# Dimensional Analysis, hydraulic similitude and model investigation. Dr. Sanghamitra Kundu

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Dimensional Analysis, hydraulic similitude and model investigation Dr. Sanghamitra Kundu

2 Introduction Although many practical engineering problems involving fluid mechanics can be solved by using the equations and analytical procedures described in the preceding chapters, there remain a large number of problems that rely on experimentally obtained data for their solution. In fact, it is probably fair to say that very few problems involving real fluids can be solved by analysis alone. The solution to many problems is achieved through the use of a combination of theoretical and numerical analysis and experimental data. Thus, engineers working on fluid mechanics problems should be familiar with the experimental approach to these problems so that they can interpret and make use of data obtained by others, such as might appear in handbooks, or be able to plan and execute the necessary experiments in their own laboratories. In this chapter we consider some techniques and ideas that are important in the planning and execution of experiments, as well as in understanding and correlating data that may have been obtained by other experimenters.

3 Introduction An obvious goal of any experiment is to make the results as widely applicable as possible. To achieve this end, the concept ofsimilitude is often used so that measurements made on one system (for example, in the laboratory) can be used to describe the behavior of other similar systems (outside the laboratory). The laboratory systems are usually thought of asmodels and are used to study the phenomenon of interest under carefully controlled conditions. From these model studies, empirical formulations can be developed, or specific predictions of one or more characteristics of some other similar system can be made. To do this, it is necessary to establish the relationship between the laboratory model and the other system.

4 Dimensional Analysis To illustrate a typical fluid mechanics problem in which experimentation is required, consider A thin rectangular plate having a widthwand a heighthis located so that it is normal to a moving stream of fluid. An important characteristic of this system, which would be of interest to an engineer is the drag force exerted by the fluid on the plate.

5 Dimensional Analysis The first step in the planning of an experiment to study this problem would be to decide on the factors, or variables, that will have an effect on the drag force (N or lb) Let s say, we expect the list to include w and h, the fluid viscosity and density, µ andρrespectively, and the velocityvof the fluid approaching the plate. To perform the experiments in a meaningful and systematic manner, it would be necessary to change one of the variables, such as the velocity, while holding all others constant, and measure the corresponding drag force This testing would require 5 4 = 625 experiments. Fortunately, there is a much simpler approach to this problem that will eliminate the difficulties described above i.e. Dimensional Analysis

6 What do we gain by using Dimensional Analysis? 1. Reduce the number of parameters we need to vary to characterize the problem. 2. Results are independent of the system of units. 3. We don t have to conduct an experiment on every single size of plate at every velocity. Our results will even work for different fluids. 4. Predict trends in the relationship between parameters.

7 Dimensional Analysis Each physical phenomena can be expressed by an equation, composed of variable (or physical quantities) which may be dimensional and nondimensional quantities. Dimensional Analysis helps in determining a systematic arrangement of variables in the physical relationship and combining dimensional variables to form non-dimensional parameters Uses: Testing the dimensional homogeneity of any equation of fluid motion Deriving equations expressed in terms of non-dimensional parameters to show the relative significance of each parameter Given a number of variables and given that they are interrelated, the nature of relation among the variables can be determined by two methods namely, Rayleigh s method, and Buckingham s method

8 Dimensions and Units Review Dimension: time, mass Measure of a physical quantity, e.g., length, Units: Assignment of a number to a dimension, e.g., (m), (sec), (kg) 7 Primary Dimensions: 1. Mass m (kg) 2. Length L (m) 3. Time t (sec) 4. Temperature T (K) 5. Current I (A) 6. Amount of Light C (cd) 7. Amount of matter N (mol)

9 Dimensions and Units Review, continued All non-primary dimensions can be formed by a combination of the 7 primary dimensions Examples {Velocity} = {Length/Time} = {L/t} {Force} = {Mass Length/Time} = {ml/t 2 }

10 Buckingham s π-method The Buckingham s π-theorem states that if there are n dimensional variables involved in a phenomenon, which can be completely described by m fundamental quantities or dimensions (such mass, length, time etc.), and are related by a dimensionally homogeneous equation, then the relationship among thenquantities can always be expressed in terms of exactly (n-m) dimensionless and independent π terms.

11 Procedure List all the physical quantities or variables involved in the phenomenon. Note their dimensions and the number m of the fundamental dimensions comprised in them. So that there will be(n-m) π-terms Selectmvariables out of these which are to serve as repeating variables. These variables should be such that none of them is dimensionless, These variables should be such that none of them is dimensionless, no two variables have the same dimensions, they themselves do not form a dimensionless parameter and all the m fundamental parameters are included collectively in them. Dependent variable should not be taken as a repeating variable In fluid flow problems, usually a characteristic linear dimension, a characteristic velocity and a characteristic fluid property (e.g. density) are chosen as repeating variables.

12 Write the general equations for different π-terms. Product of repeating variables each raised to an unknown exponent and one of the remaining variables, taken in turn, with a known power (usually taken as one) Write the dimensional equations for the equations of the π-terms obtained in step above. Write the final general equation for the phenomenon in terms of the π-terms Any π-term may be replaced by any power of that term, including negative and fractional powers. Any π-term may be replaced by multiplying it by a numerical constant.

13 Solve A thin rectangular plate having a widthwandaheighthis locatedsothatitisnormaltoamovingstreamoffluidas shown in Fig. Assume the drag, d, that the fluid exerts on the plate is a function ofwandh,thefluidviscosityand density, and,respectively,and the velocity V of the fluid approaching the plate.

14

15 Correlation of experimental data The graphical presentation of data for problems involving three pi terms. As the number of pi terms continues to increase, corresponding to an increase in the general complexity of the problem of interest, both the graphical presentation and the determination of a suitable empirical equation become intractable. For these more complicated problems, it is often more feasible to use models to predict specific characteristics of the system rather than to try to develop general correlations.

16 Modeling and Similitude Major engineering projects involving structures, aircraft, ships, rivers, harbors, dams, air and water pollution, and so on, frequently involve the use of models. Amodel is a representation of a physical system that may be used to predict the behavior of the system in some desired respect. The physical system for which the predictions are to be made is called theprototype. Although mathematical or computer models may also conform to this definition, our interest will be in physical models, that is, models that resemble the prototype but are generally of a different size, may involve different fluids, and often operate under different conditions (pressures, velocities, etc.).

17 Modeling and Similitude Usually a model is smaller than the prototype. Therefore, it is more easily handled in the laboratory and less expensive to construct and operate than a large prototype Occasionally, if the prototype is very small, it may be advantageous to have a model that is larger than the prototype so that it can be more easily studied. For example, large models have been used to study the motion of red blood cells, which are approximately 8 µm in diameter.

18 A 1 : 46.6 scale model of an U.S. Navy fleet destroyer being tested in the 100-m long towing tank at the University of Iowa. The model is m long. In tests like this, the Froude number is the most important Non-dimensional parameter. 18

19 There is more to the design than simply scaling the geometry! The theory of models can be readily developed by using the principles of dimensional analysis. If the above equation describes the behavior of a particular prototype, a similar relationship can be written for a model of this prototype The π-terms can be developed so that π 1 contains the variable that is to be predicted from observations made on the model.

20 There is more to the design than simply scaling the geometry! With the presumption that the form of φ is the same for model and prototype, it follows that

21 The Principle of Similarity Three necessary conditions for complete similarity between a model and a prototype are: 1. Geometric similarity Ratio of significant dimensions should be same in two systems (i.e. Prototype and Model). Similarity of shape. 21

22 The Principle of Similarity Geometric similarity A model and prototype are geometric similar if and only if all body dimension in all three coordinates have the same linear scale ratio. 22

23 The Principle of Similarity 2. Kinematic similarity the velocity at any point in the model flow must be proportional (by a constant scale factor) to the velocity at the corresponding point in the prototype flow. Similarity of motion. 23

24 The Principle of Similarity The motions of two systems are Kinematically similar if homologous particles lie at homologous points at homologous time.. 24

25 The Principle of Similarity 3. Dynamic similarity When all forces in the model flow scale by a constant factor to corresponding forces in the prototype flow (force-scale equivalence). Similarity of Forces 25

26 Solve.. A long structural component of a bridge has an elliptical cross section shown in Fig. It is known that when a steady wind blows past this type of bluff body, vortices may develop on the downwind side that are shed in a regular fashion at some definite frequency. Since these vortices can create harmful periodic forces acting on the structure, it is important to determine the shedding frequency. For the specific structure of interest, D=0.1 m, H=0.3 m, and a representative wind velocity is 50 km/hr. Standard air can be assumed. The shedding frequency is to be determined through the use of a small-scale model that is to be tested in a water tunnel. For the model D m = 20 mm and the water temperature is 20 C. Determine the model dimension, and the velocity at which the test should be Determine the model dimension, and the velocity at which the test should be performed. If the shedding frequency for the model is found to be 49.9 Hz, what is the corresponding frequency for the prototype? [µ air = kg/ms;ρ = 1.23 kg/m 3 ; µ water at 20 C = 10-3 kg/ms;ρ = 998 kg/m 3 ]

27 The shedding frequency is expected to depend on the lengths D and H, the approach velocity, V, and the fluid density,ρ and viscosity µ.

28 Vortex shedding is an unsteady oscillating flow that takes place when a fluid such as air or water flows past a blunt cylindrical body at certain velocities, depending to the size and shape of the body. In this flow, vortices are created at the back of the body and detach periodically from either side of the body. If the cylindrical structure is not mounted rigidly and the frequency of vortex shedding matches the resonance frequency of the structure, the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow. Strouhal number is a dimensionless number describing oscillating flow mechanisms where S t is the dimensionless Strouhal number, f is the frequency of vortex shedding, L is the characteristic length (for example hydraulic diameter) and V is the velocity of the fluid.

29 Practice Problems The pressure rise, p, across a pump can be expressed as p= f D, ρ, ω, Q ( ) wheredis the impeller diameter,ρ the fluid density,ω the rotational speed, and Q the flowrate. Determine a suitable set of dimensionless parameters. A thin elastic wire is placed between rigid supports. A fluid flows past the wire, and it is desired to study the static deflection,δ, at the center of the wire due to the fluid drag. Assume that δ = f ( l, d, ρ, µ, V, E) wherelis the wire length,d the wire diameter,ρ the fluid density, µ the fluid viscosity, V the fluid velocity, and E the modulus of elasticity of the wire material. Develop a suitable set of pi terms for this problem.

30 Practice Problems Water sloshes back and forth in a tank as shown in Fig. The frequency of sloshing,ω, is assumed to be a function of the acceleration of gravity, g, the average depth of the water, h, and the length of the tank, l. Develop a suitable set of dimensionless parameters for this problem using g and l as repeating variables. Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency ω (See Fig.) Assume thatωis a function of the sign width,b, sign height,h, wind velocity,v, air density,ρ and an elastic constant,k, for the supporting pole. The constant, k, has dimensions of FL. Develop a suitable set of pi terms for this problem.

31 Practice Problems A model of a submarine, 1 : 15 scale, is to be tested at 180 ft/s in a wind tunnel with standard sea-level air, while the prototype will be operated in seawater. Determine the speed of the prototype to ensure Reynolds number similarity. The drag characteristics of a torpedo are to be studied in a water tunnel using a 1:5 scale model. The tunnel operates with freshwater at 20 C, whereas the prototype torpedo is to be used in seawater at 15.6 C. To correctly simulate the behavior of the prototype moving with a velocity of 30 m/s, what velocity is required in the water tunnel? The fluid dynamic characteristics of an airplane flying 240 mph at 10,000 ft are to be investigated with the aid of a 1 : 20 scale model. If the model tests are to be performed in a wind tunnel using standard air, what is the required air velocity in the wind tunnel? Is this a realistic velocity?

32 A prototype automobile is designed to travel at 65 km hr. A model of this design is tested in a wind tunnel with identical standard sea-level air properties at a 1 : 5 scale. The measured model drag is 400 N, enforcing dynamic similarity. Determine (a) the drag force on the prototype and (b) the power required to overcome this drag.

33

34

35

36

37

38

39

### Dimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena.

Dimensional Analysis and Similarity Dimensional analysis is very useful for planning, presentation, and interpretation of experimental data. As discussed previously, most practical fluid mechanics problems

### Dimensional Analysis

Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous

### 1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

### E 490 Fundamentals of Engineering Review. Fluid Mechanics. M. A. Boles, PhD. Department of Mechanical & Aerospace Engineering

E 490 Fundamentals of Engineering Review Fluid Mechanics By M. A. Boles, PhD Department of Mechanical & Aerospace Engineering North Carolina State University Archimedes Principle and Buoyancy 1. A block

### OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS

Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS 3 Be able to determine the behavioural characteristics and parameters of real fluid

### CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A

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

### In this chapter, we first review the concepts of dimensions and units. We

cen72367_ch07.qxd 10/29/04 2:27 PM Page 269 DIMENSIONAL ANALYSIS AND MODELING CHAPTER 7 In this chapter, we first review the concepts of dimensions and units. We then review the fundamental principle of

### XI / PHYSICS FLUIDS IN MOTION 11/PA

Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

### L r = L m /L p. L r = L p /L m

NOTE: In the set of lectures 19/20 I defined the length ratio as L r = L m /L p The textbook by Finnermore & Franzini defines it as L r = L p /L m To avoid confusion let's keep the textbook definition,

### Experiment 3 Pipe Friction

EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A cross-sectional

### Problem 1. 12ft. Find: Velocity of truck for both drag situations. Equations: Drag F Weight. For force balance analysis: Lift and Drag: Solution:

Problem 1 Given: Truck traveling down 7% grade Width 10ft m 5 tons 50,000 lb Rolling resistance on concrete 1.% weight C 0.96 without air deflector C 0.70 with air deflector V 100 7 1ft Find: Velocity

### Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

### These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide.

Fluid Mechanics FE Review Carrie (CJ) McClelland, P.E. cmcclell@mines.edu Fluid Mechanics FE Review These slides contain some notes, thoughts about what to study, and some practice problems. The answers

### Module 2: Review of Fluid Mechanics Basic Principles for Water Resources Engineering. Basic Definitions. Basic Definitions.

Module : Review of Fluid Mechanics Basic Principles for Water Resources Engineering Robert Pitt University of Alabama and Shirley Clark Penn State - Harrisburg Mass quantity of matter that a substance

### 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

### Natural Convection. Buoyancy force

Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

### CE 3500 Fluid Mechanics / Fall 2014 / City College of New York

1 Drag Coefficient The force ( F ) of the wind blowing against a building is given by F=C D ρu 2 A/2, where U is the wind speed, ρ is density of the air, A the cross-sectional area of the building, and

### FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER

VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER? What type of fluid flow is observed? The above pictures show how the effect

### PHYSICAL QUANTITIES AND UNITS

1 PHYSICAL QUANTITIES AND UNITS Introduction Physics is the study of matter, its motion and the interaction between matter. Physics involves analysis of physical quantities, the interaction between them

### Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion

S. Widnall 6.07 Dynamics Fall 009 Version.0 Lecture L - Degrees of Freedom and Constraints, Rectilinear Motion Degrees of Freedom Degrees of freedom refers to the number of independent spatial coordinates

### Response to Harmonic Excitation Part 2: Damped Systems

Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### APPLIED FLUID MECHANICS. TUTORIAL No.6 DIMENSIONAL ANALYSIS. When you have completed this tutorial you should be able to do the following.

APPLIED FLUID MECHANICS TUTORIAL No.6 DIMENSIONAL ANALYSIS When you have completed this tutorial you should be able to do the following. Explain the basic system of dimensions. Find the relationship between

### AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

### Vortex Shedding Meters Class # Curtis Gulaga Business Development Manager CB Engineering Ltd. #20, Street S.E. Calgary, Alberta, Canada

Vortex Shedding Meters Class # 8150 Curtis Gulaga Business Development Manager CB Engineering Ltd. #20, 5920 11 Street S.E. Calgary, Alberta, Canada 1.0 Introduction Vortex meters have proven to be repeatable,

### INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

### Experiment # 3: Pipe Flow

ME 05 Mechanical Engineering Lab Page ME 05 Mechanical Engineering Laboratory Spring Quarter 00 Experiment # 3: Pipe Flow Objectives: a) Calibrate a pressure transducer and two different flowmeters (paddlewheel

### Abaqus/CFD Sample Problems. Abaqus 6.10

Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel

### NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

### Dimensional Analysis

Dimensional Analysis Mathematical Modelling Week 2 Kurt Bryan How does the escape velocity from a planet s surface depend on the planet s mass and radius? This sounds like a physics problem, but you can

### MATLAB AS A PROTOTYPING TOOL FOR HYDRONIC NETWORKS BALANCING

MATLAB AS A PROTOTYPING TOOL FOR HYDRONIC NETWORKS BALANCING J. Pekař, P. Trnka, V. Havlena* Abstract The objective of this note is to describe the prototyping stage of development of a system that is

### Fluids in Motion Supplement I

Fluids in Motion Supplement I Cutnell & Johnson describe a number of different types of flow: Compressible vs incompressible (most liquids are very close to incompressible) Steady vs Unsteady Viscous or

### Practice Problems on Viscosity. free surface. water. y x. Answer(s): base: free surface: 0

viscosity_01 Determine the magnitude and direction of the shear stress that the water applies: a. to the base b. to the free surface free surface U y x h u water u U y y 2 h h 2 2U base: yx y 0 h free

### Flow Sensors. - mass flow rate - volume flow rate - velocity. - stream line parabolic velocity profile - turbulent vortices. Methods of measurement

Flow Sensors Flow - mass flow rate - volume flow rate - velocity Types of flow - stream line parabolic velocity profile - turbulent vortices Methods of measurement - direct: positive displacement (batch

### Hydraulic Turbines and Effect of Different Parameters on output Power

Available online at www.scholarsresearchlibrary.com European Journal of Applied Engineering and Scientific Research, 0, (4):79-84 (http://scholarsresearchlibrary.com/archive.html) ISSN: 78 004 Hydraulic

### Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity

1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood

### For Water to Move a driving force is needed

RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### 01 The Nature of Fluids

01 The Nature of Fluids WRI 1/17 01 The Nature of Fluids (Water Resources I) Dave Morgan Prepared using Lyx, and the Beamer class in L A TEX 2ε, on September 12, 2007 Recommended Text 01 The Nature of

### Worked Examples of mathematics used in Civil Engineering

Worked Examples of mathematics used in Civil Engineering Worked Example 1: Stage 1 Engineering Surveying (CIV_1010) Tutorial - Transition curves and vertical curves. Worked Example 1 draws from CCEA Advanced

### Response to Harmonic Excitation

Response to Harmonic Excitation Part 1 : Undamped Systems Harmonic excitation refers to a sinusoidal external force of a certain frequency applied to a system. The response of a system to harmonic excitation

### Rotation: Moment of Inertia and Torque

Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn

### CEE 370 Fall 2015. Laboratory #3 Open Channel Flow

CEE 70 Fall 015 Laboratory # Open Channel Flow Objective: The objective of this experiment is to measure the flow of fluid through open channels using a V-notch weir and a hydraulic jump. Introduction:

### Chapter 4. Dimensionless expressions. 4.1 Dimensional analysis

Chapter 4 Dimensionless expressions Dimensionless numbers occur in several contexts. Without the need for dynamical equations, one can draw a list (real or tentative) of physically relevant parameters,

### FLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1

COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT

### Open channel flow Basic principle

Open channel flow Basic principle INTRODUCTION Flow in rivers, irrigation canals, drainage ditches and aqueducts are some examples for open channel flow. These flows occur with a free surface and the pressure

### Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

### Design and Analysis of Various Bluff Objects for Vortex flow meters

Design and Analysis of Various Bluff Objects for Vortex flow meters T. Milinda Purna 1, L. Aarya 2, K. Lakshmi Nageswari 3 1 Assistant Professor, Department Of Electronics & Instrumentation, Sree Vidyanikethan

### Basic Equations, Boundary Conditions and Dimensionless Parameters

Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

### VIBRATION OF A WIRE N N N N. Fig.1. The first five modes of vibration of a stretched wire. The nodes are marked N.

VIBRATIO OF A WIRE This experiment investigates the modes of vibration of a stretched wire. These are standing waves and the first five modes are shown in Fig.1. The observed phenomena are common to all

### Forces on a Model Rocket

Forces on a Model Rocket This pamphlet was developed using information for the Glenn Learning Technologies Project. For more information, visit their web site at: http://www.grc.nasa.gov/www/k-12/aboutltp/educationaltechnologyapplications.html

### International Journal of Engineering Research-Online A Peer Reviewed International Journal Articles available online http://www.ijoer.

RESEARCH ARTICLE ISSN: 2321-7758 DESIGN AND DEVELOPMENT OF A DYNAMOMETER FOR MEASURING THRUST AND TORQUE IN DRILLING APPLICATION SREEJITH C 1,MANU RAJ K R 2 1 PG Scholar, M.Tech Machine Design, Nehru College

### Guideway Joint Surface Properties of Heavy Machine Tools Based on the Theory of Similarity

Research Journal of Applied Sciences, Engineering and Technology 5(): 530-536, 03 ISSN: 040-7459; e-issn: 040-7467 Maxwell Scientific Organization, 03 Submitted: October, 0 Accepted: December 03, 0 Published:

### From Figure 5.1, an rms displacement of 1 mm (1000 µm) would not cause wall damage at frequencies below 3.2 Hz.

5-1 Problems and Solutions Section 5.1 (5.1 through 5.5) 5.1 Using the nomograph of Figure 5.1, determine the frequency range of vibration for which a machine oscillation remains at a satisfactory level

### Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

### Pipe Flow-Friction Factor Calculations with Excel

Pipe Flow-Friction Factor Calculations with Excel Course No: C03-022 Credit: 3 PDH Harlan H. Bengtson, PhD, P.E. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980

### Backwater Rise and Drag Characteristics of Bridge Piers under Subcritical

European Water 36: 7-35, 11. 11 E.W. Publications Backwater Rise and Drag Characteristics of Bridge Piers under Subcritical Flow Conditions C.R. Suribabu *, R.M. Sabarish, R. Narasimhan and A.R. Chandhru

### Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k

Physics 1C Midterm 1 Summer Session II, 2011 Solutions 1. If F = kx, then k m is (a) A (b) ω (c) ω 2 (d) Aω (e) A 2 ω Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of

### Peter M. Arronax Consultants, Ltd. 1954 S. Quid Street, Captainee, MO 61057

Peter M. Arronax Consultants, Ltd. 1954 S. Quid Street, Captainee, MO 61057 To: Mr. J. A. Mesmason, Crew Chief Nautilus Salvage, Inc., 20000 Buena Vista Avenue, Vulcania, Hawaii 96807 From: J. Liu, T.

CHAPTER 6 WIND LOADS C6-1 CHAPTER 6 WIND LOADS Outline 6.1 General 6.1.1 Scope of application 6.1. Estimation principle 6.1.3 Buildings for which particular wind load or wind induced vibration is taken

### Dynamic Process Modeling. Process Dynamics and Control

Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits

### What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation)

OPEN CHANNEL FLOW 1 3 Question What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation) Typical open channel shapes Figure

### Pipe Vibration and Pressure Detection

Briiel & Kjaer ffi]j W i l Pipe Vibration and Pressure Detection 13-069 I CONTENTS Page Pipe Vibration Literature 1 Detection of Pressure Variations in Thin Walled Pipes by Vibration Measurement 3 Pipe

### School of Biotechnology

Physics reference slides Donatello Dolce Università di Camerino a.y. 2014/2015 mail: donatello.dolce@unicam.it School of Biotechnology Program and Aim Introduction to Physics Kinematics and Dynamics; Position

### M. Belloli, A. Collina, F. Resta Politecnico di Milano O.I.T.A.F. SEMINAR. Grenoble 27 April 2006

Cables vibrations due to wind action M. Belloli, A. Collina, F. Resta Politecnico di Milano O.I.T.A.F. SEMINAR Grenoble 27 April 2006 Presentation Main topic of the presentation is the vibrations of cables

### ISSN: ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 4, Issue 4, July 2015

An airflow vortex-shedding flowmeter with PVDF piezoelectric film sensors: development and characterization Roberto Marsili Dipartimento di Ingegneria, Università degli Studi di Perugia Via Duranti, n

### DEVELOPMENT OF HIGH SPEED RESPONSE LAMINAR FLOW METER FOR AIR CONDITIONING

DEVELOPMENT OF HIGH SPEED RESPONSE LAMINAR FLOW METER FOR AIR CONDITIONING Toshiharu Kagawa 1, Yukako Saisu 2, Riki Nishimura 3 and Chongho Youn 4 ABSTRACT In this paper, we developed a new laminar flow

### FILTRATION. Introduction

FILTRATION Introduction Separation of solids from liquids is a common operation that requires empirical data to make predictions of performance. These data are usually obtained from experiments performed

### Heat Transfer From A Heated Vertical Plate

Heat Transfer From A Heated Vertical Plate Mechanical and Environmental Engineering Laboratory Department of Mechanical and Aerospace Engineering University of California at San Diego La Jolla, California

### A fundamental study of the flow past a circular cylinder using Abaqus/CFD

A fundamental study of the flow past a circular cylinder using Abaqus/CFD Masami Sato, and Takaya Kobayashi Mechanical Design & Analysis Corporation Abstract: The latest release of Abaqus version 6.10

### PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in

### HANDLY & FREQUENTLY USED FORMULAS FOR THERMAL ENGINEERS

HANDLY & FREQUENTLY USED FORMULAS FOR THERMAL ENGINEERS GEOMETRY & MATH GEOMETRI & MATEMATIK Cylindrical (Tube) Volume V = p / 4 d 2 L [m 3 ] Cylindrical (Tube) Surface A = p d L [m 2 ] Rectangular Triangle

### Lecture L5 - Other Coordinate Systems

S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L5 - Other Coordinate Systems In this lecture, we will look at some other common systems of coordinates. We will present polar coordinates

### HOOKE'S LAW AND A SIMPLE SPRING DONALD C. PECKHAM PHYSICS 307 FALL 1983 ABSTRACT

HOOKE'S LAW AND A SIMPLE SPRING DONALD C. PECKHAM PHYSICS 307 FALL 983 (Digitized and Revised, Fall 005) ABSTRACT The spring constant of a screen-door spring was determined both statically, by measuring

### REVIEWS ON BLUFF BODY FLOW AROUND PRISMS AND GIRDERS

REVIEWS ON BLUFF BODY FLOW AROUND PRISMS AND GIRDERS Prepared by Le Thai Hoa 2005 1 L e T h a i H o a B l u f f b o d y f l o w a r o u n d p r i s m s a n d g i r d e r s REVIEWS ON BLUFF BODY FLOW AROUND

### Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS

1 P a g e Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS The comparison of any physical quantity with its standard unit is called measurement. Physical Quantities All the quantities in terms of

### Sinking Bubble in Vibrating Tanks Christian Gentry, James Greenberg, Xi Ran Wang, Nick Kearns University of Arizona

Sinking Bubble in Vibrating Tanks Christian Gentry, James Greenberg, Xi Ran Wang, Nick Kearns University of Arizona It is experimentally observed that bubbles will sometimes sink to the bottom of their

### NEW IMPELLER DESIGN: ANTI-RAGGING IMPELLER, ARI2

14 th European Conference on Mixing Warszawa, 10-13 September 2012 NEW IMPELLER DESIGN: ANTI-RAGGING IMPELLER, ARI2 Robert Higbee a, Jason Giacomelli a, Wojciech Wyczalkowski a a Philadelphia Mixing Solutions,

### Texas Assessment of Knowledge and Skills (TAKS) 6th Grade

Texas Assessment of Knowledge and Skills (TAKS) 6th Grade 98 99 100 Grade 6 Mathematics TAKS Objectives and TEKS Student Expectations TAKS Objective 1 The student will demonstrate an understanding of numbers,

### Pre-requisites 2012-2013

Pre-requisites 2012-2013 Engineering Computation The student should be familiar with basic tools in Mathematics and Physics as learned at the High School level and in the first year of Engineering Schools.

### Rotational Mechanics CHAPTER SOME IMPORTANT OBSERVATIONS

CHAPTER 6 Rotational Mechanics In this chapter, simple single-dimensional rotational processes will be treated. Essentially, we will be concerned with wheels rotating around fixed axes. It will become

### Wind tunnel study on the Pescara footbridge

EACWE 5 Florence, Italy 9 th 3 rd July 9 Wind tunnel study on the Pescara footbridge Flying Sphere image Museo Ideale L. Da Vinci A Zasso, M. Belloli, S. Muggiasca Dipartimento di Meccanica, Politecnico

### 226 Chapter 15: OSCILLATIONS

Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion

### F mg (10.1 kg)(9.80 m/s ) m

Week 9 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### 1) The time for one cycle of a periodic process is called the A) wavelength. B) period. C) frequency. D) amplitude.

practice wave test.. Name Use the text to make use of any equations you might need (e.g., to determine the velocity of waves in a given material) MULTIPLE CHOICE. Choose the one alternative that best completes

### Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher

Higher Technological Institute Civil Engineering Department Lectures of Fluid Mechanics Dr. Amir M. Mobasher 1/14/2013 Fluid Mechanics Dr. Amir Mobasher Department of Civil Engineering Faculty of Engineering

### Fluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment

Fluid Structure Interaction VI 3 Fluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment J. Hengstler & J. Dual Department of Mechanical and Process

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A transverse wave is propagated in a string stretched along the x-axis. The equation

### ENSC 283 Introduction and Properties of Fluids

ENSC 283 Introduction and Properties of Fluids Spring 2009 Prepared by: M. Bahrami Mechatronics System Engineering, School of Engineering and Sciences, SFU 1 Pressure Pressure is the (compression) force

### FILTRATION. Introduction. Batch Filtration (Small Scale) Controlling parameters: Pressure drop, time for filtration, concentration of slurry

FILTRATION Introduction Separation of solids from liquids is a common operation that requires empirical data to make predictions of performance. These data are usually obtained from experiments performed

### Appendix 4-C. Open Channel Theory

4-C-1 Appendix 4-C Open Channel Theory 4-C-2 Appendix 4.C - Table of Contents 4.C.1 Open Channel Flow Theory 4-C-3 4.C.2 Concepts 4-C-3 4.C.2.1 Specific Energy 4-C-3 4.C.2.2 Velocity Distribution Coefficient

### ADVANCED TOOL FOR FLUID DYNAMICS- CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERODYNAMICS AND MACHINE INDUSTRY

International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 2, March-April 2016, pp. 177 186, Article ID: IJMET_07_02_019 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=2

### du u U 0 U dy y b 0 b

BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

### Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

### SIESMIC SLOSHING IN CYLINDRICAL TANKS WITH FLEXIBLE BAFFLES

SIESMIC SLOSHING IN CYLINDRICAL TANKS WITH FLEXIBLE BAFFLES Kayahan AKGUL 1, Yasin M. FAHJAN 2, Zuhal OZDEMIR 3 and Mhamed SOULI 4 ABSTRACT Sloshing has been one of the major concerns for engineers in

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### Chapter (1) Fluids and their Properties

Chapter (1) Fluids and their Properties Fluids (Liquids or gases) which a substance deforms continuously, or flows, when subjected to shearing forces. If a fluid is at rest, there are no shearing forces

### Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration