# What we know about Fluid Mechanics. What we know about Fluid Mechanics

Size: px
Start display at page:

Transcription

1 What we know about Fluid Mechanics 1. Survey says. 3. Image from: What we know about Fluid Mechanics 1. MEB (single input, single output, steady, incompressible, no rxn, no phase change, little heat; good for pipes, pumps; Moody chart; Fanning friction factor versus Re ) 1

2 What we know about Fluid Mechanics 1. MEB (single input, single output, steady, incompressible, no rxn, no phase change, little heat; good for pipes, pumps; Moody chart; Fanning friction factor versus Re ). Fluid Statics ( ; same elevation, same pressure; good for manometers, water in tanks) 3 What we know about Fluid Mechanics 1. MEB (single input, single output, steady, incompressible, no rxn, no phase change, little heat; good for pipes, pumps; Moody chart; Fanning friction factor versus Re ). Fluid Statics ( ; same elevation, same pressure; good for manometers, water in tanks) 3. Math is in our future 4

3 CM3110 Transport Processes and Unit Operations I How do fluids behave? (Ch) 1. Viscosity. Drag 3. Boundary Layers 4. Laminar versus Turbulent Flow 5. Lift 6. Supersonic 7. Surface Tension 8. Curved Streamlines 9. Magnetohydrodynamics Viscosity, A measure of a liquid s resistance to flow water (modest viscosity) honey (high viscosity) 6 3

4 Viscous fluids transmit stress from one location to another. oil honey 7 Momentum Flux Momentum () = mass * velocity vectors Viscosity determines the magnitude of momentum flux z top plate has momentum, and it transfers this momentum to the top layer of fluid v z V V y H v z 0 v z (y) momentum flux Each fluid layer transfers the momentum downward 8 4

5 How is force-to-move-plate related to V? Stress on a y-surface in the z-direction F V v v A H H 0 z y0 z yh v z y (Note choice of coordinate system) (See discussion of sign convention of stress; we use the tension-positive convention) yz dvz yz F A dy Newton s Law of Viscosity 9 9 stresses at a point in a fluid yz kgm s force kg m / s yz area area s area / Momentum Flux f ê y f A( eˆ eˆ yy yx y x eˆ ) yz z A surface whose unit normal is in the y-direction stress on a y-surface in the y-direction (See discussion of sign convention of stress; we use the tension-positive convention) in the z-direction yz flux of z-momentum 10 5

6 (p110) Example.1: What are the units of viscosity? dvz yz dy Newton s Law of Viscosity Viscosity, Greek letter mu 11 Viscosity A measure of a liquid s resistance to flow Viscous fluids transmit stress from one location to another. Viscosity is responsible for the development of pressure distributions in laminar flow. 1 6

7 (p110) Example.: How much force does it take to inject a water-like solution through a 16-gauge needle (inner diameter=1.194 mm, L=40mm)? f plunger D p L 13 Need to know: p( Q) From the methods of this course, we shall see that for Newtonian fluids: Hagen-Poiseuille equation (slow flow through tubes) Q 4 p p R 0 L 8L 14 7

8 In the momentum balance, viscosity appears because it produces a force: all forces f ma Rate of change of momentum Forces (including viscous forces) Inertia 15. Drag F drag The retarding force on an object due to a fluid (retarding implies opposite in direction to the fluid velocity) 16 8

9 . Drag F drag The retarding force on an object due to a fluid (retarding implies opposite in direction to the fluid velocity) Image from: We study how to: Calculate drag, Drag is a consequence of viscosity 1. Calculate velocity. Calculate force on the object surface 3. Calculate the component of that force in the direction of the flow When impossible to calculate, 1. Measure force on model in a wind/water tunnel. Correlate using dimensional analysis 3. Scale up to system of interest Microscopicmomentum balance 17 Without drag, objects of different weights, shapes, fall at the same speed: In 1971, astronaut David Scott conducted Galileo s experiment on the moon as part of Apollo

10 Drag Coefficient, C D True at high speeds C D F 1 v drag A p reference area Image from: Image from: 19 (p117) Example.4: How much faster will a bicycle racer traveling at 40 mph go if she adopts a racing crouch rather than riding upright? CD 1.1 CD CD CD

11 Under what conditions is drag a simple matter of knowing C D? Could vary with: Flow speed Shape Density Viscosity Temperature... C D F 1 v drag A p (i.e., Why is this so? When is this so?) 1 Drag behavior of a sphere (Similar to using the Moody Chart when interested in wall drag in pipes) 11

12 Moody Chart: Data Correlation for Friction in Straight Pipes (Review) 16 Re Moody Chart (image from: Geankoplis) 3. Boundary Layers (BL) Regions near solid surfaces in which viscosity dominates the flow behavior, especially at high speeds 4 1

13 .3 Boundary Layers (BL) BL form at high speeds Regions near solid surfaces in which viscosity dominates the flow behavior, especially at high speeds 5 There is relative motion near the surfaces (viscosity is important); Away from surfaces, the flow is uniform (viscosity is not important; inertia dominates) Newton s Law of Viscosity dvz yz dy 6 13

14 Attached boundary layer near surface Boundary layer detaches angle of attack Source: Illustrated experiments in fluid mechanics: the NCFMF book of film notes, MIT Press, Faith A. Morrison Michigan Tech. U. Why is the surface of a golf ball designed the way it is? 8 14

15 Manipulate boundary-layer separation When the boundary layer is turbulent, it detaches farther back (yielding lower drag) smooth ball rough ball H. Schlichting, Boundary Layer Theory (McGraw-Hill, NY cover: This image from a simulation of wind blowing past a building (black square) reveals the vortices that are shed downwind of the building; dark orange represents the highest air speeds, dark blue the lowest. As a result of such vortex formation and shedding, tall buildings can experience large, potentially catastrophic forces. (Courtesy of the computational fluid dynamics group at Rowan William Davies and Irwin Inc.) 30 15

16 (p14) Example.5: A new tower hotel, cylindrical in shape and 100 ft in diameter, has been built in a resort town near the sea on the windward side of an island. Hotel guests complain that there are often uncomfortably high winds near several of the entrances to the tower. How do the wind speed and pressure vary with position around the tower and with on-shore wind speed? 31 The full Navier-Stokes is hard to solve; when viscosity is zero, however, it s easy to solve the N-S for v and p Viscosity is NOT zero; however, outside the boundary layer, viscosity is not important. Boundary Layers STRATEGY: When away from surfaces, solve for outer (viscosity=0) flow For inviscid flows: v comes from stream function, ; (Diff Eqns) Pressure comes from v and the Bernoulli equation: Bernoulli equation p v z constant along a streamline (see section 8. of our text) 3 16

17 Velocity outside boundary layer Boundary Layers cylinder in uniform flow: (potential flow solution) Pressure outside boundary layer Bernoulli equation R U 1 cos r R v U1 sin r 0 r z p v z constant along a streamline (see section 8. of our text) 33 Boundary Layers in Internal Flow: Entrance flow field in pipe flow Entrance region Boundary layer Fully developed flow (see section 8. of our text) 34 Faith A. Morrison Michigan Tech. U. 17

18 4. Laminar versus Turbulent Flow Laminar versus Turbulent Flow Viscosity dominates Inertia dominates 36 18

19 Reynolds Experiment Viscosity dominates Inertia dominates 37 CM3110 Transport Processes and Unit Operations I How do fluids behave? (Ch) 1. Viscosity. Drag 3. Boundary Layers 4. Laminar versus Turbulent Flow 5. Lift 6. Supersonic 7. Surface Tension 8. Curved Streamlines Advanced 9. Magnetohydrodynamics

20 Take-Away from Today: How do fluids behave? 1. Viscosity. Drag 3. Boundary Layers dvz yz C D dy Fdrag 1 v A Viscous effects within BL; no viscous effects in main stream; Bernoulli equation (like MEB) assumes no viscous effects (outside the boundary layer) 4. Laminar versus Turbulent Flow (we know about this already) p p v z constant along a streamline 39 Viscous stress Viscous effects dominate near walls Inertial effects dominate away from walls Take-Away from Today: How do fluids behave? 1. Viscosity. Drag 3. Boundary Layers dvz yz C D dy Fdrag 1 v A Viscous effects within BL; no viscous effects in main stream; Bernoulli equation (like MEB) assumes no viscous effects (outside the boundary layer) 4. Laminar versus Turbulent Flow (we know about this already) p p v z constant along a streamline 40 0

21 What we know about Fluid Mechanics 1. MEB (single input, single output, steady, incompressible, no rxn, no phase change, little heat; good for pipes, pumps; Moody chart; Fanning friction factor versus Re ). Fluid Statics ; same elevation, same pressure; good for manometers, water in tanks) 3. Math is in our future What we know about Fluid Mechanics 1. MEB (single input, single output, steady, incompressible, no rxn, no phase change, little heat; good for pipes, pumps; Moody chart; Fanning friction factor versus Re ). Fluid Statics ; same elevation, same pressure; good for manometers, water in tanks) 3. Newton s Law of Viscosity (fluids transmit forces through momentum flux) 4. Momentum flux (=stress) has 9 components 5. Drag is a consequence of viscosity 6. Boundary layers form (viscous effects are confined near surfaces at high speeds) 4 1

22 What we know about Fluid Mechanics 8. Sometimes viscous effects dominate; sometimes inertial effects dominate 43 Need one more tool: Control Volume (Ch3) Following fluid particles is complex: It is simpler to observe the flow pass through a fixed volume control volume 44

23 Control Volume A chosen volume in a flow on which we perform balances (mass, momentum, energy) control volume Shape, size are arbitrary; choose to be convenient Because we are now balancing on control volumes instead of on bodies, the laws of physics are written differently 45 Control Volume Mass balance, flowing system (open system; control volume): rate of net mass accumulation flowing in of mass in out steady state 46 3

24 Control Volume Momentum balance, flowing system (open system; control volume): rate of sum of forces net momentum accumulation acting on control vol flowing in of momentum in out steady state momentum momentum F on i flowing in flowing out 0 in the streams in the streams i i i note that momentum is a vector quantity all forces f ma 47 We are ready to try a momentum balance. Tools: Mass balance (mass conserved) Newton s nd law (momentum conserved) Control volume Newton s law of viscosity Calculus 3 (multivariable calculus) 48 4

25 CM3110 Transport I Part I: Fluid Mechanics: Microscopic Balances Professor Faith Morrison Department of Chemical Engineering Michigan Technological University 49 5

### CM3110 Transport Processes and Unit Operations I

CM3110 Transport Processes and Unit Operations I Professor Faith Morrison Department of Chemical Engineering Michigan Technological University CM3110 - Momentum and Heat Transport CM310 Heat and Mass Transport

### Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering

### Microscopic Momentum Balance Equation (Navier-Stokes)

CM3110 Transport I Part I: Fluid Mechanics Microscopic Momentum Balance Equation (Navier-Stokes) Professor Faith Morrison Department of Chemical Engineering Michigan Technological University 1 Microscopic

### 150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

### Frictional Losses in Straight Pipe

2/2/206 CM325 Fundamentals of Chemical Engineering Laboratory Prelab Preparation for Frictional Losses in Straight Pipe Professor Faith Morrison Department of Chemical Engineering Michigan Technological

### 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

### 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

### Fluids. Fluids in Motion or Fluid Dynamics

Fluids Fluids in Motion or Fluid Dynamics Resources: Serway - Chapter 9: 9.7-9.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT - 8: Hydrostatics, Archimedes' Principle,

### 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)

### 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

### 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

### UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow

UNIT II Real fluids The flow of real fluids exhibits viscous effect that is they tend to "stick" to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons

### Microscopic Momentum Balance Equation (Navier-Stokes)

CM3110 Transport I Part I: Fluid Mechanics Microscopic Momentum Balance Equation (Naier-Stokes) Professor Faith Morrison Department of Chemical Engineering Michigan Technological Uniersity 1 Microscopic

### PHYSICAL MECHANISM OF CONVECTION

Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter

### 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.

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

### SCHOOL OF CHEMICAL ENGINEERING FACULTY OF ENGINEERING AND TECHNOLOGY SRM UNIVERSITY COURSE PLAN

SCHOOL OF CHEMICAL ENGINEERING FACULTY OF ENGINEERING AND TECHNOLOGY SRM UNIVERSITY COURSE PLAN Course code : CH0317 Course Title : Momentum Transfer Semester : V Course Time : July Nov 2011 Required Text

### Nicholas J. Giordano. Chapter 10 Fluids

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according

### τ du In his lecture we shall look at how the forces due to momentum changes on the fluid and viscous forces compare and what changes take place.

4. Real fluids The flow of real fluids exhibits viscous effect, that is they tend to stick to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons law

### Shell Balances in Fluid Mechanics

Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell

### Fluid Dynamics. Equation of continuity Bernoulli s Equation Bernoulli s Application Viscosity Poiseuilles law Stokes law Reynolds Number

Fluid Dynamics Equation of continuity Bernoulli s Equation Bernoulli s Application Viscosity Poiseuilles law Stokes law Reynolds Number Fluids in Motion steady or laminar flow, if each particle of the

### Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation

Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved

### UNIT 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: II-B.Tech & I-Sem Course & Branch:

### 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

### ME3560 Tentative Schedule Spring 2019

ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to

### Given the water behaves as shown above, which direction will the cylinder rotate?

water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0

### Chapter 6. Losses due to Fluid Friction

Chapter 6 Losses due to Fluid Friction 1 Objectives To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. To correlate this in terms of the

### 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

### MECHANICAL PROPERTIES OF FLUIDS:

Important Definitions: MECHANICAL PROPERTIES OF FLUIDS: Fluid: A substance that can flow is called Fluid Both liquids and gases are fluids Pressure: The normal force acting per unit area of a surface is

### 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

### Modelling of dispersed, multicomponent, multiphase flows in resource industries. Section 3: Examples of analyses conducted for Newtonian fluids

Modelling of dispersed, multicomponent, multiphase flows in resource industries Section 3: Examples of analyses conducted for Newtonian fluids Globex Julmester 017 Lecture # 04 July 017 Agenda Lecture

### ME3560 Tentative Schedule Fall 2018

ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read

### Flux - definition: (same format for all types of transport, momentum, energy, mass)

Fundamentals of Transport Flu - definition: (same format for all types of transport, momentum, energy, mass) flu in a given direction Quantity of property being transferred ( time)( area) More can be transported

### 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

### PART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG

1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity

### An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction

1 An-Najah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies

### 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

### Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

### Mechanical Engineering Programme of Study

Mechanical Engineering Programme of Study Fluid Mechanics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy SOLVED EXAMPLES ON VISCOUS FLOW 1. Consider steady, laminar flow between two fixed parallel

### CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic

### 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

### SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

### 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

### Only if handing in. Name: Student No.: Page 2 of 7

UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAMINATION, DECEMBER 10, 2014 2:00 PM 2.5 HOURS CHE 211F FLUID MECHANICS EXAMINER: PROFESSOR D.G. ALLEN ANSWER ALL SEVEN (7) QUESTIONS

### 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,

### M E 320 Supplementary Material Pralav Shetty

M E 320 Supplementary Material Pralav Shetty Note: In order to view the demonstrations below, you must first download CDF player to your PC/Mac/Linux. Link for CDF player http://www.wolfram.com/cdf-player/

### SENTHIL SELIYAN ELANGO ID: UB3016SC17508 AIU HYDRAULICS (FLUID DYNAMICS)

SENTHIL SELIYAN ELANGO ID: UB3016SC17508 AIU HYDRAULICS (FLUID DYNAMICS) ATLANTIC INTERNATIONAL UNIVERSITY INTRODUCTION Real fluids The flow of real fluids exhibits viscous effect, which are they tend

### Chapter 3 NATURAL CONVECTION

Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,

### Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

### Fluid Mechanics. Chapter 9 Surface Resistance. Dr. Amer Khalil Ababneh

Fluid Mechanics Chapter 9 Surface Resistance Dr. Amer Khalil Ababneh Wind tunnel used for testing flow over models. Introduction Resistances exerted by surfaces are a result of viscous stresses which create

### Theory and Fundamental of Fluid Mechanics

1 2 Lecture (1) on Fayoum University Theory and Fundamental of Fluid Mechanics By Dr. Emad M. Saad Mechanical Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Mechanical

### Chapter 10. Solids and Fluids

Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the

### Chapter 1: Basic Concepts

What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms

### The Bernoulli Equation

The Bernoulli Equation The most used and the most abused equation in fluid mechanics. Newton s Second Law: F = ma In general, most real flows are 3-D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider

### Fluid Mechanics. Spring 2009

Instructor: Dr. Yang-Cheng Shih Department of Energy and Refrigerating Air-Conditioning Engineering National Taipei University of Technology Spring 2009 Chapter 1 Introduction 1-1 General Remarks 1-2 Scope

### 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

### Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

### TOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant Forces-Archimedes Principle

Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant Forces-Archimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation

### 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 5.1.3. Pressure and Shear Stress

### 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,

### Lecture 2 Flow classifications and continuity

Lecture 2 Flow classifications and continuity Dr Tim Gough: t.gough@bradford.ac.uk General information 1 No tutorial week 3 3 rd October 2013 this Thursday. Attempt tutorial based on examples from today

### 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

### Approximate 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

### s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I

Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum

### 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

### Chapter 6: Incompressible Inviscid Flow

Chapter 6: Incompressible Inviscid Flow 6-1 Introduction 6-2 Nondimensionalization of the NSE 6-3 Creeping Flow 6-4 Inviscid Regions of Flow 6-5 Irrotational Flow Approximation 6-6 Elementary Planar Irrotational

### Chapter 9 Fluids. Pressure

Chapter 9 Fluids States of Matter - Solid, liquid, gas. Fluids (liquids and gases) do not hold their shapes. In many cases we can think of liquids as being incompressible. Liquids do not change their volume

### B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I

Department of Chemical Engineering B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I LP: CH 16304 Rev. No: 00

### 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

### Universal Viscosity Curve Theory

TM Universal Viscosity Curve Theory Turbine Flow Meters and Flow Viscosity Introduction Like any transducer, a turbine flow meter is sensitive to physical parameters other than the one which is of interest.

### AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics

AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:

### 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:

### 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

### Chapter 9: Differential Analysis

9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control

### Page 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)

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. Vlachos Prof. Ardekani

### S.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

### 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

### ACCOUNTING FOR FRICTION IN THE BERNOULLI EQUATION FOR FLOW THROUGH PIPES

ACCOUNTING FOR FRICTION IN THE BERNOULLI EQUATION FOR FLOW THROUGH PIPES Some background information first: We have seen that a major limitation of the Bernoulli equation is that it does not account for

### Reference : McCabe, W.L. Smith J.C. & Harriett P., Unit Operations of Chemical

1 Course materials (References) Textbook: Welty J. R., Wicks, C. E., Wilson, R. E., & Rorrer, G., Fundamentals of Momentum Heat, and Mass Transfer, 4th Edition, John Wiley & Sons.2000 Reference : McCabe,

### Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment:

7 STEADY FLOW IN PIPES 7.1 Reynolds Number Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment: Laminar flow Turbulent flow Reynolds apparatus

### Fluid Mechanics II Viscosity and shear stresses

Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small

### Recap: Static Fluids

Recap: Static Fluids Archimedes principal states that the buoyant force acting on an object is equal to the weight of fluid displaced. If the average density of object is greater than density of fluid

### 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

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

### Chapter 6. Losses due to Fluid Friction

Chapter 6 Losses due to Fluid Friction 1 Objectives ä To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. ä To correlate this in terms of

### V/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0

UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational

### Chapter 9: Differential Analysis of Fluid Flow

of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known

### 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

### The E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012

The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel

### Chemical Engineering 374

Chemical Engineering 374 Fluid Mechanics Exam 3 Review 1 Spiritual Thought 2 Ether 12:27 6 And now, I, Moroni, would speak somewhat concerning these things; I would show unto the world that faith is things

### Stream line, turbulent flow and Viscosity of liquids - Poiseuille s Method

Stream line, turbulent flow and Viscosity of liquids - Poiseuille s Method Dr D. Arun Kumar Assistant Professor Department of Physical Sciences Bannari Amman Institute of Technology Sathyamangalam General

### PROPERTIES OF BULK MATTER

PROPERTIES OF BULK MATTER CONCEPTUAL PROBLEMS Q-01 What flows faster than honey. Why? Ans According to poiseuille s formula, the volume V of a liquid flowing per second through a horizontal narrow tube

### Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

### Heat and Mass Transfer Unit-1 Conduction

1. State Fourier s Law of conduction. Heat and Mass Transfer Unit-1 Conduction Part-A The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature

### Lecture 7 Boundary Layer

SPC 307 Introduction to Aerodynamics Lecture 7 Boundary Layer April 9, 2017 Sep. 18, 2016 1 Character of the steady, viscous flow past a flat plate parallel to the upstream velocity Inertia force = ma

### 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

### FE Exam Fluids Review October 23, Important Concepts

FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning

### MULTIPLE-CHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)

MULTIPLE-CHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.