5. Secondary Current and Spiral Flow

Size: px
Start display at page:

Download "5. Secondary Current and Spiral Flow"

Transcription

1 5. Secondary Current and Spiral Flow The curve of constant velocity for rectangular and triangular cross-section obtained by Nikuradse are shown in Figures and 2. In all cases the velocities at the corners are comparatively very large with stems from the fact that in all straight pipes of non-circular cross-section there exist secondary flows. These are such that the fluid flows towards the corner along the bisectrix of the angle and then outwards in both directions. The secondary flows continuously transport momentum from the centre to the corners and generate high velocities there. Schematic diagrams of secondary flows in triangular and rectangular pipes are shown in Fig. 3. It is seen that the secondary flow in the rectangular cross-section which proceeds from the wall inwards in the neighborhood of the ends of the larger sides and of the middle of the shorter sides creates zones of low velocity. They appear very clearly in the picture of curves of constant velocity in Fig. Such secondary flows come into play also in open channels, as evidenced by the pattern of curves of constant velocity in Fig. 4. The maximum velocity does not occur near the free surface but at about one fifth of the depth down of the free surface.

2 Fig.. Curves of constant velocity for pipe of rectangular cross-section, after Nikuradse Fig. 2. Curves of constant velocity for a pipe of equilateral triangular cross-section after Nikuradse a b Fig. 3. Schematic representation of Secondary flows in pipes of triangular and rectangular (open channel) cross-section

3 water level Fig. 4. Curves of constant velocity for a rectangular open channel after Nikuradse Secondary circulation is that flow wherein the velocity can be resolved into two components, one in the longitudinal direction of the channel and the other in transverse to the direction of the channel. The transverse component of the velocity gives rise to the secondary circulation. It can occur in both straight and curved channels and for different reasons. Secondary circulation is affected by temperature gradients, sediment, turbulence, non-uniformity of boundary shear, and the curvature of streamlines. Secondary circulation has been associated with turbulent flow in prismatic channels wherein the shear at the boundary is not constant. In straight circular pipes as shear at the boundary is constant for both laminar and turbulent flow the secondary circulation

4 has not been observed. When secondary circulation does occur, it seems to take place in an even number of cells as depicted in Figure 5. The non-uniformity of sediment across a channel has been associated with secondary circulation. Fig. 5. Secondary circulation in straight channel Secondary current is the flow taking place in transverse direction of the main flow. The secondary currents are of four types viz.. The 'weak' secondary currents in straight-non-circular channel sections and in pipes due to boundary resistance (figure 5). 2. Secondary flow developed due to non-uniform bed configuration as in case of alluvial channels. 3. The ' strong ' currents caused in bends due to centrifugal force.

5 SPIRAL FLOW O y INSIDE OUTSIDE WALL SECTION ON A-A ILLUSTRATION OF SECONDARY FLOW AND SPIRAL CURRENTS IN A 90 BEND 4. Secondary currents due to the unsteadiness of the oscillating boundary layer. The occurrence of the maximum velocity filament in a straight channel just below the free surface (see figure below) to the findings of secondary current.

6 Secondary currents Isovels (a) Open channel (b) Equivalent closed conduit Comparison of Open Channel Flow with Closed-Conduit Flow The lens shaped figure is drawn such that it is orthogonal to each isovel. It may be noted that the maximum velocity occurs slightly below the free surface. On the lens shaped line no velocity gradient exist. The shear on the free surface is negligible and their is no shear resistance to balance the component of the weight of the prism along the main flow direction. The equivalent closed conduit is symmetrical about the central line and the shear stress is distributed along the boundary line. Side Slope, m: =.5 : 4y y 0.750γySo 0.970γySo 0.750γyS o Tractive force distribution obtained using membrane analogy This distribution varies depending on the cross section and material Gibson, explained the origination of the secondary current. Darcy, Cunningham, Sterns, Moseley, Francis and Wood (Thandaveswara, 969) recognized the presence of this secondary current and superposition of the main flow leads to spiral flow. If there is any slight disturbance in approach flow conditions instead of double spiral, then single spiral exists. Kennedy and Fulton established that the secondary current has a definite effect on the frictional resistance of the channel. The second type of secondary currents were observed by Schlichting, Jacob, Schultz Grunov. The projection of spheres from the surface is just similar to the spherical sand particles fixed uniformly over the surface, then this type of secondary current can be expected when the sand roughness is used. The flow pattern which exists behind an obstacle placed in the boundary layer near a wall differs markedly from that behind an obstacle placed in the free stream. This

7 circumstance emerges clearly from an experiment performed by Schlichting and shown in figure. The experiment consisted in the measurement of the velocity field behind a row of spheres placed on a smooth flat surface. The pattern of curves of constant velocity clearly shows a kind of negative wake effect. The smallest velocities have been measured in the free gaps in which no spheres are present over the whole length of the plate; on the other hand, the largest velocities have been measured behind the rows of spheres where precisely the smaller velocities. 0d 0d 2 3 0d measuring station V [m/s) d d 5d Isovels behind a row of spheres as measured by Schlichting. Secondary flow in the boundary layer is marked behind (), as calculated by K. Schultz-Grunow. In the neighbourhood of the wall, the velocity behind the spheres is larger than that in the gaps. The spheres produce a "negative wake effect" which is explained by the existence of secondary flow. Diameter of spheres d= 4mm When the spacing of roughness is close, the wavy water surface will not exist as the formation of vortices will be confined to roughness elements and forms a pseudo-wall and does not affect the main flow.

8 y k s s Isolated - roughness flow (k/s) - Form drag dominates The wake and the vortex are dissipated before the next element is reached. The ratio of (k/s) is a significant parameter for this type of flow

9 y k s Wake interference flow (y/s) s s When the roughness elements are placed closer, the wake and the vortex at each element will interfere with those developed by the following element and results in complex vorticity and turbulent mixing. The height of the roughness is not important, but the spacing becomes an important parameter. The depth 'y' controls the vertical extent of the surface region of high level turbulence. (y/s) is an important correlating parameter. y k j j j j s s s k is surface roughness height s is the spacing of the elements j is the groove width y is the depth of flow Quasi smooth flow - k/s or j/s becomes significant acts as Pseudo wall Quasi smooth flow is also known as skimming flow. The roughness elements are so closed placed. The fluid that fills in the groove acts as a pseudo wall and hence flow essentially skims the surface of roughness elements. In such a flow (k/s) or (j/s) play a significant role. Concept of three basic types of rough surface flow In the following paragraphs 3rd type of secondary current has been discussed briefly. The third type of secondary currents will come into picture while the fluid flows in a curved channel. The fluid in a curved channel will be subjected to centrifugal force. Due to this centrifugal force, a pressure gradient normal to the direction of the main flow is created. Then the particles near the inside wall are thrown outside and they reach the outside boundary moving in transverse direction. Thus a sort of centripetal lift will be created causing the heaving up of the fluid. If the flow is irrotational and the fluid enters with uniform velocity into bend, then it is analogous to the potential vortex.

10 v Vr =CONSTANT r O r i r c B r 0 VELOCITY DISTRIBUTION IN POTENTIAL FLOW IN A CURVED CHANNEL But in actual case due to the presence of shear stress at the boundary, the velocity of main flow decreases abruptly at the boundary setting a velocity gradient in the boundary layer. It may be observed that the energy in the boundary regions is less than in the potential zone. It follows that at the outside of the bend the pressure intensity falls away abruptly towards the wall, unless a secondary flow takes place in the direction of outer wall. Continuity equation requires an inward flow along the side walls to compensate since the pressure gradient normal to the wall is exactly opposite to that of potential motion. The spiral flow motion induced by the centrifugal force is very pronounced and irregular in the bend. The complicated pattern of flow is caused by the superposition of secondary current in the bend over the spiral flow of the approach channel. The spiral flow of bend begins as a lateral boundary current near the point where the stream line curvature begins and at the bottom inside corner of the bend. This type of spiral motion also called helicoidal flow and was recognized by Thomson in 876 and was demonstrated by him in the laboratory in an 80 circular bend with rectangular channel section in 879. This was supported further by Engles, Beyerhams and others. During 883 to 990 several researchers while investigating the flow

11 characteristics in meanderings observed the action of scouring and deposition in the river bends. Several investigators (refer to Thandaveswara's Thesis, 969) mostly conducted the experiments in channel whose aspect ratios were of the same order of magnitude. Thus the mean flow occurring was essentially three dimensional in character. But Betz, Wilcken, Maccol and Wattendrof conducted experiments in two dimensional channel (rectangular conduit). Watterdrof showed the potential character of the spiral flow and drew the following conclusions. (i). There is only slight increase in channel resistance due to the presence of bends as indicated in pipe bends. (ii). The velocity distribution follows free vortex law. (iii). Rayleigh's stability criterion based on the calculation of mixing length and exchange factor showed the instability and increased mixing at the outer walls of the curved channels and decreasing mixing and stability at the inner wall. (iv). If the depth to breadth ratio is large enough so that the lateral currents occupy only a relatively small part of the area of the cross-section near the bottom and if form losses are ignored near the bend, then the bend loss scarcely exists. 5. Strength of spiral The term "Strength of Spiral" is defined as the percentage ratio of the mean kinetic energy of the lateral motion to the kinetic energy of flow and is denoted by S xy. 2 V xy 2 2g ( V xy ) S m m xy = * 00 = * V V 2g The strength of secondary current can be qualitatively estimated to be proportional to the extent of distortion of isovels. The concentration of velocity near boundary means the secondary flow concentration near boundary. This bears the hypothesis that the mechanism of secondary motion arises out of the boundary shear turbulence. It may be noted that the approach flow plays an important role and has a direct effect on the number of spirals, strength of spiral and other characteristics of spiral flow.

12 Following equations relate the deflection angle α along the centre line of bed, geometry of the channel and the hydraulic properties of flow, in channel bends. (i) (ii) (iii) For a smooth rectangular bend P r tan α =7.4 for 2000 R c 0.25 e Re For a smooth triangular channel P r c tanα =3.4 for 2000 R 0.25 e 5000 Re In general, P r c Re tanα =K If the channel is wide then y r 05. c 4 R 0.25 e tanα =K But Russian authors found that for a rectangular wide channel In general for a wide rectangular channel, y tanα = r c tanα =K ( ) b Φ R 0 e r c tanα =K 0 b y Φ rc Ks for smooth flow for rough flow tanα =K f 0 a b rc

13 where f = friction coefficient and "a" is an exponent >. The last equation can be 8g expressed in Chezy terms of coefficient C= f in the form a 8g b tanα K 2 0 C r c = The value of tanα can be assumed to indicate the strength spiral to some scale. Reference: Thandaveswara B.S., "Characteristics of flow around a 90 open channel bend", M.Sc (Engineering), Department of Civil and Hydraulic Engineering, Indian Institute of Science, Bangalore, 969.

Prof. B.S. Thandaveswara. Superelevation is defined as the difference in elevation of water surface between inside (1)

Prof. B.S. Thandaveswara. Superelevation is defined as the difference in elevation of water surface between inside (1) 36.4 Superelevation Superelevation is defined as the difference in elevation of water surface between inside and outside wall of the bend at the same section. y=y y (1) 1 This is similar to the road banking

More information

1. Introduction, tensors, kinematics

1. Introduction, tensors, kinematics 1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and

More information

Chapter 3 Lecture 8. Drag polar 3. Topics. Chapter-3

Chapter 3 Lecture 8. Drag polar 3. Topics. Chapter-3 Chapter 3 ecture 8 Drag polar 3 Topics 3.2.7 Boundary layer separation, adverse pressure gradient and favourable pressure gradient 3.2.8 Boundary layer transition 3.2.9 Turbulent boundary layer over a

More information

7. Basics of Turbulent Flow Figure 1.

7. Basics of Turbulent Flow Figure 1. 1 7. Basics of Turbulent Flow Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds

More information

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing.

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Thus, it is very important to form both a conceptual understanding and a quantitative

More information

Turbulence Laboratory

Turbulence Laboratory Objective: CE 319F Elementary Mechanics of Fluids Department of Civil, Architectural and Environmental Engineering The University of Texas at Austin Turbulence Laboratory The objective of this laboratory

More information

THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL

THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL Tenth International Water Technology Conference, IWTC10 2006, Alexandria, Egypt 281 THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL Karima Attia 1 and Gamal El Saied 2 1

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

Flow and Bed Topography in a 180 Curved Channel

Flow and Bed Topography in a 180 Curved Channel Flow and Bed Topography in a 180 Curved Channel Jae Wook Jung 1, Sei Eui Yoon 2 Abstract The characteristics of flow and bed topography has been analyzed by changing the bed materials in a 180-degree,

More information

Chapter 10 Flow in Conduits

Chapter 10 Flow in Conduits Chapter 10 Flow in Conduits 10.1 Classifying Flow Laminar Flow and Turbulent Flow Laminar flow Unpredictable Turbulent flow Near entrance: undeveloped developing flow In developing flow, the wall shear

More information

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

ENGINEERING 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 information

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In

More information

Laboratory Investigation of Submerged Vane Shapes Effect on River Banks Protection

Laboratory Investigation of Submerged Vane Shapes Effect on River Banks Protection Australian Journal of Basic and Applied Sciences, 5(12): 1402-1407, 2011 ISSN 1991-8178 Laboratory Investigation of Submerged Vane Shapes Effect on River Banks Protection Touraj Samimi Behbahan Department

More information

Boundary-Layer Theory

Boundary-Layer Theory Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22

More information

External Flow and Boundary Layer Concepts

External Flow and Boundary Layer Concepts 1 2 Lecture (8) on Fayoum University External Flow and Boundary Layer Concepts By Dr. Emad M. Saad Mechanical Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Mechanical

More information

Uniform Channel Flow Basic Concepts Hydromechanics VVR090

Uniform 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 information

Visualization of flow pattern over or around immersed objects in open channel flow.

Visualization 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 information

Turbulent boundary layer

Turbulent boundary layer Turbulent boundary layer 0. Are they so different from laminar flows? 1. Three main effects of a solid wall 2. Statistical description: equations & results 3. Mean velocity field: classical asymptotic

More information

Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m

Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m 1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)

More information

Investigation of Flow Profile in Open Channels using CFD

Investigation of Flow Profile in Open Channels using CFD Investigation of Flow Profile in Open Channels using CFD B. K. Gandhi 1, H.K. Verma 2 and Boby Abraham 3 Abstract Accuracy of the efficiency measurement of a hydro-electric generating unit depends on the

More information

UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

More information

FLOW IN CONDUITS. Shear stress distribution across a pipe section. Chapter 10

FLOW 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 information

Module 3: Velocity Measurement Lecture 15: Processing velocity vectors. The Lecture Contains: Data Analysis from Velocity Vectors

Module 3: Velocity Measurement Lecture 15: Processing velocity vectors. The Lecture Contains: Data Analysis from Velocity Vectors The Lecture Contains: Data Analysis from Velocity Vectors Velocity Differentials Vorticity and Circulation RMS Velocity Drag Coefficient Streamlines Turbulent Kinetic Energy Budget file:///g /optical_measurement/lecture15/15_1.htm[5/7/2012

More information

Basic Fluid Mechanics

Basic Fluid Mechanics Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

More information

Streams. Water. Hydrologic Cycle. Geol 104: Streams

Streams. Water. Hydrologic Cycle. Geol 104: Streams Streams Why study streams? Running water is the most important geologic agent in erosion, transportation and deposition of sediments. Water The unique physical and chemical properties of water make it

More information

EFFECT OF CHANNEL BENDS ON TRANSVERSE MIXING

EFFECT OF CHANNEL BENDS ON TRANSVERSE MIXING NIJOTECH VOL. 10. NO. 1 SEPTEMBER 1986 ENGMANN 57 EFFECT OF CHANNEL BENDS ON TRANSVERSE MIXING BY E. O. ENGMANN ABSTRACT Velocity and tracer concentration measurements made in a meandering channel are

More information

Introduction to Turbulence AEEM Why study turbulent flows?

Introduction to Turbulence AEEM Why study turbulent flows? Introduction to Turbulence AEEM 7063-003 Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Peter.disimile@uc.edu Intro to Turbulence: C1A Why 1 Most flows encountered in engineering and

More information

R09. d water surface. Prove that the depth of pressure is equal to p +.

R09. d water surface. Prove that the depth of pressure is equal to p +. Code No:A109210105 R09 SET-1 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 information

Day 24: Flow around objects

Day 24: Flow around objects Day 24: Flow around objects case 1) fluid flowing around a fixed object (e.g. bridge pier) case 2) object travelling within a fluid (cars, ships planes) two forces are exerted between the fluid and the

More information

FLUID MECHANICS. Chapter 9 Flow over Immersed Bodies

FLUID 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 information

Lecture 4 1/28/2019. CM3120 Transport/Unit Operations 2

Lecture 4 1/28/2019. CM3120 Transport/Unit Operations 2 CM3120 ransport/unit Operations 2 State Heat ransfer Professor Faith Morrison Department of Chemical Engineering Michigan echnological University wwwchemmtuedu/~fmorriso/cm3120/cm3120html 1 o get started,

More information

Part A: 1 pts each, 10 pts total, no partial credit.

Part A: 1 pts each, 10 pts total, no partial credit. Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

More information

NPTEL Quiz Hydraulics

NPTEL 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 information

UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes

More information

CHAPTER 2- BACKGROUND. INVESTIGATIONS OF COMPOSITE ROUGHNESS COEFFICIENT IN A RIVER WITH LOW FLOW

CHAPTER 2- BACKGROUND. INVESTIGATIONS OF COMPOSITE ROUGHNESS COEFFICIENT IN A RIVER WITH LOW FLOW 2. Background 2.1 Introduction The estimation of resistant coefficient and hence discharge capacity in a channel or river is one of the fundamental problems facing river engineers. When applying Manning

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

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

Department of Mechanical Engineering

Department of Mechanical Engineering Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible

More information

Lecture Note for Open Channel Hydraulics

Lecture 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 information

Self-Excited Vibration in Hydraulic Ball Check Valve

Self-Excited Vibration in Hydraulic Ball Check Valve Self-Excited Vibration in Hydraulic Ball Check Valve L. Grinis, V. Haslavsky, U. Tzadka Abstract This paper describes an experimental, theoretical model and numerical study of concentrated vortex flow

More information

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

FE 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 information

Module 2: External Flows Lecture 12: Flow Over Curved Surfaces. The Lecture Contains: Description of Flow past a Circular Cylinder

Module 2: External Flows Lecture 12: Flow Over Curved Surfaces. The Lecture Contains: Description of Flow past a Circular Cylinder The Lecture Contains: Description of Flow past a Circular Cylinder Experimental Results for Circular Cylinder Flow file:///d /Web%20Course%20(Ganesh%20Rana)/Dr.%20gautam%20biswas/Final/convective_heat_and_mass_transfer/lecture12/12_1.htm[12/24/2014

More information

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

More information

Quasi-three dimensional computations for flows and bed variations in curved channel with gently sloped outer bank

Quasi-three dimensional computations for flows and bed variations in curved channel with gently sloped outer bank River Sedimentation Wieprecht et al. (Eds) 2017 Taylor & Francis Group, London, ISBN 978-1-138-02945-3 Quasi-three dimensional computations for flows and bed variations in curved channel with gently sloped

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

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES Liquid or gas flow through pipes

More information

Numerical Study of the Three-dimensional Flow in a Flat Plate Solar Collector with Baffles

Numerical Study of the Three-dimensional Flow in a Flat Plate Solar Collector with Baffles Numerical Study of the Three-dimensional Flow in a Flat Plate Solar Collector with Baffles M.A. AMRAOUI a, K. ALIANE b a. Department of Mechanical Engineering, Faculty of Technology, University of Tlemcen,

More information

Turbulent Boundary Layers & Turbulence Models. Lecture 09

Turbulent Boundary Layers & Turbulence Models. Lecture 09 Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects

More information

BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)

BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) No. of Printed Pages : 6 BME-028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) Term-End Examination December, 2011 00792 BME-028 : FLUID MECHANICS Time : 3 hours

More information

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.

INSTITUTE 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 : II-I- B. Tech Year : 0 0 Course Coordinator

More information

Friction Factors and Drag Coefficients

Friction Factors and Drag Coefficients Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the

More information

Iran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics

Iran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics 1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration

More information

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,

More information

NUMERICAL SIMULATION OF OPEN CHANNEL FLOW BETWEEN BRIDGE PIERS

NUMERICAL SIMULATION OF OPEN CHANNEL FLOW BETWEEN BRIDGE PIERS TASK QUARTERLY 15 No 3 4, 271 282 NUMERICAL SIMULATION OF OPEN CHANNEL FLOW BETWEEN BRIDGE PIERS MICHAŁ SZYDŁOWSKI Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza

More information

Table of Contents. Foreword... xiii. Preface... xv

Table of Contents. Foreword... xiii. Preface... xv Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

More information

Inertial Microfluidic Physics

Inertial Microfluidic Physics Electronic Supplementary Material (ESI) for Lab on a Chip. This journal is The Royal Society of Chemistry 2014 Inertial Microfluidic Physics Hamed Amini 1,2, Wonhee Lee 3, Dino Di Carlo 1,2* 1. Department

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

Steady waves in compressible flow

Steady waves in compressible flow Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

More information

External Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

External Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. External Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Drag and Heat Transfer in External flow Fluid flow over solid bodies is responsible

More information

Keywords: flow characteristics, compound straight channel, bed morphology, floodplain

Keywords: flow characteristics, compound straight channel, bed morphology, floodplain Flow Characteristics on Floodplain Vegetation in Compound Straight Channels Nur Amirah Nabilah Mohd Zamri 1, a, Zulhilmi Ismail 1,b,Zulkiflee Ibrahim 1,c 1 Faculty of Civil Engineering, Universiti Teknologi

More information

1. Fluid Dynamics Around Airfoils

1. Fluid Dynamics Around Airfoils 1. Fluid Dynamics Around Airfoils Two-dimensional flow around a streamlined shape Foces on an airfoil Distribution of pressue coefficient over an airfoil The variation of the lift coefficient with the

More information

Dual Vortex Structure Shedding from Low Aspect Ratio, Surface-mounted Pyramids

Dual Vortex Structure Shedding from Low Aspect Ratio, Surface-mounted Pyramids Dual Vortex Structure Shedding from Low Aspect Ratio, Surface-mounted Pyramids Robert J. Martinuzzi Department of Mechanical and Manufacturing Engineering Schulich School of Engineering University of Calgary

More information

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 35 Boundary Layer Theory and Applications Welcome back to the video course on fluid

More information

Detailed Outline, M E 521: Foundations of Fluid Mechanics I

Detailed Outline, M E 521: Foundations of Fluid Mechanics I Detailed Outline, M E 521: Foundations of Fluid Mechanics I I. Introduction and Review A. Notation 1. Vectors 2. Second-order tensors 3. Volume vs. velocity 4. Del operator B. Chapter 1: Review of Basic

More information

Fundamentals of Fluid Mechanics

Fundamentals 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 information

Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers)

Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers) Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers) T-S Leu May. 3, 2018 Chapter 5: Phenomena of laminar-turbulent boundary layer transition (including free

More information

Engineering Fluid Mechanics

Engineering 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 information

6. Basic basic equations I ( )

6. Basic basic equations I ( ) 6. Basic basic equations I (4.2-4.4) Steady and uniform flows, streamline, streamtube One-, two-, and three-dimensional flow Laminar and turbulent flow Reynolds number System and control volume Continuity

More information

Numerical Validation of Flow Through an S-shaped Diffuser

Numerical Validation of Flow Through an S-shaped Diffuser 2012 International Conference on Fluid Dynamics and Thermodynamics Technologies (FDTT 2012) IPCSIT vol.33(2012) (2012) IACSIT Press, Singapore Numerical Validation of Flow Through an S-shaped Diffuser

More information

J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and

J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and turbulent, was discovered by Osborne Reynolds (184 191) in 1883

More information

PROPERTIES OF THE FLOW AROUND TWO ROTATING CIRCULAR CYLINDERS IN SIDE-BY-SIDE ARRANGEMENT WITH DIFFERENT ROTATION TYPES

PROPERTIES OF THE FLOW AROUND TWO ROTATING CIRCULAR CYLINDERS IN SIDE-BY-SIDE ARRANGEMENT WITH DIFFERENT ROTATION TYPES THERMAL SCIENCE, Year, Vol. 8, No. 5, pp. 87-9 87 PROPERTIES OF THE FLOW AROUND TWO ROTATING CIRCULAR CYLINDERS IN SIDE-BY-SIDE ARRANGEMENT WITH DIFFERENT ROTATION TYPES by Cheng-Xu TU, a,b Fu-Bin BAO

More information

Helical Coil Flow: a Case Study

Helical Coil Flow: a Case Study Excerpt from the Proceedings of the COMSOL Conference 2009 Milan Helical Coil Flow: a Case Study Marco Cozzini Renewable Energies and Environmental Technologies (REET) Research Unit, Fondazione Bruno Kessler

More information

Table of Contents. Preface... xiii

Table of Contents. Preface... xiii Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...

More information

Turbulence Instability

Turbulence Instability Turbulence Instability 1) All flows become unstable above a certain Reynolds number. 2) At low Reynolds numbers flows are laminar. 3) For high Reynolds numbers flows are turbulent. 4) The transition occurs

More information

Vortex Induced Vibrations

Vortex Induced Vibrations Vortex Induced Vibrations By: Abhiroop Jayanthi Indian Institute of Technology, Delhi Some Questions! What is VIV? What are the details of a steady approach flow past a stationary cylinder? How and why

More information

Turbulence Modeling Applied to Flow over a Hydraulic Ball Check Valve

Turbulence Modeling Applied to Flow over a Hydraulic Ball Check Valve Engineering, 2,, 68-6 http://dx.doi.org/.426/eng.2.88 Published Online August 2 (http://www.scirp.org/journal/eng) Turbulence Modeling Applied to Flow over a Hydraulic Ball Check Valve Leonid Grinis, Vitaly

More information

The most common methods to identify velocity of flow are pathlines, streaklines and streamlines.

The most common methods to identify velocity of flow are pathlines, streaklines and streamlines. 4 FLUID FLOW 4.1 Introduction Many civil engineering problems in fluid mechanics are concerned with fluids in motion. The distribution of potable water, the collection of domestic sewage and storm water,

More information

Surface Roughness Effects in Near-Bed Turbulence: Implications to Sediment Entrainment

Surface Roughness Effects in Near-Bed Turbulence: Implications to Sediment Entrainment Surface Roughness Effects in Near-Bed Turbulence: Implications to Sediment Entrainment by A.N. Papanicolaou, P. Diplas, C. L. Dancey, and M. Balakrishnan Journal of Engineering Mechanics, Vol. 127, No.

More information

11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an

11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior

More information

Conclusion Evaluating Methods for 3D CFD Models in Sediment Transport Computations

Conclusion Evaluating Methods for 3D CFD Models in Sediment Transport Computations Conclusion Evaluating Methods for 3D CFD Models in Sediment Transport Computations Hamid Reza Madihi* 1, Bagher Keshtgar 2, Sina Hosseini Fard 3 1, 2, 3 M.Sc. Coastal Environmental Engineering, Graduate

More information

Experiments on the perturbation of a channel flow by a triangular ripple

Experiments on the perturbation of a channel flow by a triangular ripple Experiments on the perturbation of a channel flow by a triangular ripple F. Cúñez *, E. Franklin Faculty of Mechanical Engineering, University of Campinas, Brazil * Correspondent author: fernandodcb@fem.unicamp.br

More information

Fluid Mechanics. du dy

Fluid 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 information

Figure 34: Coordinate system for the flow in open channels.

Figure 34: Coordinate system for the flow in open channels. OE466 redging Processes 5. SCOUR 5.. Steady uniform flow in open channels This chapter is written with a view to bottom scour. The main outcome is the scour velocity as a function of the particle diameter.

More information

The Reynolds experiment

The Reynolds experiment Chapter 13 The Reynolds experiment 13.1 Laminar and turbulent flows Let us consider a horizontal pipe of circular section of infinite extension subject to a constant pressure gradient (see section [10.4]).

More information

1. Introduction. Keywords Compound channel, Momentum transfer, Relative roughness, Relative depth, Relative width

1. Introduction. Keywords Compound channel, Momentum transfer, Relative roughness, Relative depth, Relative width International Journal of Hydraulic Engineering, (): -8 DOI:.9/j.ijhe.. Investigating the Effect of and Relative Roughness on Momentum Transfer in Symmetric Rectangular Compound Channels with Varius Relative

More information

Fluid 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 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 information

International Conference on Energy Efficient Technologies For Automobiles (EETA 15) Journal of Chemical and Pharmaceutical Sciences ISSN:

International Conference on Energy Efficient Technologies For Automobiles (EETA 15) Journal of Chemical and Pharmaceutical Sciences ISSN: HEAT TRANSFER ENHANCEMENT WITH PRESSURE LOSS REDUCTION IN COMPACT HEAT EXCHANGERS USING VORTEX GENERATORS Viswajith M V*, Gireesh Kumaran Thampi, James Varghese Department of Mechanical Engineering, School

More information

CLASS SCHEDULE 2013 FALL

CLASS 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 information

(1) Transition from one to another laminar flow. (a) Thermal instability: Bernard Problem

(1) Transition from one to another laminar flow. (a) Thermal instability: Bernard Problem Professor Fred Stern Fall 2014 1 Chapter 6: Viscous Flow in Ducts 6.2 Stability and Transition Stability: can a physical state withstand a disturbance and still return to its original state. In fluid mechanics,

More information

[8] Bending and Shear Loading of Beams

[8] Bending and Shear Loading of Beams [8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight

More information

Consider a control volume in the form of a straight section of a streamtube ABCD.

Consider a control volume in the form of a straight section of a streamtube ABCD. 6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream

More information

MATHEMATICAL MODELING OF FLUVIAL SEDIMENT DELIVERY, NEKA RIVER, IRAN. S.E. Kermani H. Golmaee M.Z. Ahmadi

MATHEMATICAL MODELING OF FLUVIAL SEDIMENT DELIVERY, NEKA RIVER, IRAN. S.E. Kermani H. Golmaee M.Z. Ahmadi JOURNAL OF ENVIRONMENTAL HYDROLOGY The Electronic Journal of the International Association for Environmental Hydrology On the World Wide Web at http://www.hydroweb.com VOLUME 16 2008 MATHEMATICAL MODELING

More information

Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow

Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow Sutardi 1, Wawan A. W., Nadia, N. and Puspita, K. 1 Mechanical Engineering

More information

Channel Pattern. Channel Pattern, Meanders, and Confluences. Description of Channel Pattern. Bridge (2003)

Channel Pattern. Channel Pattern, Meanders, and Confluences. Description of Channel Pattern. Bridge (2003) Channel Pattern Channel Pattern, Meanders, and Confluences Outline Description of channel pattern Alternate bars Channel pattern continua and evolution Controls of channel pattern Description of Channel

More information

Lecture-4. Flow Past Immersed Bodies

Lecture-4. Flow Past Immersed Bodies Lecture-4 Flow Past Immersed Bodies Learning objectives After completing this lecture, you should be able to: Identify and discuss the features of external flow Explain the fundamental characteristics

More information

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

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

Detailed Investigation of Velocity Distributions in Compound Channels for both Main Channel and Flood Plain

Detailed Investigation of Velocity Distributions in Compound Channels for both Main Channel and Flood Plain Detailed Investigation of Velocity Distributions in Compound Channels for both Main Channel and Flood Plain Jarmina Nake 1, Dr. Mimi Das Saikia 2 M.Tech Student, Dept. of Civil engineering, ADTU, Guwahati,

More information

The Long Profile Characteristics. Why does a river meander in its middle and lower course?

The Long Profile Characteristics. Why does a river meander in its middle and lower course? QU: How are Meanders formed? AIM: To describe and explain meander formation and identify the difference between GCSE and A/S knowledge and expectations. ST: Get the key rivers terms from the pictures.

More information