Hydromechanics: Course Summary


 Phyllis Holt
 2 years ago
 Views:
Transcription
1 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 of sample problems in open channel flow Exam: 8th of May in MA0G
2 Fundamental Equations Conservation of mass: Q = ua Conservation of momentum: F =ρq( u u ) Conservation of energy: u H = z+ y+ g H = H + h L Laboratory Experiments Often difficult to solve fluid flow problems by analytical or numerical methods. Also, data are required for validation. The need for experiments Difficult to do experiment at the true size (prototype), so they are typically carried out at another scale (model). Develop rules for design of experiments and interpretation of measurement results.
3 Similitude and Dimenisional Analysis Similitude: how to carry out model tests and how to transfer model results to prototype (laws of similarity) Dimensional analysis: how to describe physical relationships in an efficient, general way so that the extent of necessary experiments is minimized (Buckingham s Ptheorem) Basic Types of Similitude geometric kinematic dynamic d d p m lp = =λ l m All of these must be obtained for complete similarity between model and prototype. 3
4 Important Forces for the Flow Field pressure (F P ) inertia (F I ) gravity (F G ) viscosity (F V ) elasticity (F E ) surface tension (F T ) Dimensionless Numbers Reynolds Froude Cauchy (Mach) Weber Vl Vl Re = = μ/ ρ ν V Fr = gl V V C = = = M E/ ρ c ρlv W = σ Euler E = V ρ Δp Dimensionless numbers same in prototype and model produces dynamic similarity. 4
5 Dimensional Analysis Dimensions (e.g., length, mass, time, temperature) Units (e.g., m, kg, s, K) Three independent dimensions of primary interest: length (L) mass (M) time (t) Metric system F = ML t Force: [ ] Buckingham s PTheorem Buckingham provided a systematic approach to dimensional analysis through his theorem expressed as:. If n variables are involved in the problem, then k equations of their exponents can be written. In most cases k is the number of independent dimensions (e.g., M, L, t) 3. The functional relationship may be expressed in terms of n k distinct dimensionless groups 5
6 Example of Dimensional Analysis Drag force (D) on a ship. Assume that D is related to length (l), density (ρ), viscosity (m), speed (V), and acceleration due to gravity (g): { } f D,, l ρμ,, V, g = 0 Problem involves n = 6 variables and k = 3 fundamental dimensions Æ k  n = 6 3 = 3 dimensionless groups can be formed: { } f ' Π, Π, Π = 0 3 Many different ways to combine the variables into dimensionless groups rational approach needed. Method for Deriving Dimensionless Groups. Find the largest number of variables which do not form a dimensionless Pgroup. Determine the number of Pgroups to be formed 3. Combine sequentially the variables in. with the remaining variables to form Pgroups. Present example: select ρ, V, and l and combine with remaining variables: 3 3 {, ρ,, } { μ, ρ, Vl, } {, ρ,, } Π = f D V l Π = f Π = f g V l 6
7 First Pgroup: Π = D ρ V l a b c d Analyze dimensions: M Lt a b c ML M L = 3 t L t ( L) d M : 0= a+ b L: 0= a 3b+ c+ d t: 0= a+ c b= a c= a d = a Result: D Π = ρlv a Fluid Flow About Immersed Objects Flow about an object may induce: drag forces lift forces vortex motion Asymmetric flow field generates a net force Drag forces arise from pressure differences over the body (due to its shape) and frictional forces along the surface (in the boundary layer) 7
8 Drag force: o A D= psin θ da+ τ cosθda A Pressure drag (D p ) Frictional drag (D f ) (form drag) Pressure drag function of the body shape and flow separation Frictional drag function of the boundary layer properties (surface roughness etc) Results of Dimensional Analysis Total drag force: D = CD ρav C = f D 3 o { Re,M} Total lift force: L= CL ρav C = f L 4 o { Re,M} 8
9 Drag Coefficient for Various Bodies D 3D Example of Drag Force Calculation parachute jumping sedimentation of particle popcorn popper Basic equation for drag force: D = C D ρav o C D obtained from empirical studies A is the projected area on a plane perpendicular to the flow direction 9
10 Vortex Shedding Under certain conditions vortices are generated from the edges of a body in a flow. Æ Von Karman s vortex street Vortex street behind a cylinder If 6 < Re < 5000, regular vortex sheeding may occur at a frequency n determined by Strouhal s number: nd S = V o (S = 0. over a wide range of Re) Vortices at Aleutian Island Boundary Layer on a Flat Plate Boundary layer: the zone in which the velocity profile is governed by frictional action 0
11 Drag Coefficient for Smooth, Flat Plates Df = Cf ρvo A A: surface area of plate Open Channel Flow Open channel: a conduit for flow which has a free surface Free surface: interface between two fluids of different density Characteristics of open channel flow: pressure constant along water surface gravity drives the motion pressure is approximately hydrostatic flow is turbulent and unaffected by surface tension
12 Flow Classification steady unsteady uniform nonuniform varied flow (= nonuniform): gradually varied rapidly varied Flow Classification subcritical supercritical flow characterized by the Froude number Fr = U gl L taken to be the hydraulic depth D=A/T Fr < subcritical flow Fr = critical flow Fr > supercritical flow
13 Definition of Channel and Flow Properties Hydraulic radius (R): ratio of flow area to wetted perimeter R = A P Hydraulic depth (D): ratio of flow area to top width A D = T Energy Equation Total energy of a parcel of water traveling on a streamline (no friction): H p u = z+ + γ g elevation head pressure head velocity head p z + γ hydraulic grade line 3
14 Critical Flow Specific energy: u Q E = y+α = y+α g ga Minimum specific energy yields: u = gd u Fr = = gd Critical Flow Rectangular channel of width b: Q q = b q u = y y c q = g uc yc = g yc = Ec 3 /3 4
15 Step in Rectangular Channel Bernoulli equation (between upstream and downstream points): u u + y = + y +Δz g g E = E Δz Total energy: Water Surface Variation from the Energy Equation u H = z+ y+ g Differentiating with respect to distance: ( / ) dh dz dy = + + d u g dx dx dx dx Resulting equation: dy dx So Sf = Fr 5
16 Momentum Equation Hydraulic jump Momentum equation (rectangular channel): y y q = u u γ γ γ g ( ) Momentum equation for rectangular section: q = g y y ( y y ) Solutions: y y ( 8Fr ) = + y y ( 8Fr ) = + Energy loss: Δ E = ( y y ) 3 4y y 6
17 Uniform occurs when: Uniform Flow. The depth, flow area, and velocity at every cross section is constant. The energy grade line, water surface, and channel bottom are all parallel: Sf = Sw = So S f = slope of energy grade line S w = slope of water surface S o = slope of channel bed Uniform Flow Formula Mannings equation for velocity: n /3 u = R S Uniform flow rate: n /3 Q= ua= AR S Section factor: /3 AR (increases with depth) Conveyance: K = AR n /3 7
18 Computation of Uniform Flow. Channel cross section and shape, water depth, and slope known => Q or u can be calculated directly. Channel cross section and shape, water velcoity or flow, and slope known => water depth may be calculated through some iterative procedure Roughness known and constant. Manning s Roughness n
19 Gradually Varied Flow Depth of flow varies with longitudinal distance. Occurs upstream and downstream control sections. Governing equation: dy dx So Sf = Fr Classification of Gradually Varied Flow Profiles Water surface profiles may be classified with respect to: the channel slope the relationship between y, y N, and y c Prevailing conditions: If y < y N, then S f > S o If y > y N, then S f < S o If Fr >, then y < y c Profile categories: M (mild) 0 < S o < S c S (steep) S o > S c > 0 C (critical) S o = S c A (adverse) S o < 0 If Fr <, then y > y c If S f = S o, then y = y N 9
20 Gradually Varied Flow Profile Classification II Flow Transition Subcritical to supercritical Supercritical to subcritical 0
21 Strategy for Analysis of Open Channel Flow Typical approach in the analysis:. Start at control points. Proceed upstream or downstream depending on whether subcritical or supercritical flow occurs, respectively Control points typically occur at physical barriers, for example, sluice gates, dams, weirs, drop structures, or changes in channel slope. Uniform Channel Prismatic channel with constant slope and resistance coefficient. Apply energy equation over a small distance Dx: d u y So S dx + = g f Express the equation in difference form: u Δ y+ = ( So Sf ) Δx g S f nu = R 4/3
22 y i y i+ u i u i+ Reach i Computation of Gradually Varied Flow Dx i x Δ x = i ( y+ u / g) ( y+ u /g) i+ i 4/3 So ( n u / R ) i+ / All quantities known at i. Assume y i+ and compute Dx i (u i+ given by the continuity equation). TrialandError Approach Wellsuited for computations in nonprismatic channels. Channel properties (e.g., resistance coefficient and shape) are a function of longitudinal distance. Depth is obtained at specific xlocations. Apply energy equation between two stations located Dx apart (z is the elevation of the water surface): u Δ z+ = Sf Δx g u u z+ = z + + Sf Δx g g
23 Estimate of frictional losses: S = S + S ( ) f f f Equation is solved by trialanderror (from to ):. Assume y Æ u (continuity equation). Compute S f 3. Compute y from governing equation. If this value agrees with the assumed y, the solution has been found. Otherwise continue calculations. Examples of Gradually Varied Flow Flow in channel between two reservoirs (lakes):. Steep slope, low downstream water level. Steep slope, high downstream water level 3. Mild slope, long channel 4. Mild slope, short channel 5. Sluice gate located in the channel Study flow situation that develops + calculation procedure 3
24 Spatially Varied Flow Flow varies with longitudinal distance. Examples: sidechannel spillways, side weirs, channels with permeable boundaries, gutters for conveying storm water runoff, and drop structures in the bottom of channels. Two types of flow: discharge increases with distance discharge decreases with distance Different principles govern => different analysis approach Increasing discharge: use momentum equation (hard to quantify energy losses) γyb o γ yb a =ρqx ( a) u( xa) 0 Decreasing discharge: use energy equation Q H = z+ y+ ga 4
25 Weirs Types of weirs (classified according to shape): rectangular Vnotch trapezoidal parabolic special type (e.g., Cipoletti, Sutro) Distinguish between: Broadcrested Sharpcrested Discharge Formula for Rectangular BroadCrested Weir h Apply Bernoulli equation between upstream section and the control section (critical depth occurs here). / Q = CDCv g Th 3 3 3/ 5
26 Discharge Formula for SharpCrested Weirs h z Rectangular: Triangular: Q = C g bh 3 e ( ) / 3/ 8 Q = C ( g) tan ( θ/) h 5 e / 5/ Parshall Flume Critical flow occurs in the flume throat followed by a hydraulic jump downstream. General discharge formula: B Q = AWH a 6
27 Venturimeters Involves a constriction in the flow. The constriction produces an accelerated flow and a fall in the hydraulic grade line (pressure) directly related to the flow rate. CA v p p Q = g + z z / γ γ ( A A ) Orifices Used for many purposes in engineering, including measuring the flow rate. A difference compared to nozzles is that the minimum flow section does not occur at the orifice but some distance downstream (in vena contracta). Flow rate is given by: CCA v c p p Q = g z + z γ γ ( A A ) Cc / Area in vena contracta is: A = CA c 7
28 Submerged Orifice Discharge from one large reservoir to another: ( ) Q= C C A g h h c v Discharge to the atmosphere: Q = C C A gh = CA gh c v Sluice Gate Special case of orifice flow: only contraction on the top of the jet. Pressure in vena contracta is assumed to be hydrostatic. CCA v c Q= g y y / ( y y ) ( ) 8
Gradually 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 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 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 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 informationENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids
CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific
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 informationOPEN CHANNEL FLOW. Onedimensional  neglect vertical and lateral variations in velocity. In other words, Q v = (1) A. Figure 1. Onedimensional 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 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 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 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 informationOpen Channel Flow  General. Open Channel Flow
Open Channel Flow  General Hydromechanics VVR090 Open Channel Flow Open channel: a conduit for flow which has a free surface Free surface: interface between two fluids of different density Characteristics
More informationR09. d water surface. Prove that the depth of pressure is equal to p +.
Code No:A109210105 R09 SET1 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal
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 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 informationCE 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
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 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 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 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 BroadCrested Weir Consider the
More informationUNIT I FLUID PROPERTIES AND STATICS
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: IIB.Tech & ISem Course & Branch:
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 informationDimensions represent classes of units we use to describe a physical quantity. Most fluid problems involve four primary dimensions
BEE 5330 Fluids FE Review, Feb 24, 2010 1 A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container will form a free
More informationINSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.
Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad  00 0 AERONAUTICAL ENGINEERING : Mechanics of Fluids : A00 : III B. Tech Year : 0 0 Course Coordinator
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 NonRectangular Channels Consider an irregular channel: da w dd dd d Specific energy is defined as: E
More informationCIE4491 Lecture. Hydraulic design
CIE4491 Lecture. Hydraulic design Marieclaire ten Veldhuis 199013 Delft University of Technology Challenge the future Hydraulic design of urban stormwater systems Focus on sewer pipes Pressurized and
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 informationEngineering Fluid Mechanics
Engineering Fluid Mechanics Eighth Edition Clayton T. Crowe WASHINGTON STATE UNIVERSITY, PULLMAN Donald F. Elger UNIVERSITY OF IDAHO, MOSCOW John A. Roberson WASHINGTON STATE UNIVERSITY, PULLMAN WILEY
More informationUNIT IV DIMENSIONAL AND MODEL ANALYSIS
UNIT IV DIMENSIONAL AND MODEL ANALYSIS INTRODUCTION Dimensional analysis is a method of dimensions. It is a mathematical technique used in research work for design and for conducting model tests. It deals
More informationy 2 = 1 + y 1 This is known as the broadcrested 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 informationUNIT V : DIMENSIONAL ANALYSIS AND MODEL STUDIES
UNIT V : DIMENSIONAL ANALYSIS AND MODEL STUDIES 1. Define dimensional analysis. Dimensional analysis is a mathematical technique which makes use of the study of dimensions as an aid to solution of several
More informationFLUID MECHANICS. Chapter 9 Flow over Immersed Bodies
FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1
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. OpenChannel Flow Pipe/duct flow closed, full,
More informationHydraulic Engineering
PDHonline Course H146 (4 PDH) Hydraulic Engineering Instructor: Mohamed Elsanabary, Ph.D., Prov. Lic. Engineering. 2013 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone & Fax:
More informationFluid Mechanics. du dy
FLUID MECHANICS Technical English  I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's
More informationDr. Muhammad Ali Shamim ; Internal 652
Dr. Muhammad Ali Shamim ali.shamim@uettaxila.edu.pk 051904765; 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 informationFundamentals of Fluid Mechanics
Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department
More informationUniform 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 informationPROPERTIES OF FLUIDS
Unit  I Chapter  PROPERTIES OF FLUIDS Solutions of Examples for Practice Example.9 : Given data : u = y y, = 8 Poise = 0.8 Pas To find : Shear stress. Step  : Calculate the shear stress at various
More informationSOE2156: Fluids Lecture 7
Weirs and SOE2156: Fluids Lecture 7 Vee Vee Last lecture { assumed the channel was uniform (constant depth, shape, slope etc.) { steady uniform Found that : location of free surface to be determined 2
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 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 informationV. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems.
V. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems. However, analytical methods are not always satisfactory due
More informationUNIT IV. Flow through Orifice and Mouthpieces and Flow through Notchs and Weirs
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : FM(15A01305) Year & Sem: IIB.Tech & ISem Course & Branch: B.Tech 
More informationChapter 7 DIMENSIONAL ANALYSIS AND SIMILITUDE Because so few real flows can be solved exactly by analytical methods alone, the development of fluid
Chapter 7 DIMENSIONAL ANALYSIS AND SIMILITUDE Because so few real flows can be solved exactly by analytical methods alone, the development of fluid mechanics has depended heavily on experimental results.
More informationVisualization of flow pattern over or around immersed objects in open channel flow.
EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:
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 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 informationPresented by: Civil Engineering Academy
Presented by: Civil Engineering Academy OpenChannel Flow Uniform Flow (See CERM Ch. 19) Characterized by constant depth volume, and cross section. It can be steady or unsteady Nonuniform Flow *Not on
More informationInstitute of Aeronautical Engineering
Institute of Aeronautical Engineering Hydraulics & Hydraulic Machinery (ACE011) R16 B.Tech III Year V Semester Prepared by Dr. G. Venkata Ramana Professor& HOD Civil Engineering 1 Unit I OPEN CHANNEL FLOW
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 informationAPPLIED FLUID DYNAMICS HANDBOOK
APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /
More information2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.
CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise
More informationFE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)
Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.
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 information3. GraduallyVaried Flow
5/6/18 3. Graduallyaried Flow Normal Flow vs Graduallyaried Flow Normal Flow /g EGL (energy grade line) iction slope Geometric slope S Normal flow: Downslope component of weigt balances bed friction
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 informationChapter 3 Bernoulli Equation
1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around
More informationBUCKINGHAM PI THEOREM
BUCKINGHAM PI THEOREM Dimensional Analysis It is used to determine the equation is right or wrong. The calculation is depends on the unit or dimensional conditions of the equations. For example; F=ma F=MLT
More informationBACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)
No. of Printed Pages : 6 BME028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) TermEnd Examination December, 2011 00792 BME028 : FLUID MECHANICS Time : 3 hours
More informationS.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100
Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum
More informationDimensional and Model Analysis
Dimensional and Model Analysis 5.1 Fundamental dimensions 5.2 Rayleigh s and Buckingham s method 5.3 Dimension less numbers and their significance 5.4 Hydraulic similitude 5.5 Type of models 5.6 Distorted
More informationCLASS SCHEDULE 2013 FALL
CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties
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 informationEFFECT OF VERTICAL CURVATURE OF FLOW AT WEIR CREST ON DISCHARGE COEFFICIENT
Ninth International Water Technology Conference, IWTC9 2005, Sharm ElSheikh, Egypt 249 EFFECT OF VERTICAL CURVATURE OF FLOW AT WEIR CREST ON DISCHARGE COEFFICIENT Kassem Salah ElAlfy Associate Prof.,
More informationUniversity of Engineering and Technology, Taxila. Department of Civil Engineering
University of Engineering and Technology, Taxila Department of Civil Engineering Course Title: CE201 Fluid Mechanics  I Prerequisite(s): None Credit Hours: 2 + 1 Contact Hours: 2 + 3 Text Book(s): Reference
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 informationEXAMPLES (SEDIMENT TRANSPORT) AUTUMN 2018
EXAMPLES (SEDIMENT TRANSPORT) AUTUMN 2018 Q1. Using Cheng s formula estimate the settling velocity of a sand particle of diameter 1 mm in: (a) air; (b) water. Q2. Find the critical Shields parameter diameter
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 220306658 Phone & Fax:
More informationIf a stream of uniform velocity flows into a blunt body, the stream lines take a pattern similar to this: Streamlines around a blunt body
Venturimeter & Orificemeter ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 5 Applications of the Bernoulli Equation The Bernoulli equation can be applied to a great
More informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF CIVIL ENGINEERING QUESTION BANK III SEMESTER CE 8302 FLUID MECHANICS Regulation 2017 Academic Year 2018 19 Prepared by Mrs.
More informationHOW TO GET A GOOD GRADE ON THE MME 2273B FLUID MECHANICS 1 EXAM. Common mistakes made on the final exam and how to avoid them
HOW TO GET A GOOD GRADE ON THE MME 2273B FLUID MECHANICS 1 EXAM Common mistakes made on the final exam and how to avoid them HOW TO GET A GOOD GRADE ON THE MME 2273B EXAM Introduction You now have a lot
More informationFLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation
FLUID MECHANICS Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation CHAP 3. ELEMENTARY FLUID DYNAMICS  THE BERNOULLI EQUATION CONTENTS 3. Newton s Second Law 3. F = ma along a Streamline 3.3
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 informationLongThroated Flumes. 6. Hydraulic Theory and Computations for. 6.1 Continuity Equation
6. Hydraulic Theory and Computations for LongThroated Flumes The purpose of this chapter is to explain the fimdamental principles involved in analytically modeling the flow through weirs and flumes, so
More informationFluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
More informationExperiment To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter.
SUBJECT: FLUID MECHANICS VIVA QUESTIONS (M.E 4 th SEM) Experiment To determine the coefficient of impact for vanes. Q1. Explain impulse momentum principal. Ans1. Momentum equation is based on Newton s
More informationAn Introduction to Engineering Fluid Mechanics
An Introduction to Engineering Fluid Mechanics Other Macmillan titles of related interest Jonas M. K. Dake: Essentials of Engineering Hydrology L. Huisman: Groundwater Recovery L. M. MilneThomson: Theoretical
More informationP = 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.
Uniform Flow in a Partly Full, Circular Pipe Fig. 10.6 shows a partly full, circular pipe with uniform flow. Since frictional resistance increases with wetted perimeter, but volume flow rate increases
More informationApproximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.
Appendix FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface
More informationOpen Channel Hydraulics III  Sharpcrested
PDHonline Course H140 (2 PDH) Open Channel Hydraulics III  Sharpcrested Weirs Instructor: Harlan H. Bengtson, Ph.D., PE 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone
More informationP10.5 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 informationCEE 3310 Dimensional Analysis & Similitude, Oct. 22,
CEE 3310 Dimensional Analysis & Similitude, Oct., 018 115 5.5 Review vorticity twice the local rotation rate: ω x = w y v z, ω y = u z w x, ω z = v x u y Dimensional Analysis Buckingham Pi Theorem: k =
More informationFluid Mechanics c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational
Fluid Mechanics 1. Which is the cheapest device for measuring flow / discharge rate. a) Venturimeter b) Pitot tube c) Orificemeter d) None of the mentioned 2. Which forces are neglected to obtain Euler
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 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 informationCEE 3310 Control Volume Analysis, Oct. 7, D Steady State Head Form of the Energy Equation P. P 2g + z h f + h p h s.
CEE 3310 Control Volume Analysis, Oct. 7, 2015 81 3.21 Review 1D Steady State Head Form of the Energy Equation ( ) ( ) 2g + z = 2g + z h f + h p h s out where h f is the friction head loss (which combines
More informationOPEN CHANNELS (OPEN CHANNEL FLOW AND HYDRAULIC MACHINERY)
OPEN CHANNELS (OPEN CHANNEL FLOW AND HYDRAULIC MACHINERY) UNIT I IARE Dr.G. Venkata Ramana Professor& HOD Civil Engineering Learning Objectives 1. Types of Channels 2. Types of Flows 3. Velocity Distribution
More information6.4 HeadDischarge Equations Based on Experimentation
~ contracted, we have found that L = 0.25bC does not produce an accurate rating, but an accurate rating is obtained with L = 2b,. At the present time the WinFlume computer program will warn the designer
More information1.060 Engineering Mechanics II Spring Problem Set 4
1.060 Engineering Mechanics II Spring 2006 Due on Monday, March 20th Problem Set 4 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More informationProf. Scalo Prof. Vlachos Prof. Ardekani Prof. Dabiri 08:30 09:20 A.M 10:30 11:20 A.M. 1:30 2:20 P.M. 3:30 4:20 P.M.
Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Scalo Prof. Vlachos
More informationExperimental Investigation on the Influence of Density of Fluid. On Efficiency of V Notch
International Journal of Advances in Scientific Research and Engineering (ijasre) EISSN : 24548006 DOI: http://dx.doi.org/10.7324/ijasre.2017.32515 Vol.3 (9) Oct  2017 Experimental Investigation on
More informationFlow Characteristics and Modelling of Headdischarge Relationships for Weirs
Chapter 8 Flow Characteristics and Modelling of Headdischarge Relationships for Weirs 8.1 Introduction In Chapters 5 and 7, the formulations of the numerical models for the simulations of flow surface
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 informationUniform Flow in Open Channels
1 UNIT 2 Uniform Flow in Open Channels Lecture01 Introduction & Definition Openchannel flow, a branch of hydraulics, is a type of liquid flow within a conduit with a free surface, known as a channel.
More informationIt is important to develop a meaningful and systematic way to perform an experiment.
Chapter 7: Dimensional Analysis, Modeling and Similitude. The solution to many engineering problems is achieved through the use of a combination of analysis and experimental data. One of the goals of an
More informationLateral Inflow into HighVelocity Channels
Lateral Inflow into HighVelocity Channels by Richard L. Stockstill PURPOSE: This Coastal and Hydraulics Engineering Technical Note (CHETN) investigates lateral flow discharging into a highvelocity channel.
More informationEFFECT OF BAFFLE BLOCKS ON THE PERFORMANCE OF RADIAL HYDRAULIC JUMP
Fourth International Water Technology Conference IWTC 99, Alexandria, Egypt 255 EFFECT OF BAFFLE BLOCKS ON THE PERFORMANCE OF RADIAL HYDRAULIC JUMP O. S. Rageh Irrigation & Hydraulics Dept., Faculty of
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 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 information1.The pressure drop per unit length that develops due to friction cannot generally be solved analytically. A. True B. False
CHAPTER 07 1.The pressure drop per unit length that develops due to friction cannot generally be solved analytically. 2.A qualitative description of physical quantities can be given in terms of. YOUR ANSWER:
More information