals. 9/10/16 M. J. Roberts - All Rights Reserved 1

Mathematical Description of Discrete-Time Signals. 9/10/16 M. J. Roberts - All Rights Reserved 1 Mathematical Descriptio of Discrete-Time Sigals 9/10/16 M. J. Roberts - All Rights Reserved 1 Samplig ad Discrete Time Samplig is the acquisitio of the values of a cotiuous-time sigal at discrete poits

More information

Problem 1. Problem Engineering Dynamics Problem Set 9--Solution. Find the equation of motion for the system shown with respect to:

Problem 1. Problem Engineering Dynamics Problem Set 9--Solution. Find the equation of motion for the system shown with respect to: 2.003 Egieerig Dyamics Problem Set 9--Solutio Problem 1 Fid the equatio of motio for the system show with respect to: a) Zero sprig force positio. Draw the appropriate free body diagram. b) Static equilibrium

More information

Poornima University, For any query, contact us at: ,18

Poornima University, For any query, contact us at: ,18 AIEEE/1/MAHS 1 S. No Questios Solutios Q.1 he circle passig through (1, ) ad touchig the axis of x at (, ) also passes through the poit (a) (, ) (b) (, ) (c) (, ) (d) (, ) Q. ABCD is a trapezium such that

More information

CE 6403 APPLIED HYDRAULIC ENGINEERING UNIT - II GRADUALLY VARIED FLOW

CE 6403 APPLIED HYDRAULIC ENGINEERING UNIT - II GRADUALLY VARIED FLOW CE 6403 APPLIED HYDRAULIC ENGINEERING UNIT - II GRADUALLY VARIED FLOW Dynamic equations of gradually varied and spatially varied flows - Water surface flow profile classifications: Hydraulic Slope, Hydraulic

More information

Uniform Channel Flow Basic Concepts. Definition of Uniform Flow

Uniform Channel Flow Basic Concepts. Definition of Uniform Flow Uniform Channel Flow Basic Concepts Hydromechanics VVR090 Uniform occurs when: Definition of Uniform Flow 1. The depth, flow area, and velocity at every cross section is constant 2. The energy grade line,

More information

Phys 6303 Final Exam Solutions December 19, 2012

Phys 6303 Final Exam Solutions December 19, 2012 Phys 633 Fial Exam s December 19, 212 You may NOT use ay book or otes other tha supplied with this test. You will have 3 hours to fiish. DO YOUR OWN WORK. Express your aswers clearly ad cocisely so that

More information

Double Diffusive Convection from a Permeable Horizontal Cylinder of Elliptic Cross Section in a Saturated Porous Medium

Double Diffusive Convection from a Permeable Horizontal Cylinder of Elliptic Cross Section in a Saturated Porous Medium Proceedigs o the 4th WSEAS It. Co. o HEAT TRANSFER, THERMAL ENGINEERING ad ENVIRONMENT, Elouda, Greece, August -3, 6 (pp357-36) Double Diusive Covectio rom a Permeable Horizotal Cylider o Elliptic Cross

More information

AP Calculus BC 2011 Scoring Guidelines Form B

AP Calculus BC 2011 Scoring Guidelines Form B AP Calculus BC Scorig Guidelies Form B The College Board The College Board is a ot-for-profit membership associatio whose missio is to coect studets to college success ad opportuity. Fouded i 9, the College

More information

VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM (A) 10th Standard Reg.No. : MATHEMATICS - MOD EXAM 1(A)

VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM (A) 10th Standard Reg.No. : MATHEMATICS - MOD EXAM 1(A) Time : 0:30:00 Hrs VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM 018-19(A) 10th Stadard Reg.No. : MATHEMATICS - MOD EXAM 1(A) Total Mark : 100 I. CHOOSE THE BEST ANSWER WITH CORRECT OPTION:-

More information

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018 CHAPTER 4 Structure of the Atom PHYS-3301 Lecture 7 4.1 The Atomic Models of Thomso ad Rutherford 4.2 Rutherford Scatterig 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydroge Atom 4.5 Successes

More information

Exercises and Problems

Exercises and Problems HW Chapter 4: Oe-Dimesioal Quatum Mechaics Coceptual Questios 4.. Five. 4.4.. is idepedet of. a b c mu ( E). a b m( ev 5 ev) c m(6 ev ev) Exercises ad Problems 4.. Model: Model the electro as a particle

More information

The picture in figure 1.1 helps us to see that the area represents the distance traveled. Figure 1: Area represents distance travelled

The picture in figure 1.1 helps us to see that the area represents the distance traveled. Figure 1: Area represents distance travelled 1 Lecture : Area Area ad distace traveled Approximatig area by rectagles Summatio The area uder a parabola 1.1 Area ad distace Suppose we have the followig iformatio about the velocity of a particle, how

More information

LECTURE 8: ORTHOGONALITY (CHAPTER 5 IN THE BOOK)

LECTURE 8: ORTHOGONALITY (CHAPTER 5 IN THE BOOK) LECTURE 8: ORTHOGONALITY (CHAPTER 5 IN THE BOOK) Everythig marked by is ot required by the course syllabus I this lecture, all vector spaces is over the real umber R. All vectors i R is viewed as a colum

More information

Flow in Open Channel Flow Conditions

Flow in Open Channel Flow Conditions Civil Engineering Hydraulics Flow The graduate with a Science degree asks, "Why does it work?" The graduate with an Engineering degree asks, "How does it work?" The graduate with an Accounting degree asks,

More information

Review Problems Math 122 Midterm Exam Midterm covers App. G, B, H1, H2, Sec , 8.9,

Review Problems Math 122 Midterm Exam Midterm covers App. G, B, H1, H2, Sec , 8.9, Review Problems Math Midterm Exam Midterm covers App. G, B, H, H, Sec 8. - 8.7, 8.9, 9.-9.7 Review the Cocept Check problems: Page 6/ -, Page 690/- 0 PART I: True-False Problems Ch. 8. Page 6 True-False

More information

Maximum and Minimum Values

Maximum and Minimum Values Sec 4.1 Maimum ad Miimum Values A. Absolute Maimum or Miimum / Etreme Values A fuctio Similarly, f has a Absolute Maimum at c if c f f has a Absolute Miimum at c if c f f for every poit i the domai. f

More information

1 Cabin. Professor: What is. Student: ln Cabin oh Log Cabin! Professor: No. Log Cabin + C = A Houseboat!

1 Cabin. Professor: What is. Student: ln Cabin oh Log Cabin! Professor: No. Log Cabin + C = A Houseboat! MATH 4 Sprig 0 Exam # Tuesday March st Sectios: Sectios 6.-6.6; 6.8; 7.-7.4 Name: Score: = 00 Istructios:. You will have a total of hour ad 50 miutes to complete this exam.. A No-Graphig Calculator may

More information

Office: JILA A709; Phone ;

Office: JILA A709; Phone ; Office: JILA A709; Phoe 303-49-7841; email: weberjm@jila.colorado.edu Problem Set 5 To be retured before the ed of class o Wedesday, September 3, 015 (give to me i perso or slide uder office door). 1.

More information

: Transforms and Partial Differential Equations

: Transforms and Partial Differential Equations Trasforms ad Partial Differetial Equatios 018 SUBJECT NAME : Trasforms ad Partial Differetial Equatios SUBJECT CODE : MA 6351 MATERIAL NAME : Part A questios REGULATION : R013 WEBSITE : wwwharigaeshcom

More information

MATH Exam 1 Solutions February 24, 2016

MATH Exam 1 Solutions February 24, 2016 MATH 7.57 Exam Solutios February, 6. Evaluate (A) l(6) (B) l(7) (C) l(8) (D) l(9) (E) l() 6x x 3 + dx. Solutio: D We perform a substitutio. Let u = x 3 +, so du = 3x dx. Therefore, 6x u() x 3 + dx = [

More information

The Relative Angle Distribution Function in the Langevin Theory of Dilute Dipoles. Robert D. Nielsen

The Relative Angle Distribution Function in the Langevin Theory of Dilute Dipoles. Robert D. Nielsen The Relative Agle Distributio Fuctio i the agevi Theory of Dilute Dipoles Robert D. Nielse ExxoMobil Research ad Egieerig Co., Clito Towship, 545 Route East, Aadale, NJ 0880 robert.ielse@exxomobil.com

More information

Classical Mechanics Qualifying Exam Solutions Problem 1.

Classical Mechanics Qualifying Exam Solutions Problem 1. Jauary 4, Uiversity of Illiois at Chicago Departmet of Physics Classical Mechaics Qualifyig Exam Solutios Prolem. A cylider of a o-uiform radial desity with mass M, legth l ad radius R rolls without slippig

More information

A Use of HEC-RAS as Instructional Tool

A Use of HEC-RAS as Instructional Tool A Use o HEC-RAS as Instructional Tool Gregory H. Nail, PhD, PE Abstract A Hydraulics and Hydrology elective course has been made available or Civil Engineering students at The University o Tennessee at

More information

MATH 2411 Spring 2011 Practice Exam #1 Tuesday, March 1 st Sections: Sections ; 6.8; Instructions:

MATH 2411 Spring 2011 Practice Exam #1 Tuesday, March 1 st Sections: Sections ; 6.8; Instructions: MATH 411 Sprig 011 Practice Exam #1 Tuesday, March 1 st Sectios: Sectios 6.1-6.6; 6.8; 7.1-7.4 Name: Score: = 100 Istructios: 1. You will have a total of 1 hour ad 50 miutes to complete this exam.. A No-Graphig

More information

OPEN CHANNEL FLOW. One-dimensional - neglect vertical and lateral variations in velocity. In other words, Q v = (1) A. Figure 1. One-dimensional Flow

OPEN CHANNEL FLOW. One-dimensional - neglect vertical and lateral variations in velocity. In other words, Q v = (1) A. Figure 1. One-dimensional Flow OPEN CHANNEL FLOW Page 1 OPEN CHANNEL FLOW Open Channel Flow (OCF) is flow with one boundary exposed to atmospheric pressure. The flow is not pressurized and occurs because of gravity. Flow Classification

More information

The time evolution of the state of a quantum system is described by the time-dependent Schrödinger equation (TDSE): ( ) ( ) 2m "2 + V ( r,t) (1.

The time evolution of the state of a quantum system is described by the time-dependent Schrödinger equation (TDSE): ( ) ( ) 2m 2 + V ( r,t) (1. Adrei Tokmakoff, MIT Departmet of Chemistry, 2/13/2007 1-1 574 TIME-DEPENDENT QUANTUM MECHANICS 1 INTRODUCTION 11 Time-evolutio for time-idepedet Hamiltoias The time evolutio of the state of a quatum system

More information

Beaver Creek Corridor Design and Analysis. By: Alex Previte

Beaver Creek Corridor Design and Analysis. By: Alex Previte Beaver Creek Corridor Design and Analysis By: Alex Previte Overview Introduction Key concepts Model Development Design Accuracy Conclusion Refresh v = Beaver Creek Site = Wittenberg Introduction Low head

More information

Uniform Flow in Open Channels

Uniform Flow in Open Channels 1 UNIT 2 Uniform Flow in Open Channels Lecture-01 Introduction & Definition Open-channel flow, a branch of hydraulics, is a type of liquid flow within a conduit with a free surface, known as a channel.

More information

Lecture 5-2: Polytropes. Literature: MWW chapter 19

Lecture 5-2: Polytropes. Literature: MWW chapter 19 Lecture 5-2: Polytropes Literature: MWW chapter 9!" Preamble The 4 equatios of stellar structure divide ito two groups: Mass ad mometum describig the mechaical structure ad thermal equilibrium ad eergy

More information

STEADY UNIFORM FLOW IN OPEN CHANNEL

STEADY UNIFORM FLOW IN OPEN CHANNEL 11/4/018 School of Environmental Engineering STEY UNIFORM FLOW IN OEN CHNNEL ZULKRNIN BIN HSSN COURSE OUTCOMES CO1: ble to analyze and design the steady flow in pipeline (O1) CO: ble to analyze and design

More information

Using vegetation properties to predict flow resistance and erosion rates. Nick Kouwen University of Waterloo Waterloo, Canada

Using vegetation properties to predict flow resistance and erosion rates. Nick Kouwen University of Waterloo Waterloo, Canada 1/37 INTERNATIONAL WORKSHOP o RIParia FORest Vegetated Chaels: Hydraulic Morphological ad Ecological Aspects Treto, Italy, 20-22 February 2003 Usig vegetatio properties to predict flow resistace ad erosio

More information

1 1 2 = show that: over variables x and y. [2 marks] Write down necessary conditions involving first and second-order partial derivatives for ( x0, y

1 1 2 = show that: over variables x and y. [2 marks] Write down necessary conditions involving first and second-order partial derivatives for ( x0, y Questio (a) A square matrix A= A is called positive defiite if the quadratic form waw > 0 for every o-zero vector w [Note: Here (.) deotes the traspose of a matrix or a vector]. Let 0 A = 0 = show that:

More information

EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 4 - CALCULUS

EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 4 - CALCULUS EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 4 - CALCULUS TUTORIAL 1 - DIFFERENTIATION Use the elemetary rules of calculus arithmetic to solve problems that ivolve differetiatio

More information

Wave Motion

Wave Motion Wave Motio Wave ad Wave motio: Wave is a carrier of eergy Wave is a form of disturbace which travels through a material medium due to the repeated periodic motio of the particles of the medium about their

More information

Solid State Device Fundamentals

Solid State Device Fundamentals Solid State Device Fudametals ENS 345 Lecture Course by Alexader M. Zaitsev alexader.zaitsev@csi.cuy.edu Tel: 718 982 2812 4N101b 1 Thermal motio of electros Average kietic eergy of electro or hole (thermal

More information

Correlation Regression

Correlation Regression Correlatio Regressio While correlatio methods measure the stregth of a liear relatioship betwee two variables, we might wish to go a little further: How much does oe variable chage for a give chage i aother

More information

What about water... What about open channel flow... Continuity Equation. HECRAS Basic Principles of Water Surface Profile Computations

What about water... What about open channel flow... Continuity Equation. HECRAS Basic Principles of Water Surface Profile Computations What about water... HECRA Basic Principles o Water urace Proile Computations b G. Parodi WR ITC The Netherlands Incompressible luid must increase or decrease its velocit and depth to adjust to the channel

More information

HEC-RAS River Analysis System

HEC-RAS River Analysis System US Army Corps of Engineers Hydrologic Engineering Center HEC-RAS River Analysis System Hydraulic Reference Manual Version 3.1 November 00 Approved for Public Release. Distribution Unlimited CPD-69 Table

More information

Mock Exam 1. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q1 (4 - x) 3

Mock Exam 1. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q1 (4 - x) 3 Moc Exam Moc Exam Sectio A. Referece: HKDSE Math M 06 Q ( - x) + C () (-x) + C ()(-x) + (-x) 6 - x + x - x 6 ( x) + x (6 x + x x ) + C 6 6 6 6 C C x + x + x + x 6 6 96 (6 x + x x ) + + + + x x x x \ Costat

More information

1988 AP Calculus BC: Section I

1988 AP Calculus BC: Section I 988 AP Calculus BC: Sectio I 9 Miutes No Calculator Notes: () I this eamiatio, l deotes the atural logarithm of (that is, logarithm to the base e). () Uless otherwise specified, the domai of a fuctio f

More information

Fundamental Concepts: Surfaces and Curves

Fundamental Concepts: Surfaces and Curves UNDAMENTAL CONCEPTS: SURACES AND CURVES CHAPTER udametal Cocepts: Surfaces ad Curves. INTRODUCTION This chapter describes two geometrical objects, vi., surfaces ad curves because the pla a ver importat

More information

APPLICATION OF ERGUN EQUATION TO COMPUTATION OF CRITICAL SHEAR VELOCITY SUBJECT TO SEEPAGE

APPLICATION OF ERGUN EQUATION TO COMPUTATION OF CRITICAL SHEAR VELOCITY SUBJECT TO SEEPAGE Citatio: Cheg, N. S. (). Applicatio of Ergu equatio to computatio of critical shear velocity subject to seepage. Joural of Irrigatio ad Draiage Egieerig, ASCE. 9(4), 78-8. APPLICATION OF ERGUN EQUATION

More information

CALCULATION IN THE FIELD OF SEGMENTAL ROTOR MACHINES TAKING INTO ACCOUNT WINDING HARMONICS AND ROTOR AIRGAP IRREGULARITIES

CALCULATION IN THE FIELD OF SEGMENTAL ROTOR MACHINES TAKING INTO ACCOUNT WINDING HARMONICS AND ROTOR AIRGAP IRREGULARITIES CLCULTION IN THE FIELD OF SEGENTL OTO CHINES TKING INTO CCOUNT WINDING HONICS ND OTO IGP IEGULITIES Y STCT The stator mmf over a segmet of the segmetal rotor reluctace machie is treated as a ifiite array

More information

DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS

DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS Ivaa Štimac 1, Ivica Kožar 1 M.Sc,Assistat, Ph.D. Professor 1, Faculty of Civil Egieerig, Uiverity of Rieka, Croatia INTRODUCTION The vehicle-iduced

More information

Molecular Mechanisms of Gas Diffusion in CO 2 Hydrates

Molecular Mechanisms of Gas Diffusion in CO 2 Hydrates Supportig Iformatio Molecular Mechaisms of Gas Diffusio i CO Hydrates Shuai Liag, * Deqig Liag, Negyou Wu,,3 Lizhi Yi, ad Gaowei Hu,3 Key Laboratory of Gas Hydrate, Guagzhou Istitute of Eergy Coversio,

More information

Closed duct flows are full of fluid, have no free surface within, and are driven by a pressure gradient along the duct axis.

Closed duct flows are full of fluid, have no free surface within, and are driven by a pressure gradient along the duct axis. OPEN CHANNEL FLOW Open channel flow is a flow of liquid, basically water in a conduit with a free surface. The open channel flows are driven by gravity alone, and the pressure gradient at the atmospheric

More information

Mathematics Extension 2

Mathematics Extension 2 009 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Etesio Geeral Istructios Readig time 5 miutes Workig time hours Write usig black or blue pe Board-approved calculators may be used A table of stadard

More information

SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES

SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS STANDARD LEVEL PAPER 1 SPECIMEN PAPER 45 miutes INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper util istructed to do so. Aswer all the questios. For each questio,

More information

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense, 3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [

More information

Boundary Element Method (BEM)

Boundary Element Method (BEM) Boudary Elemet Method BEM Zora Ilievski Wedesday 8 th Jue 006 HG 6.96 TU/e Talk Overview The idea of BEM ad its advatages The D potetial problem Numerical implemetatio Idea of BEM 3 Idea of BEM 4 Advatages

More information

Fluvial Dynamics. M. I. Bursik ublearns.buffalo.edu October 26, Home Page. Title Page. Contents. Page 1 of 18. Go Back. Full Screen. Close.

Fluvial Dynamics. M. I. Bursik ublearns.buffalo.edu October 26, Home Page. Title Page. Contents. Page 1 of 18. Go Back. Full Screen. Close. Page 1 of 18 Fluvial Dynamics M. I. Bursik ublearns.buffalo.edu October 26, 2008 1. Fluvial Dynamics We want to understand a little of the basic physics of water flow and particle transport, as so much

More information

The Space Redundant Robotic Manipulator Chaotic Motion Dynamics Control Algorithm

The Space Redundant Robotic Manipulator Chaotic Motion Dynamics Control Algorithm Sesors & rasducers, Vol. 75, Issue 7, July 24, pp. 27-3 Sesors & rasducers 24 by IFSA Publishig, S. L. http://www.sesorsportal.com he Space Redudat Robotic Maipulator Chaotic Motio Dyamics Cotrol Algorithm

More information

Lecture 7: Polar representation of complex numbers

Lecture 7: Polar representation of complex numbers Lecture 7: Polar represetatio of comple umbers See FLAP Module M3.1 Sectio.7 ad M3. Sectios 1 ad. 7.1 The Argad diagram I two dimesioal Cartesia coordiates (,), we are used to plottig the fuctio ( ) with

More information

Lecture 10: River Channels

Lecture 10: River Channels GEOG415 Lecture 10: River Channels 10-1 Importance of channel characteristics Prediction of flow was the sole purpose of hydrology, and still is a very important aspect of hydrology. - Water balance gives

More information

Intrinsic Carrier Concentration

Intrinsic Carrier Concentration Itrisic Carrier Cocetratio I. Defiitio Itrisic semicoductor: A semicoductor material with o dopats. It electrical characteristics such as cocetratio of charge carriers, deped oly o pure crystal. II. To

More information

Hydraulics for Urban Storm Drainage

Hydraulics for Urban Storm Drainage Urban Hydraulics Hydraulics for Urban Storm Drainage Learning objectives: understanding of basic concepts of fluid flow and how to analyze conduit flows, free surface flows. to analyze, hydrostatic pressure

More information

CHAPTER 8 SYSTEMS OF PARTICLES

CHAPTER 8 SYSTEMS OF PARTICLES CHAPTER 8 SYSTES OF PARTICLES CHAPTER 8 COLLISIONS 45 8. CENTER OF ASS The ceter of mass of a system of particles or a rigid body is the poit at which all of the mass are cosidered to be cocetrated there

More information

39.1 Gradually Varied Unsteady Flow

39.1 Gradually Varied Unsteady Flow 39.1 Gradually Varied Unsteady Flow Gradually varied unsteady low occurs when the low variables such as the low depth and velocity do not change rapidly in time and space. Such lows are very common in

More information

PAIR OF STRAIGHT LINES.

PAIR OF STRAIGHT LINES. PAIR OF STRAIGHT LINES PREVIOUS EAMCET BITS 1. The value of λ with λ < 16 suh that x 1xy + 1y + 5x + λy 3 = represets a pair of straight lies, is [EAMCET 9] 1) 1 ) 9 3) 1 4)9 As: Sol. Δ= λ= 9. The area

More information

EGN 3353C Fluid Mechanics

EGN 3353C Fluid Mechanics Chapter 7: DIMENSIONAL ANALYSIS AND MODELING Lecture 3 dimesio measure of a physical quatity ithout umerical values (e.g., legth) uit assigs a umber to that dimesio (e.g., meter) 7 fudametal dimesios from

More information

Academic. Grade 9 Assessment of Mathematics. Released assessment Questions

Academic. Grade 9 Assessment of Mathematics. Released assessment Questions Academic Grade 9 Assessmet of Mathematics 2014 Released assessmet Questios Record your aswers to the multiple-choice questios o the Studet Aswer Sheet (2014, Academic). Please ote: The format of this booklet

More information

We will conclude the chapter with the study a few methods and techniques which are useful

We will conclude the chapter with the study a few methods and techniques which are useful Chapter : Coordiate geometry: I this chapter we will lear about the mai priciples of graphig i a dimesioal (D) Cartesia system of coordiates. We will focus o drawig lies ad the characteristics of the graphs

More information

2C09 Design for seismic and climate changes

2C09 Design for seismic and climate changes 2C09 Desig for seismic ad climate chages Lecture 02: Dyamic respose of sigle-degree-of-freedom systems I Daiel Grecea, Politehica Uiversity of Timisoara 10/03/2014 Europea Erasmus Mudus Master Course Sustaiable

More information

Principle Of Superposition

Principle Of Superposition ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give

More information

Damped Vibration of a Non-prismatic Beam with a Rotational Spring

Damped Vibration of a Non-prismatic Beam with a Rotational Spring Vibratios i Physical Systems Vol.6 (0) Damped Vibratio of a No-prismatic Beam with a Rotatioal Sprig Wojciech SOCHACK stitute of Mechaics ad Fudametals of Machiery Desig Uiversity of Techology, Czestochowa,

More information

CHAPTER 2 SEQUENCES AND SERIES OUTLINE Geometric Series Infinite Geometric Series and Sigma Notation 4 Review

CHAPTER 2 SEQUENCES AND SERIES OUTLINE Geometric Series Infinite Geometric Series and Sigma Notation 4 Review CHAPTER SEQUENCES AND SERIES OUTLINE Day Sectio Topic.7 Geometric Sequeces.8 Geometric Series 3.9 Ifiite Geometric Series ad Sigma Notatio 4 Review 5 Review 6 Chapter Test Terry Fox Math 007 .7 GEOMETRIC

More information

PHYC - 505: Statistical Mechanics Homework Assignment 4 Solutions

PHYC - 505: Statistical Mechanics Homework Assignment 4 Solutions PHYC - 55: Statistical Mechaics Homewor Assigmet 4 Solutios Due February 5, 14 1. Cosider a ifiite classical chai of idetical masses coupled by earest eighbor sprigs with idetical sprig costats. a Write

More information

1.3 Convergence Theorems of Fourier Series. k k k k. N N k 1. With this in mind, we state (without proof) the convergence of Fourier series.

1.3 Convergence Theorems of Fourier Series. k k k k. N N k 1. With this in mind, we state (without proof) the convergence of Fourier series. .3 Covergece Theorems of Fourier Series I this sectio, we preset the covergece of Fourier series. A ifiite sum is, by defiitio, a limit of partial sums, that is, a cos( kx) b si( kx) lim a cos( kx) b si(

More information

IYGB. Special Extension Paper E. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas

IYGB. Special Extension Paper E. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas YGB Special Extesio Paper E Time: 3 hours 30 miutes Cadidates may NOT use ay calculator. formatio for Cadidates This practice paper follows the Advaced Level Mathematics Core ad the Advaced Level Further

More information

Honors Calculus Homework 13 Solutions, due 12/8/5

Honors Calculus Homework 13 Solutions, due 12/8/5 Hoors Calculus Homework Solutios, due /8/5 Questio Let a regio R i the plae be bouded by the curves y = 5 ad = 5y y. Sketch the regio R. The two curves meet where both equatios hold at oce, so where: y

More information

GRADE 12 SEPTEMBER 2015 MATHEMATICS P2

GRADE 12 SEPTEMBER 2015 MATHEMATICS P2 NATIONAL SENIOR CERTIFICATE GRADE SEPTEMBER 05 MATHEMATICS P MARKS: 50 TIME: 3 hours *MATHE* This questio paper cosists of 3 pages icludig iformatio sheet, ad a SPECIAL ANSWERBOOK. MATHEMATICS P (EC/SEPTEMBER

More information

(c) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is

(c) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is Calculus BC Fial Review Name: Revised 7 EXAM Date: Tuesday, May 9 Remiders:. Put ew batteries i your calculator. Make sure your calculator is i RADIAN mode.. Get a good ight s sleep. Eat breakfast. Brig:

More information

ENGI 9420 Engineering Analysis Assignment 3 Solutions

ENGI 9420 Engineering Analysis Assignment 3 Solutions ENGI 9 Egieerig Aalysis Assigmet Solutios Fall [Series solutio of ODEs, matri algebra; umerical methods; Chapters, ad ]. Fid a power series solutio about =, as far as the term i 7, to the ordiary differetial

More information

6 BRANCHING PIPES. One tank to another 1- Q 1 = Q 2 +Q 3. One tank to two or more tanks 1- Q 1 = Q 2 + Q 3 or Q 3 =Q 1 + Q 2

6 BRANCHING PIPES. One tank to another 1- Q 1 = Q 2 +Q 3. One tank to two or more tanks 1- Q 1 = Q 2 + Q 3 or Q 3 =Q 1 + Q 2 6 RNHING PIPES Oe tak to aother - Q Q Q - pply eroulli s equatio betwee & through s & as well as & Oe tak to two or more taks - Q Q Q or Q Q Q - pply eroulli s equatio betwee each two taks 6. ischarge

More information

MECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION

MECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION MECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION Hisao Izuchi, Pricipal Egieerig Cosultat, Egieerig Solutio Uit, ChAS Project Operatios Masato Nishiguchi, Egieerig Solutio Uit, ChAS

More information

Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati

Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 2 Uniform Flow Lecture - 1 Introduction to Uniform Flow Good morning everyone,

More information

Topics in Probability Theory and Stochastic Processes Steven R. Dunbar. Evaluation of the Gaussian Density Integral

Topics in Probability Theory and Stochastic Processes Steven R. Dunbar. Evaluation of the Gaussian Density Integral Steve R. Dubar Departmet of Mathematics 3 Avery Hall Uiversity of Nebraska-Licol Licol, NE 68588-13 http://www.math.ul.edu Voice: 4-47-3731 Fax: 4-47-8466 Topics i Probability Theory ad Stochastic Processes

More information

CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS

CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS C.PRAX ad H.SADAT Laboratoire d'etudes Thermiques,URA CNRS 403 40, Aveue du Recteur Pieau 86022 Poitiers Cedex,

More information

Acoustic Field inside a Rigid Cylinder with a Point Source

Acoustic Field inside a Rigid Cylinder with a Point Source Acoustic Field iside a Rigid Cylider with a Poit Source 1 Itroductio The ai objectives of this Deo Model are to Deostrate the ability of Coustyx to odel a rigid cylider with a poit source usig Coustyx

More information