P = 2Rθ. The previous Manning formulas are used to predict V o and Q for uniform flow when the above expressions are substituted for A, P, and R h.
|
|
- Francine Jones
- 5 years ago
- Views:
Transcription
1 Uniform Flow in a Partly Full, Circular Pipe Fig shows a partly full, circular pipe with uniform flow. Since frictional resistance increases with wetted perimeter, but volume flow rate increases with cross sectional flow area, the maximum velocity and flow rate occur before the pipe is completely full. For this condition, the geometric properties of the flow are given by the equations below. Fig Uniform Flow in a Partly Full, Circular Channel A = R 2 θ sin2θ 2 P = 2Rθ R h = R 2 sin2θ 1 2θ The previous Manning formulas are used to predict V o and Q for uniform flow when the above expressions are substituted for A, P, and R h. V o α n R 2 sin2θ 1 2θ 2/3 S o Q = V o R 2 θ sin2θ 2 These equations have respective maxima for V o and Q given by X-7
2 V max = α n R 2/3 S o Q max = α n R 8/3 S o at θ = Þ and y = 0.813D at θ = Þ and y = 0.938D Efficient Uniform Flow Channels A common problem in channel flow is that of finding the most efficient lowresistance sections for given conditions. This is typically obtained by maximizing R h for a given area and flow rate. This is the same as minimizing the wetted perimeter. Note: Minimizing the wetted perimeter for a given flow should minimize the frictional pressure drop per unit length for a given flow. It is shown in the text that for constant value of area A and α = cot θ, the minimum value of wetted perimeter is obtained for 2 1/ 2 ( + α ) 2 A = y 2 1 α P = 4y 1+α 2 ( ) 1/ 2 2α y R h = 1 2 y Note: For any trapezoid angle, the most efficient cross section occurs when the hydraulic radius is one-half the depth. For the special case of a rectangle (α = 0, θ = 90 ), the most efficient cross section occurs with A = 2y 2 P = 4y R h = 1 2 y b = 2y X-8
3 Best Trapezoid Angle The general equations listed previously are valid for any value of α. For a given, fixed value of area A and depth y, the best trapezoid angle is given by α = cotθ = 1 3 or θ = 60Þ Example 10.3 What are the best dimensions for a rectangular brick channel designed to carry 5 m 3 /s of water in uniform flow with S o = 0.001? Taking n = from Table 10.1, A = 2 y 2, and R h = y ; Manning s formula is written as Q 1.0 n AR 2/3 h S o or 5 m 3 / s = y2 ( ) 1 2 y 2/3 ( 0.001) This can be solved to obtain y 8/3 = m 8/3 or y = 1.27m The corresponding area and width are A = 2y 2 = 3.21m 2 and b = A y = 2.53 m Note: The text compares these results with those for two other geometries having the same area. X-9
4 Specific Energy: Critical Depth One useful parameter in channel flow is the specific energy E, where y is the local water depth. E = y + V 2 2g Defining a flow per unit channel width as q = Q/b we write E = y + q2 2gy 2 Fig Illustration of a specific energy curve, depth y vs. the specific energy E. The curve for each flow rate Q has a minimum energy E min that occurs at a critical water depth y c corresponding to critical flow. For E > E min there are two possible states, one subcritical and one supercritical. Fig Specific Energy Illustration E min occurs at y = y c = q2 g 1/3 = Q 2 b 2 g 1/3 The value of E min is given by E min = 3 2 y c At this value of minimum energy and minimum depth we can write V c = ( gy c ) = C o and Fr = 1 X-10
5 Depending on the value of E min and V, one of several flow conditions can exist. For a given flow, if E < E min E = E min E > E min, V < V c E > E min, V > V c No solution is possible Flow is critical, y = y c, V = V c Fr = 1 Flow is subcritical, y > y c, Fr < 1, disturbances can propagate upstream as well as downstream Flow is supercritical, y < y c, Fr > 1, disturbances can only propagate downstream within a wave angle given by µ = sin -1 C o V = sin-1 ( gy) V Nonrectangular Channels For flows where the local channel width varies with depth y, critical values can be expressed as A c = b Q 2 o g 1/3 and V c = Q = ga c A c where = channel width at the free surface. These equations must be solved iteratively to determine the critical area A c and critical velocity V c. For critical channel flow that is also moving with constant depth (y c ), the slope corresponds to a critical slope S c given by X-11
6 and S c = n2 ga c α 2 = R h,c n2 2 V c α 2 4/3 R = n2 g h,c α 2 R h,c 1/ 3 α = 1. for S I units and for B. G. units P = f 8 P Example 10.6 Given: a 50, triangular channel has a flow rate of Q = 16 m 3 /s. Compute: (a) y c, (b) V c, (c) S c for n = a. For the given geometry, we have P = 2 ( y csc 50 ) A = 2[y ( y cot 50 )] R h = A/P = y/2 cos 50 = 2 ( y cot 50 ) For critical flow, we can write g A 3 2 c = bo Q or g c = 2 o 3 o ( y cot 50 ) ( 2 y cot 50 ) Q 2 c y c = 2.37 m ans. b. With y c, we compute P c = 6.18 m A c = 4.70 m 2,c = 3.97 m The critical velocity is now V c = Q A c = 16m3 /s 4.70m = 3.41 m /s ans. c. With n = 0.018, we compute the critical slope as S c = gn2 P 9.81 α 2 1/3 = ( )2 ( 6.18) R h /3 = ( )( 0.76) X-12
P10.5 Water flows down a rectangular channel that is 4 ft wide and 3 ft deep. The flow rate is 15,000 gal/min. Estimate the Froude number of the flow.
P10.5 Water flows down a rectangular channel that is 4 ft wide and ft deep. The flow rate is 15,000 gal/min. Estimate the Froude number of the flow. Solution: Convert the flow rate from 15,000 gal/min
More informationy 2 = 1 + y 1 This is known as the broad-crested weir which is characterized by:
CEE 10 Open Channel Flow, Dec. 1, 010 18 8.16 Review Flow through a contraction Critical and choked flows The hydraulic jump conservation of linear momentum y = 1 + y 1 1 + 8Fr 1 8.17 Rapidly Varied Flows
More informationUniform 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 informationPresented 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 informationconservation of linear momentum 1+8Fr = 1+ Sufficiently short that energy loss due to channel friction is negligible h L = 0 Bernoulli s equation.
174 Review Flow through a contraction Critical and choked flows The hydraulic jump conservation of linear momentum y y 1 = 1+ 1+8Fr 1 8.1 Rapidly Varied Flows Weirs 8.1.1 Broad-Crested Weir Consider the
More informationDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING Urban Drainage: Hydraulics. Solutions to problem sheet 2: Flows in open channels
DEPRTMENT OF CIVIL ND ENVIRONMENTL ENGINEERING Urban Drainage: Hydraulics Solutions to problem sheet 2: Flows in open channels 1. rectangular channel of 1 m width carries water at a rate 0.1 m 3 /s. Plot
More informationQ = α n AR2/3 h S1/2 0. bd 2d + b d if b d. 0 = ft1/3 /s
CEE 330 Open Channel Flow, Nov., 00 7 8.8 Review Open Channel Flow Gravity friction balance. In general we take an energy equation approach. y Uniform Flow x = 0 z = S 0L = h f where we could find h f
More informationFluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 42 Flows with a Free Surface Part II Good morning. I welcome you to this session
More informationHydraulics 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 informationClosed 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 informationWe will assume straight channels with simple geometries (prismatic channels) and steady state flow (in time).
56 Review Drag & Lift Laminar vs Turbulent Boundary Layer Turbulent boundary layers stay attached to bodies longer Narrower wake! Lower pressure drag! 8. Open-Channel Flow Pipe/duct flow closed, full,
More informationUNIFORM 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 informationCEE 3310 Open Channel Flow, Nov. 26,
CEE 3310 Open Channel Flow, Nov. 6, 018 175 8.10 Review Open Channel Flow Gravity friction balance. y Uniform Flow x = 0 z = S 0L = h f y Rapidly Varied Flow x 1 y Gradually Varied Flow x 1 In general
More informationOpen Channel Flow Part 2. Ch 10 Young, notes, handouts
Open Channel Flow Part 2 Ch 10 Young, notes, handouts Uniform Channel Flow Many situations have a good approximation d(v,y,q)/dx=0 Uniform flow Look at extended Bernoulli equation Friction slope exactly
More informationClosed 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 informationOPEN 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 informationFlow 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 informationGradually Varied Flow I+II. Hydromechanics VVR090
Gradually Varied Flow I+II Hydromechanics VVR090 Gradually Varied Flow Depth of flow varies with longitudinal distance. Occurs upstream and downstream control sections. Governing equation: dy dx So Sf
More informationOpen-channel hydraulics
Open-channel hydraulics STEADY FLOW IN OPEN CHANNELS constant discharge, other geometric and flow characteristics depended only on position Uniform flow Non-uniform flow S; y; v const. i i 0 i E y 1 y
More informationOpen Channel Hydraulics I - Uniform Flow
PDHonline Course H138 (2 PDH) Open Channel Hydraulics I - Uniform Flow Instructor: Harlan H. Bengtson, Ph.D., PE 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax:
More informationCIE4491 Lecture. Hydraulic design
CIE4491 Lecture. Hydraulic design Marie-claire ten Veldhuis 19-9-013 Delft University of Technology Challenge the future Hydraulic design of urban stormwater systems Focus on sewer pipes Pressurized and
More informationOpen Channel Flow I - The Manning Equation and Uniform Flow COURSE CONTENT
Open Channel Flow I - The Manning Equation and Uniform Flow Harlan H. Bengtson, PhD, P.E. COURSE CONTENT 1. Introduction Flow of a liquid may take place either as open channel flow or pressure flow. Pressure
More information3.2 CRITICAL DEPTH IN NONRECTANGULAR CHANNELS AND OCCUR- RENCE OF CRITICAL DEPTH
3.2 CRITICAL DEPTH IN NONRECTANGULAR CHANNELS AND OCCUR- RENCE OF CRITICAL DEPTH Critical Depth in Non-Rectangular Channels Consider an irregular channel: da w dd dd d Specific energy is defined as: E
More informationOPEN CHANNEL FLOW. Computer Applications. Numerical Methods and. Roland Jeppson. CRC Press UNIVERSITATSB'BUOTHEK TECHNISCHE. INFORMATlONSBiBUOTHEK
OPEN CHANNEL FLOW Numerical Methods and Computer Applications Roland Jeppson TECHNISCHE INFORMATlONSBiBUOTHEK UNIVERSITATSB'BUOTHEK HANNOVER Si. i. CRC Press Taylor &.Francis Group Boca Raton London New
More informationGuo, James C.Y. (1999). "Critical Flow Section in a Collector Channel," ASCE J. of Hydraulic Engineering, Vol 125, No. 4, April.
Guo, James C.Y. (1999). "Critical Flow Section in a Collector Channel," ASCE J. of Hydraulic Engineering, Vol 15, No. 4, April. CRITICAL FLOW SECTION IN A COLLECTOR CHANNEL By James C.Y. Guo, PhD, P.E.
More informationLateral Inflow into High-Velocity Channels
Lateral Inflow into High-Velocity Channels by Richard L. Stockstill PURPOSE: This Coastal and Hydraulics Engineering Technical Note (CHETN) investigates lateral flow discharging into a high-velocity channel.
More informationHydromechanics: Course Summary
Hydromechanics: Course Summary Hydromechanics VVR090 Material Included; French: Chapters to 9 and 4 + Sample problems Vennard & Street: Chapters 8 + 3, and (part of it) Roberson & Crowe: Chapter Collection
More informationA note on critical flow section in collector channels
Sādhan ā, Vol. 26, Part 5, October 2001, pp. 439 445. Printed in India A note on critical flow section in collector channels 1. Introduction SUBHASISH DEY Department of Civil Engineering, Indian Institute
More informationCE 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 informationLECTURE 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 informationBeaver 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 informationWater Flow in Open Channels
The Islamic Universit of Gaza Facult of Engineering Civil Engineering Department Hdraulics - ECIV 33 Chapter 6 Water Flow in Open Channels Introduction An open channel is a duct in which the liquid flows
More information28.2 Classification of Jumps
28.2 Classification of Jumps As mentioned earlier, the supercritical flow Froude number influences the characteristics of the hydraulic jump. Bradley and Peterka, after extensive experimental investigations,
More informationSummer Packet Greetings Future AP Calculus Scholar,
Summer Packet 2017 Greetings Future AP Calculus Scholar, I am excited about the work that we will do together during the 2016-17 school year. I do not yet know what your math capability is, but I can assure
More informationVARIED FLOW IN OPEN CHANNELS
Chapter 15 Open Channels vs. Closed Conduits VARIED FLOW IN OPEN CHANNELS Fluid Mechanics, Spring Term 2011 In a closed conduit there can be a pressure gradient that drives the flow. An open channel has
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Chapter Practice Dicsclaimer: The actual eam is different. On the actual eam ou must show the correct reasoning to receive credit for the question. SHORT ANSWER. Write the word or phrase that best completes
More informationLecture Note for Open Channel Hydraulics
Chapter -one Introduction to Open Channel Hydraulics 1.1 Definitions Simply stated, Open channel flow is a flow of liquid in a conduit with free space. Open channel flow is particularly applied to understand
More informationHydraulics 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 informationMath 005A Prerequisite Material Answer Key
Math 005A Prerequisite Material Answer Key 1. a) P = 4s (definition of perimeter and square) b) P = l + w (definition of perimeter and rectangle) c) P = a + b + c (definition of perimeter and triangle)
More informationNumerical Hydraulics
ETH Zurich, Fall 2017 Numerical Hydraulics Assignment 2 Numerical solution of shallow water wave propagation (www.surfertoday.com) 1 Introduction 1.1 Equations Understanding the propagation of shallow
More informationLab 7: Nonuniform Flow and Open Channel Transitions
CE 3620: Water Resources Engineering Spring 2015 Lab 7: Nonuniform Flow and Open Channel Transitions BACKGROUND An open channel transition may be defined as a change either in the direction, slope, or
More informationBlock 3 Open channel flow
Numerical Hydraulics Block 3 Open channel flow Markus Holzner Contents of the course Block 1 The equations Block Computation of pressure surges Block 3 Open channel flow (flow in rivers) Block 4 Numerical
More information1.060 Engineering Mechanics II Spring Problem Set 8
1.060 Engineering Mechanics II Spring 2006 Due on Monday, May 1st Problem Set 8 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More informationNumbers Content Points. Reference sheet (1 pt. each) 1-7 Linear Equations (1 pt. each) / Factoring (2 pt. each) /28
Summer Packet 2015 Your summer packet will be a major test grade for the first nine weeks. It is due the first day of school. You must show all necessary solutions. You will be tested on ALL material;
More informationFLOW IN CONDUITS. Shear stress distribution across a pipe section. Chapter 10
Chapter 10 Shear stress distribution across a pipe section FLOW IN CONDUITS For steady, uniform flow, the momentum balance in s for the fluid cylinder yields Fluid Mechanics, Spring Term 2010 Velocity
More informationDepartment of Hydro Sciences, Institute for Urban Water Management. Urban Water
Department of Hydro Sciences, Institute for Urban Water Management Urban Water 1 Global water aspects Introduction to urban water management 3 Basics for systems description 4 Water transport 5 Matter
More information1. Open Channel Hydraulics
Open Channel Flow. Open Channel Hydraulics.... Definition and differences between pipe flow and open channel flow.... Types of flow.... Properties of open channels...4.4 Fundamental equations... 5.4. The
More informationChapter 8: Flow in Pipes
8-1 Introduction 8-2 Laminar and Turbulent Flows 8-3 The Entrance Region 8-4 Laminar Flow in Pipes 8-5 Turbulent Flow in Pipes 8-6 Fully Developed Pipe Flow 8-7 Minor Losses 8-8 Piping Networks and Pump
More informationIterated, double, and triple integrals
Iterated, double, and triple integrals Double integrals in polar coordinates We ve discussed integration over rectangular regions, and integration over general regions where the bounds for the regions
More informationDr. Muhammad Ali Shamim ; Internal 652
Dr. Muhammad Ali Shamim ali.shamim@uettaxila.edu.pk 051-904765; Internal 65 Channel Tranistions A channel transition is defined as change in channel cross section e.g. change in channel width and/or channel
More informationBryn Mawr College Department of Physics Mathematics Readiness Examination for Introductory Physics
Brn Mawr College Department of Phsics Mathematics Readiness Eamination for Introductor Phsics There are 7 questions and ou should do this eam in two and a half hours. Do not use an books, calculators,
More informationNON UNIFORM FLOW IN OPEN CHANNEL
For updated version, please click on http://ocw.ump.edu.my HYDRAULICS NON - UNIFORM FLOW IN OPEN CHANNEL TOPIC 3.3 by Nadiatul Adilah Ahmad Abdul Ghani Faculty of Civil Engineering and Earth Resources
More informationNPTEL Quiz Hydraulics
Introduction NPTEL Quiz Hydraulics 1. An ideal fluid is a. One which obeys Newton s law of viscosity b. Frictionless and incompressible c. Very viscous d. Frictionless and compressible 2. The unit of kinematic
More informationChapter 4: Non uniform flow in open channels
Chapter 4: Non uniform flow in open channels Learning outcomes By the end of this lesson, students should be able to: Relate the concept of specific energy and momentum equations in the effect of change
More informationSTEADY 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 informationComparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow
Archives of Hydro-Engineering and Environmental Mechanics Vol. 61 (2014), No. 3 4, pp. 89 109 DOI: 10.1515/heem-2015-0006 IBW PAN, ISSN 1231 3726 Comparison of Average Energy Slope Estimation Formulas
More informationAnalysis of Flow Resistance for Different Bed Materials with Varying Discharge Experimentally in Open Channels
Analysis of Flow Resistance for Different Bed Materials with Varying Discharge Experimentally in Open Channels Lakshmi Mitra 1, Dr.Mimi Das Saikia 2 M.Tech. Student, Department of Civil Engineering, Assam
More informationMath 112 (Calculus I) Midterm Exam 3 KEY
Math 11 (Calculus I) Midterm Exam KEY Multiple Choice. Fill in the answer to each problem on your computer scored answer sheet. Make sure your name, section and instructor are on that sheet. 1. Which of
More informationQuick Review Sheet for A.P. Calculus Exam
Quick Review Sheet for A.P. Calculus Exam Name AP Calculus AB/BC Limits Date Period 1. Definition: 2. Steps in Evaluating Limits: - Substitute, Factor, and Simplify 3. Limits as x approaches infinity If
More informationChapter 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
More informationFluvial 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 information14.1. Multiple Integration. Iterated Integrals and Area in the Plane. Iterated Integrals. Iterated Integrals. MAC2313 Calculus III - Chapter 14
14 Multiple Integration 14.1 Iterated Integrals and Area in the Plane Objectives Evaluate an iterated integral. Use an iterated integral to find the area of a plane region. Copyright Cengage Learning.
More informationPressure Head: Pressure head is the height of a column of water that would exert a unit pressure equal to the pressure of the water.
Design Manual Chapter - Stormwater D - Storm Sewer Design D- Storm Sewer Sizing A. Introduction The purpose of this section is to outline the basic hydraulic principles in order to determine the storm
More informationMathematics, Algebra, and Geometry
Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................
More informationSection 6.2 Trigonometric Functions: Unit Circle Approach
Section. Trigonometric Functions: Unit Circle Approach The unit circle is a circle of radius centered at the origin. If we have an angle in standard position superimposed on the unit circle, the terminal
More informationThe University cannot take responsibility for any misprints or errors in the presented formulas. Please use them carefully and wisely.
Aide Mémoire Suject: Useful formulas for flow in rivers and channels The University cannot take responsiility for any misprints or errors in the presented formulas. Please use them carefully and wisely.
More informationMODELING FLUID FLOW IN OPEN CHANNEL WITH HORSESHOE CROSS SECTION
July. 2. Vol. 7. No. 2 MODELING FLUID FLOW IN OPEN CHANNEL WITH HORSESHOE CROSS SECTION 1 J. JOMBA, 2 D.M.THEURI, 2 E. MWENDA, 2 C. CHOMBA ABSTRACT Flow in a closed conduit is regarded as open channel
More informationContinuing Education Course #101 Drainage Design with WinTR-55
1 of 5 Continuing Education Course #101 Drainage Design with WinTR-55 1. WinTR-55 uses the Kinematic Wave method for calculating storm runoff rates and volumes. 2. According to the Velocity Method, the
More informationHEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1
HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the
More informationManning Equation - Open Channel Flow using Excel. Harlan H. Bengtson, PhD, P.E. COURSE CONTENT
Manning Equation - Open Channel Flow using Excel Harlan H. Bengtson, PhD, P.E. COURSE CONTENT 1. Introduction The Manning equation is a widely used empirical equation for uniform open channel flow of water.
More information5. ROADSIDE AND MEDIAN CHANNELS
5. ROADSIDE AND MEDIAN CHANNELS Roadside and median channels are open-channel systems which collect and convey stormwater from the pavement surface, roadside, and median areas. These channels may outlet
More informationAdvanced 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 informationLone Star College-CyFair Formula Sheet
Lone Star College-CyFair Formula Sheet The following formulas are critical for success in the indicated course. Student CANNOT bring these formulas on a formula sheet or card to tests and instructors MUST
More informationUniform Channel Flow Basic Concepts Hydromechanics VVR090
Uniform Channel Flow Basic Concepts Hydromechanics VVR090 ppt by Magnus Larson; revised by Rolf L Feb 2014 SYNOPSIS 1. Definition of Uniform Flow 2. Momentum Equation for Uniform Flow 3. Resistance equations
More informationExperiment 7 Energy Loss in a Hydraulic Jump
Experiment 7 Energ Loss in a Hdraulic Jump n Purpose: The purpose of this experiment is to examine the transition from supercritical (rapid) flow to subcritical (slow) flow in an open channel and to analze
More informationI) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11)
AP Calculus Summer Packet Answer Key Reminders:. This is not an assignment.. This will not be collected.. You WILL be assessed on these skills at various times throughout the course.. You are epected to
More informationBryn Mawr College Department of Physics Mathematics Readiness Examination for Introductory Physics
Brn Mawr College Department of Phsics Mathematics Readiness Eamination for Introductor Phsics There are 7 questions and ou should do this eam in two and a half hours. Do not use an books, calculators,
More informationSect 7.4 Trigonometric Functions of Any Angles
Sect 7.4 Trigonometric Functions of Any Angles Objective #: Extending the definition to find the trigonometric function of any angle. Before we can extend the definition our trigonometric functions, we
More informationViscous Flow in Ducts
Dr. M. Siavashi Iran University of Science and Technology Spring 2014 Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate
More informationAP Calculus BC Summer Assignment. Please show all work either in the margins or on separate paper. No credit will be given without supporting work.
AP Calculus BC Summer Assignment These problems are essential practice for AP Calculus BC. Unlike AP Calculus AB, BC students need to also be quite familiar with polar and parametric equations, as well
More informationBasic Hydraulics. Rabi H. Mohtar ABE 325
Basic Hydraulics Rabi H. Mohtar ABE 35 The river continues on its way to the sea, broken the wheel of the mill or not. Khalil Gibran The forces on moving body of fluid mass are:. Inertial due to mass (ρ
More informationMath Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More informationChapter (3) Water Flow in Pipes
Chapter (3) Water Flow in Pipes Water Flow in Pipes Bernoulli Equation Recall fluid mechanics course, the Bernoulli equation is: P 1 ρg + v 1 g + z 1 = P ρg + v g + z h P + h T + h L Here, we want to study
More informationMATH 2053 Calculus I Review for the Final Exam
MATH 05 Calculus I Review for the Final Exam (x+ x) 9 x 9 1. Find the limit: lim x 0. x. Find the limit: lim x + x x (x ).. Find lim x (x 5) = L, find such that f(x) L < 0.01 whenever 0 < x
More informationstorage tank, or the hull of a ship at rest, is subjected to fluid pressure distributed over its surface.
Hydrostatic Forces on Submerged Plane Surfaces Hydrostatic forces mean forces exerted by fluid at rest. - A plate exposed to a liquid, such as a gate valve in a dam, the wall of a liquid storage tank,
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More informationExample 2.1. Draw the points with polar coordinates: (i) (3, π) (ii) (2, π/4) (iii) (6, 2π/4) We illustrate all on the following graph:
Section 10.3: Polar Coordinates The polar coordinate system is another way to coordinatize the Cartesian plane. It is particularly useful when examining regions which are circular. 1. Cartesian Coordinates
More informationTHE EFFECTS OF OBSTACLES ON SURFACE LEVELS AND BOUNDARY RESISTANCE IN OPEN CHANNELS
Manuscript submitted to 0th IAHR Congress, Thessaloniki, 4-9 August 00 THE EFFECTS OF OBSTACLES ON SURFACE LEVELS AND BOUNDARY RESISTANCE IN OPEN CHANNELS J. D. FENTON Department of Civil and Environmental
More information1 Conduction Heat Transfer
Eng6901 - Formula Sheet 3 (December 1, 2015) 1 1 Conduction Heat Transfer 1.1 Cartesian Co-ordinates q x = q xa x = ka x dt dx R th = L ka 2 T x 2 + 2 T y 2 + 2 T z 2 + q k = 1 T α t T (x) plane wall of
More information1993 AP Calculus AB: Section I
99 AP Calculus AB: Section I 9 Minutes Scientific Calculator Notes: () The eact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among
More informationMath 1431 Final Exam Review. 1. Find the following limits (if they exist): lim. lim. lim. lim. sin. lim. cos. lim. lim. lim. n n.
. Find the following its (if they eist: sin 7 a. 0 9 5 b. 0 tan( 8 c. 4 d. e. f. sin h0 h h cos h0 h h Math 4 Final Eam Review g. h. i. j. k. cos 0 n nn e 0 n arctan( 0 4 l. 0 sin(4 m. cot 0 = n. = o.
More informationTrigonometry LESSON SIX - Trigonometric Identities I Lesson Notes
LESSON SIX - Trigonometric Identities I Example Understanding Trigonometric Identities. a) Why are trigonometric identities considered to be a special type of trigonometric equation? Trigonometric Identities
More informationDownloaded from AREAS RELATED TO CIRCLES
AREAS RELATED TO CIRCLES #,&#,&#!#'&*(#6$&#)(,,#&()!,&&!!&###&#%#&#&.,.&#$#*&.*- 1. In the adjoining figure ABC right angled triangle right angled at A. Semi circles are drawn on the sides of the triangle
More informationTechnical Calculus I Homework. Instructions
Technical Calculus I Homework Instructions 1. Each assignment is to be done on one or more pieces of regular-sized notebook paper. 2. Your name and the assignment number should appear at the top of the
More informationFluid Mechanics II 3 credit hour. Fluid flow through pipes-minor losses
COURSE NUMBER: ME 323 Fluid Mechanics II 3 credit hour Fluid flow through pipes-minor losses Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Losses in Noncircular
More informationLong-Throated Flumes. 6. Hydraulic Theory and Computations for. 6.1 Continuity Equation
6. Hydraulic Theory and Computations for Long-Throated Flumes The purpose of this chapter is to explain the fimdamental principles involved in analytically modeling the flow through weirs and flumes, so
More informationChapter 3.8: Energy Dissipators. By Dr. Nuray Denli Tokyay
Chapter 3.8: Energy Dissipators By Dr. Nuray Denli Tokyay 3.1 Introduction A stilling basin is a short length of paved channel placed at the foot of a spillway or any other source of supercritical flow
More informationBusiness Calculus
Business Calculus 978-1-63545-025-5 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Senior Contributing Authors: Gilbert
More informationOpen Channel Flow - General. Hydromechanics VVR090
Open Channel Flow - General Hydromechanics VVR090 ppt by Magnus Larson; revised by Rolf L Jan 2014, Feb 2015 SYNOPSIS 1. Introduction and Applications 2. The History of Open Channel Flow 3. Flow Classification
More informationOpen Channel Hydraulics
30 Open Channel Hydraulics Aldo Giorgini (deceased) Donald D. Gray West Virginia University 30. Definitions and Principles Classification of Flows Flow Regimes 30. Balance and Conservation Principles Conservation
More information