Thick & Thin cylinders

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Thick & Thin cylinders Objectives:- Introduction Thin wall pressure vessel Stress in the Thin cylinders Cylindrical pressure vessels Thick cylinders Stress in the Thick cylinders Development of Lame s s equation (1833) Error in the Thin Cylinder Formula Problem sheet (Lecturer, MECH KSK) 1 A pressure vessel is used for storing liquid or under pressure. A pipe line through which pressurized fluid flows is treated as pressure vessel. Normally pressure vessels are of cylindrical or spherical shape. There are several examples of pressure vessels which are used for engineering purpose. They include boilers, gas storage tanks, metal tires & pipelines (Lecturer, MECH KSK) 2 Thin cylinders If the wall thickness of the cylinder is less than 1/20th of the internal diameter di,the variation of the tangential stresses through the wall thickness is small & the radial stresses may be neglected. The solution can be then treated as statically determinate & the vessel is said to be thin pressure vessel. Thus a thin pressure vessel is one whose thickness to inner radius ratio is not greater than 1/10. (Lecturer, MECH KSK) 3 (Lecturer, MECH KSK) 4

2 Thick Cylinders The problem of determination of stresses in a thick cylinders was first attempted more than 160 years ago by a French mathematician Lame in His solution very logically assumed that a thick cylinder to consist of series of thin cylinders such that each exerts pressure on the other. (Lecturer, MECH KSK) 5 (Lecturer, MECH KSK) 6 This will essentially focus attention on three stress components at any point these stress components are: 1) Stress along the circumferential direction, called hoop or tangential stress. 2) Radial stress which is stress similar to the pressure on free internal or external surface. (This stress will also vary in the radial direction & not with Ѳ as in tangential stress case.) 3) Longitudinal stress in the direction the axis of the cylinder. This stress is perpendicular to the plane of the paper. So the longitudinal stress will remain same /constant for any section of the thick cylinder. This will be associated with the assumption that any section of thick cylinder will remain plane before & after the application of pressure. This assumption will mean that the strain along the axis or length remain constant. Thick cylinders also have the external pressure, not only the internal pressure. (Lecturer, MECH KSK) 7 (Lecturer, MECH KSK) 8

3 Lame s s Theory (Lecturer, MECH KSK) 9 (Lecturer, MECH KSK) 10 Assuming now that plane sections remain plane, Le. the longitudinal strain is constant across the wall of the cylinder, For small angles: Therefore, neglecting second-order small quantities, It is also assumed that the longitudinal stress is constant across the cylinder walls at points remote from the ends (B) (Lecturer, MECH KSK) 11 (Lecturer, MECH KSK) 12

4 The above equations yield the radial and hoop stresses at any radius r in terms of constants A and B. For any pressure condition there will always be two known conditions of stress (Lecturer, MECH KSK) 13 (Lecturer, MECH KSK) 14 Thick cylinder - internal pressure only Consider now the thick cylinder shown in Fig. subjected to an internal pressure P, the external pressure being zero. The two known conditions of stress which enable the Lame constants A and B to be determined are: (Lecturer, MECH KSK) 15 (Lecturer, MECH KSK) 16

5 (C) --- Errors in the Thin Cylinder Formula: (D) As r = R1 σ h = p i [ K 2 + 1] / [ K 2-1] similarly, σ r = -p i (Lecturer, MECH KSK) 17 At inner Radius when r = R 1 & P = pi the Equation (c) becomes As t = R2 R1 R2 = R1 + t Substitute the values in Equation (D) σ h = p i { R (R 1 +t) 2 } / { (R 1 +t) 2 R 1 2 } \ = p i {2(R 1 /t) 2 + 2(R 1 /t ) + 1} / 2(R 1 /t) + 1 For the Thin cylinders t < R 1 / 10 (Lecturer, MECH KSK) 18 To find the Max. error in the thin cylinder formula, put the Max. i.e. the limiting value for t = R 1 / 10 or R 1 / t = 10 σ h = p i {2(10) 2 + 2(10 ) + 1} / 2(10) + 1 = p i And from the Thin Cylinder Formula: σ h = p i R 1 / t = 10p i As R 1 / t = 10p i %age Error = 10.52p i -10p i / 10p i = 5.2 % (Lecturer, MECH KSK) 19

Stack Contents. Pressure Vessels: 1. A Vertical Cut Plane. Pressure Filled Cylinder

Pressure Vessels: 1 Stack Contents Longitudinal Stress in Cylinders Hoop Stress in Cylinders Hoop Stress in Spheres Vanishingly Small Element Radial Stress End Conditions 1 2 Pressure Filled Cylinder A

W2L3. Stresses in Engineering Components (problems 14, 15, 16) (Courseware pg 43-46) τda

Stresses in Engineering Components (problems 14, 15, 16) (combining elastic moduli with geometry elastic behaviour) W2L3 (Courseware pg 43-46) Free Body Analysis: common technique to develop stress equations

Begin creating the geometry by defining two Circles for the spherical endcap, and Subtract Areas to create the vessel wall.

ME 477 Pressure Vessel Example 1 ANSYS Example: Axisymmetric Analysis of a Pressure Vessel The pressure vessel shown below is made of cast iron (E = 14.5 Msi, ν = 0.21) and contains an internal pressure

Thin Walled Pressure Vessels

3 Thin Walled Pressure Vessels 3 1 Lecture 3: THIN WALLED PRESSURE VESSELS TABLE OF CONTENTS Page 3.1. Introduction 3 3 3.2. Pressure Vessels 3 3 3.3. Assumptions 3 4 3.4. Cylindrical Vessels 3 4 3.4.1.

AC 2008-2887: MATERIAL SELECTION FOR A PRESSURE VESSEL

AC 2008-2887: MATERIAL SELECTION FOR A PRESSURE VESSEL Somnath Chattopadhyay, Pennsylvania State University American Society for Engineering Education, 2008 Page 13.869.1 Material Selection for a Pressure

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 22.P.053 The figure below shows a portion of an infinitely

The small increase in x is. and the corresponding increase in y is. Therefore

Differentials For a while now, we have been using the notation dy to mean the derivative of y with respect to. Here is any variable, and y is a variable whose value depends on. One of the reasons that

ENGI 8673 Subsea Pipeline Engineering Faculty of Engineering and Applied Science

GUIDANCE NOTE LECTURE 12 THERMAL EXPANSION ANALYSIS OVERVIEW The calculation procedure for determining the longitudinal pipeline response can be formulated on the basis of strain. The longitudinal strain

Coefficient of Potential and Capacitance

Coefficient of Potential and Capacitance Lecture 12: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We know that inside a conductor there is no electric field and that

Dr. P. Srinivasa Rao & Chamanooru Kartik Chandra Indian Institute of Technology Kharagpur

Modeling of Pressure Profiles in a High Pressure Chamber using COMSOL Multiphysics Presented at COMSOL Conference 2012 Bangalore Dr. P. Srinivasa Rao & Chamanooru Kartik Chandra Indian Institute of Technology

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

p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh

IVE1400: n Introduction to Fluid Mechanics Statics : Pressure : Statics r P Sleigh: P..Sleigh@leeds.ac.uk r J Noakes:.J.Noakes@leeds.ac.uk January 008 Module web site: www.efm.leeds.ac.uk/ive/fluidslevel1

superimposing the stresses and strains cause by each load acting separately

COMBINED LOADS In many structures the members are required to resist more than one kind of loading (combined loading). These can often be analyzed by superimposing the stresses and strains cause by each

Chapter 16. Mensuration of Cylinder

335 Chapter 16 16.1 Cylinder: A solid surface generated by a line moving parallel to a fixed line, while its end describes a closed figure in a plane is called a cylinder. A cylinder is the limiting case

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

PRESSURE VESSELS. David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139

PRESSURE VESSELS David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 August 23, 2001 Introduction A good deal of the Mechanics of Materials

Module 1 : A Crash Course in Vectors Lecture 2 : Coordinate Systems

Module 1 : A Crash Course in Vectors Lecture 2 : Coordinate Systems Objectives In this lecture you will learn the following Define different coordinate systems like spherical polar and cylindrical coordinates

A Proposed Method for Finding Stress and Allowable Pressure in Cylinders with Radial Nozzles

A Proposed Method for Finding Stress and Allowable Pressure in Cylinders with Radial Nozzles Les M. Bildy Codeware ABSTRACT A simple technique is presented for calculating the local primary stress from

Module 6 : Wave Guides. Lecture 41 : Transverse Electric and Magnetic Mode. Objectives. In this course you will learn the following

Objectives In this course you will learn the following Important features of Transverse Electric Waves. Fields for Transverse Magnetic (TM) Mode. Important features for Transverse Magnetic (TM) Mode. Important

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

Heat Transfer Prof. Dr. Aloke Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 02 One Dimensional Steady State Heat Transfer Lecture No. # 05 Extended

FLUID FORCES ON CURVED SURFACES; BUOYANCY

FLUID FORCES ON CURVED SURFCES; BUOYNCY The principles applicable to analysis of pressure-induced forces on planar surfaces are directly applicable to curved surfaces. s before, the total force on the

AN EXPLANATION OF JOINT DIAGRAMS

AN EXPLANATION OF JOINT DIAGRAMS When bolted joints are subjected to external tensile loads, what forces and elastic deformation really exist? The majority of engineers in both the fastener manufacturing

Lecture 11: Introduction to Constitutive Equations and Elasticity

Lecture : Introduction to Constitutive quations and lasticity Previous lectures developed the concepts and mathematics of stress and strain. The equations developed in these lectures such as Cauchy s formula

Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t

Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a load-carrying

1.7 Cylindrical and Spherical Coordinates

56 CHAPTER 1. VECTORS AND THE GEOMETRY OF SPACE 1.7 Cylindrical and Spherical Coordinates 1.7.1 Review: Polar Coordinates The polar coordinate system is a two-dimensional coordinate system in which the

Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION ( )

a. Using Faraday s law: Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION The overall sign will not be graded. For the current, we use the extensive hints in the

Module 3 : Electromagnetism Lecture 13 : Magnetic Field

Module 3 : Electromagnetism Lecture 13 : Magnetic Field Objectives In this lecture you will learn the following Electric current is the source of magnetic field. When a charged particle is placed in an

ME 354, MECHANICS OF MATERIALS LABORATORY PRESSURE VESSELS AND COMPOUND STRESSES/STRAINS

PURPOS M 354, MCHANICS O MATRIAS ABORATORY PRSSUR VSSS AND COMPOUND STRSSS/STRAINS 7 november 00 / mgj The purposes of this exercise are to evaluate the compound stress/strain states in a thin walled closed

Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long

SURFACE AREAS AND VOLUMES

CHAPTER 1 SURFACE AREAS AND VOLUMES (A) Main Concepts and Results Cuboid whose length l, breadth b and height h (a) Volume of cuboid lbh (b) Total surface area of cuboid 2 ( lb + bh + hl ) (c) Lateral

Pressure in Fluids. Introduction

Pressure in Fluids Introduction In this laboratory we begin to study another important physical quantity associated with fluids: pressure. For the time being we will concentrate on static pressure: pressure

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

Exam 1 Practice Problems Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8 Spring 13 Exam 1 Practice Problems Solutions Part I: Short Questions and Concept Questions Problem 1: Spark Plug Pictured at right is a typical

Viscous flow in pipe

Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum - Navier-Stokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................

Math 1B, lecture 5: area and volume

Math B, lecture 5: area and volume Nathan Pflueger 6 September 2 Introduction This lecture and the next will be concerned with the computation of areas of regions in the plane, and volumes of regions in

Chapter 22: Electric Flux and Gauss s Law

22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we

SURFACE TENSION. Definition

SURFACE TENSION Definition In the fall a fisherman s boat is often surrounded by fallen leaves that are lying on the water. The boat floats, because it is partially immersed in the water and the resulting

Sheet metal operations - Bending and related processes

Sheet metal operations - Bending and related processes R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Table of Contents 1.Quiz-Key... Error! Bookmark not defined. 1.Bending

Solution: The draft attempted in this rolling operation is

Example: 1 A 300-mm-wide strip 25 mm thick is fed through a rolling mill with two powered rolls each of radius = 250 mm. The work thickness is to be reduced to 22 mm in one pass at a roll speed of 50 rev/min.

Force measurement. Forces VECTORIAL ISSUES ACTION ET RÉACTION ISOSTATISM

Force measurement Forces VECTORIAL ISSUES In classical mechanics, a force is defined as "an action capable of modifying the quantity of movement of a material point". Therefore, a force has the attributes

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 4 AREAS AND VOLUMES This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.

Torsion Tests. Subjects of interest

Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test

THE MODIFICATION OF WIND-TUNNEL RESULTS BY THE WIND-TUNNEL DIMENSIONS

THE MODIFICATION OF WIND-TUNNEL RESULTS BY THE WIND-TUNNEL DIMENSIONS 13\' MAX M. MONK, Ph.D., Dr.Eng. Technical Assistant, National Advisory Committee for Aeronautics RIlPRINTED FROM THII JOURNAL OF THE

Burst Pressure Prediction of Pressure Vessel using FEA

Burst Pressure Prediction of Pressure Vessel using FEA Nidhi Dwivedi, Research Scholar (G.E.C, Jabalpur, M.P), Veerendra Kumar Principal (G.E.C, Jabalpur, M.P) Abstract The main objective of this paper

AS CHALLENGE PAPER 2014

AS CHALLENGE PAPER 2014 Name School Total Mark/50 Friday 14 th March Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

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

FRACTURE ANALYSIS OF FILAMENT-WOUND FRP COMPOSITES USING RING BURST TEST

FRACTURE ANALYSIS OF FILAMENT-WOUND FRP COMPOSITES USING RING BURST TEST Shuichi Wakayama, Akihiro Horide and Masanori Kawahara Department of Mechanical Engineering, Tokyo Metropolitan University, 1-1

Section 16: Neutral Axis and Parallel Axis Theorem 16-1

Section 16: Neutral Axis and Parallel Axis Theorem 16-1 Geometry of deformation We will consider the deformation of an ideal, isotropic prismatic beam the cross section is symmetric about y-axis All parts

Removing chips is a method for producing plastic threads of small diameters and high batches, which cause frequent failures of thread punches.

Plastic Threads Technical University of Gabrovo Yordanka Atanasova Threads in plastic products can be produced in three ways: a) by direct moulding with thread punch or die; b) by placing a threaded metal

Analysis of Stress CHAPTER 1 1.1 INTRODUCTION

CHAPTER 1 Analysis of Stress 1.1 INTRODUCTION The basic structure of matter is characterized by nonuniformity and discontinuity attributable to its various subdivisions: molecules, atoms, and subatomic

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

Openings in ASME Code Pressure Vessels. Introduction

Copyright 2005-2009 Randall W. Whitesides, P.E. Introduction Working one s way through the ASME Code (hereafter referred to simply as the Code) on the subject of unfired pressure vessel openings has been

Design Project 2. Sizing of a Bicycle Chain Ring Bolt Set. Statics and Mechanics of Materials I. ENGR 0135 Section 1040.

Design Project 2 Sizing of a Bicycle Chain Ring Bolt Set Statics and Mechanics of Materials I ENGR 0135 Section 1040 November 9, 2014 Derek Nichols Michael Scandrol Mark Vavithes Nichols, Scandrol, Vavithes

Analysis of Stresses and Strains

Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4

Theory of turbo machinery / Turbomaskinernas teori Chapter 4 Note direction of α 2 FIG. 4.1. Turbine stage velocity diagrams. Assumptions: Hub to tip ratio high (close to 1) Negligible radial velocities

PROPERTIES OF THIN LENSES. Paraxial-ray Equations

PROPERTIES OF THIN LENSES Object: To measure the focal length of lenses, to verify the thin lens equation and to observe the more common aberrations associated with lenses. Apparatus: PASCO Basic Optical

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

Torsion Testing. Objectives

Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials

Question 6.5: A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm

14:440:407 Ch6 Question 6.3: A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

Vector surface area Differentials in an OCS

Calculus and Coordinate systems EE 311 - Lecture 17 1. Calculus and coordinate systems 2. Cartesian system 3. Cylindrical system 4. Spherical system In electromagnetics, we will often need to perform integrals

Blasius solution. Chapter 19. 19.1 Boundary layer over a semi-infinite flat plate

Chapter 19 Blasius solution 191 Boundary layer over a semi-infinite flat plate Let us consider a uniform and stationary flow impinging tangentially upon a vertical flat plate of semi-infinite length Fig

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

LESSON SUMMARY. Measuring Shapes

LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given

2 A Dielectric Sphere in a Uniform Electric Field

Dielectric Problems and Electric Susceptability Lecture 10 1 A Dielectric Filled Parallel Plate Capacitor Suppose an infinite, parallel plate capacitor with a dielectric of dielectric constant ǫ is inserted

PIPELINE INSPECTION UTILIZING ULTRASOUND TECHNOLOGY: ON THE ISSUE OF RESOLUTION By, M. Beller, NDT Systems & Services AG, Stutensee, Germany

ABSTRACT: PIPELINE INSPECTION UTILIZING ULTRASOUND TECHNOLOGY: ON THE ISSUE OF RESOLUTION By, M. Beller, NDT Systems & Services AG, Stutensee, Germany Today, in-line inspection tools are used routinely

ASME Boiler and Pressure Vessel Code vs. PED and EN-standards and nuclear safety requirements. Juha Purje Inspecta Tarkastus Oy

ASME Boiler and Pressure Vessel Code vs. PED and EN-standards and nuclear safety requirements Juha Purje Inspecta Tarkastus Oy 1 2 Pressure Equipment Directive (PED) or ASME The PED shall be applied to

ME 111: Engineering Drawing

ME 111: Engineering Drawing Lecture # 14 (10/10/2011) Development of Surfaces http://www.iitg.ernet.in/arindam.dey/me111.htm http://www.iitg.ernet.in/rkbc/me111.htm http://shilloi.iitg.ernet.in/~psr/ Indian

Fundamentals of Geometry

10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount

CIP Cleaning in place

CIP Cleaning in place The circulation of non foaming cleaners without dismantling the equipment. An automatic and systematic cleaning of the inner surfaces of tanks, heat exchangers, pumps, valves and

VOLUME AND SURFACE AREAS OF SOLIDS

VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b

Week 8 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

Technical Report Example (1) Chartered (CEng) Membership

Technical Report Example (1) Chartered (CEng) Membership A TECHNICAL REPORT IN SUPPORT OF APPLICATION FOR CHARTERED MEMBERSHIP OF IGEM DESIGN OF 600 (103 BAR) 820MM SELF SEALING REPAIR CLAMP AND VERIFICATION

VISCOSITY OF A LIQUID. To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied.

VISCOSITY OF A LIQUID August 19, 004 OBJECTIVE: EQUIPMENT: To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied. Viscosity apparatus

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

Density Measurement. Technology: Pressure. Technical Data Sheet 00816-0100-3208 INTRODUCTION. S min =1.0 S max =1.2 CONSTANT LEVEL APPLICATIONS

Technical Data Sheet 00816-0100-3208 Density Measurement Technology: Pressure INTRODUCTION Pressure and differential pressure transmitters are often used to measure the density of a fluid. Both types of

Solution Derivations for Capa #11

Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform

Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings

1 of 11 9/7/2012 1:06 PM Logged in as Julie Alexander, Instructor Help Log Out Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings Course Home Assignments Roster Gradebook Item Library

General Allowances for Insulation & Cladding

TRADE OF Industrial Insulation PHASE 2 Module 1 Sheet Metal and Insulation Fundamentals UNIT: 4 General Allowances for Insulation & Cladding Produced by In cooperation with subject matter expert: Michael

Maximum and minimum problems. Information sheet. Think about

Maximum and minimum problems This activity is about using graphs to solve some maximum and minimum problems which occur in industry and in working life. The graphs can be drawn using a graphic calculator

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

ECH 4224L Unit Operations Lab I Thin Film Evaporator. Introduction. Objective

Introduction In this experiment, you will use thin-film evaporator (TFE) to separate a mixture of water and ethylene glycol (EG). In a TFE a mixture of two fluids runs down a heated inner wall of a cylindrical

MASTER DEGREE PROJECT

MASTER DEGREE PROJECT Finite Element Analysis of a Washing Machine Cylinder Thesis in Applied Mechanics one year Master Degree Program Performed : Spring term, 2010 Level Author Supervisor s Examiner :

Liquid Hydrogen Pressure Vessel Analysis

OAK RIDGE NATIONAL LABORATORY Liquid Hydrogen Pressure Vessel Analysis Claire R. Luttrell 9/18/2007 1.0 INTRODUCTION An SNS experiment is being designed that includes a 20 liter liquid hydrogen (LH2) target.

Mechanical Properties - Stresses & Strains

Mechanical Properties - Stresses & Strains Types of Deformation : Elasic Plastic Anelastic Elastic deformation is defined as instantaneous recoverable deformation Hooke's law : For tensile loading, σ =

Chapter 3. Gauss s Law

3 3 3-0 Chapter 3 Gauss s Law 3.1 Electric Flux... 3-2 3.2 Gauss s Law (see also Gauss s Law Simulation in Section 3.10)... 3-4 Example 3.1: Infinitely Long Rod of Uniform Charge Density... 3-9 Example

CHAPTER 10 THICK CYLINDERS. Summary. radial stress cr, = A - - longitudinal strain = - - v- - v-

CHAPTER 10 THICK CYLINDERS Summary The hoop and radial stresses at any point in the wall cross-section of a thick cylinder at radius r are given by the Lam6 equations: B hoop stress OH = A + - r2 B radial

To find a maximum or minimum: Find an expression for the quantity you are trying to maximise/minimise (y, say) in terms of one other variable (x).

Maxima and minima In this activity you will learn how to use differentiation to find maximum and minimum values of functions. You will then put this into practice on functions that model practical contexts.

Convex Mirrors. Ray Diagram for Convex Mirror

Convex Mirrors Center of curvature and focal point both located behind mirror The image for a convex mirror is always virtual and upright compared to the object A convex mirror will reflect a set of parallel

Geometric Optics Converging Lenses and Mirrors Physics Lab IV

Objective Geometric Optics Converging Lenses and Mirrors Physics Lab IV In this set of lab exercises, the basic properties geometric optics concerning converging lenses and mirrors will be explored. The

Students Manual for the Exam

Students Manual for the Exam General Engineering and Mechanical Engineering Discipline - March 2014 - COPYRIGHT NOTICE COPYRIGHTS 2013 NATIONAL CENTER FOR ASSESSMENT IN HIGHER EDUCATION (QIYAS) UNLESS

Analysis of Experimental Uncertainties: Density Measurement Physics Lab II

Analysis of Experimental Uncertainties: Density Measurement Physics Lab II Objective This laboratory exercise allows students to estimate and analyze experimental uncertainties. Students will calculate

Announcements. Dry Friction

Announcements Dry Friction Today s Objectives Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Class Activities Applications Characteristics

Seismic Analysis and Design of Steel Liquid Storage Tanks

Vol. 1, 005 CSA Academic Perspective 0 Seismic Analysis and Design of Steel Liquid Storage Tanks Lisa Yunxia Wang California State Polytechnic University Pomona ABSTRACT Practicing engineers face many

Formulas for gear calculation external gears. Contents:

Formulas for gear calculation external gears Contents: Relationship between the involute elements Determination of base tooth thickness from a known thickness and vice-versa. Cylindrical spur gears with

Section 2.6 Cylindrical and Spherical Coordinates A) Review on the Polar Coordinates

Section.6 Cylindrical and Spherical Coordinates A) Review on the Polar Coordinates The polar coordinate system consists of the origin O,the rotating ray or half line from O with unit tick. A point P in

Problem #1 [Sound Waves and Jeans Length]

Roger Griffith Astro 161 hw. # 8 Proffesor Chung-Pei Ma Problem #1 [Sound Waves and Jeans Length] At typical sea-level conditions, the density of air is 1.23 1 3 gcm 3 and the speed of sound is 3.4 1 4

Double integrals. Notice: this material must not be used as a substitute for attending the lectures

ouble integrals Notice: this material must not be used as a substitute for attending the lectures . What is a double integral? Recall that a single integral is something of the form b a f(x) A double integral