Civil Engineering Hydraulics. Pressure and Fluid Statics
|
|
- Clement Payne
- 5 years ago
- Views:
Transcription
1 Civil Engineering Hydraulics and Fluid Statics Leonard: It wouldn't kill us to meet new people. Sheldon: For the record, it could kill us to meet new people. Common Units 2 In order to be able to discuss and analyze fluid problems we need to be able to understand some fundamental terms commonly used 1
2 Common Units The most used term in hydraulics and fluid mechanics is probably pressure is defined as the normal force exerted by a fluid per unit of area l 3 The important part of that definition is the normal (perpendicular) to the unit of area Common Units 4 The Pascal is a very small unit of pressure so it is most often encountered with a prefix to allow the numerical values to be easy to display Common prefixes are the Kilopascal (kpa=103pa), the Megapascal (MPa=106Pa), and sometimes the Gigapascal (GPa=109Pa) 2
3 Common Units A bar is defined as 105 Pa so a millibar (mbar) is defined as 10-3 bar so the millibar is 102 Pa The word bar finds its origin in the Greek word báros, meaning weight. 5 Common Units 6 Standard atmospheric pressure or "the standard atmosphere" (1 atm) is defined as kilopascals (kpa). 3
4 Common Units This "standard pressure" is a purely arbitrary representative value for pressure at sea level, and real atmospheric pressures vary from place to place and moment to moment everywhere in the world. 7 Common Units is usually given in reference to some datum l 8 Absolute pressure is given in reference to a system with no pressure whatsoever (a vacuum) 4
5 Common Units is usually given in reference to some datum l 9 Gage pressure, the more commonly used pressure, is the difference between local pressure and the absolute pressure of the system being measured Common Units If the gage pressure of the system being measured is less than local atmospheric pressure, the pressure may be termed a vacuum pressure This does not imply that it has no pressure, just that the pressure is less then local atmospheric 10 5
6 Common Units 11 Common Units To be the most precise, when giving pressure, you should state if it is an absolute or a gage pressure There is a difference 12 6
7 at a point What can appear as non-intuitive is that the pressure at any point in a fluid is the same in all directions It would seem to make more sense if the pressure was greater on the top of the point than on the bottom and not at all on the sides but remember we are talking about a point. 13 at a point 14 The statics (yes I said statics) of the situation can be used to define just what is happening 7
8 at a point We can start with a fluid at rest and therefore at static equilibrium In that fluid, we can pick a segment with a triangular cross section and a unit depth, into the fluid or into the page, with a thickness of 1 unit 15 at a point The shape was a thickness of 1 in the ydirection. Remember the pressure is defined as the force exerted normal to the surface. Since we have the FBD of this wedge, we are showing forces action on the wedge. 16 8
9 at a point We need to include one more force on this FBD and that is the weight of this wedge of fluid. 17 W at a point We can start by writing our expressions for force balances along each axis. F F F F 18 z =0 z = W + P2 ( Δx )(1) P3 ( l ) (1)( cos θ ) x =0 x = P1 ( Δz )(1) P3 ( l ) (1)( sin θ ) W 9
10 at a point The weight of the wedge can be found by solving for the volume of the wedge and then using the mass density and gravity to find the weight. W = ρvg W = ρg {( W } 1 Δx )( Δz ) 1 2 ρ is the mass density of the fluid and g is the universal gravitational constant. 19 at a point Substituting for W in our initial expressions we have F =0 F = ρ g z z Fx = 0 F x {( W } 1 Δx )( Δz ) 1 + P2 ( Δx )(1) P3 ( l ) (1)( cos θ ) 2 = P1 ( Δz )(1) P3 ( l ) (1)( sin θ ) Since the left side of all the expressions are equal to 0, we can divide both sides by 1 and get rid of the 1 s in both expressions
11 at a point Now we have { } 1 ( Δx )( Δz ) + P2 ( Δx ) - P3 ( l ) ( cos θ ) 2 0 = P1 ( Δz ) P3 ( l ) ( sin θ ) 0 = -ρ g W In the second expression, the term l sin θ is equal to Δz so we have {( } 1 Δx )( Δz ) + P2 ( Δx ) - P3 ( l ) ( cos θ ) 2 0 = P1 ( Δz ) P3 ( Δz ) 0 = -ρ g P1 = P3 21 at a point {( } 1 Δx )( Δz ) + P2 ( Δx ) - P3 ( l ) ( cos θ ) 2 0 = P1 ( Δz ) P3 ( Δz ) 0 = -ρ g W P1 = P3 In the first expression, the term l cos θ is equal to Δx so we have 1 0 = - ρ g ( Δx ) ( Δz ) + P2 ( Δx ) - P3 ( Δx )
12 at a point 0 = -ρ g {( } 1 Δx )( Δz ) + P2 ( Δx ) - P3 ( Δx ) 2 W P1 = P3 Dividing all the terms by Δx we have 1 0 = - ρ g ( Δz ) + P2 - P at a point Remember that we are talking about pressure at a point in the fluid. W We can reduce our wedge to a point by allowing the Δx and Δz dimensions to approach 0. As Δz approaches 0, the weight term also approaches = - ρ g ( Δz ) + P2 - P3 2 0 = P2 - P3 This reduces our expression to P1 = P3 P2 = P3 = P
13 at a point Notice that the value for θ was not critical for our derivation and the density of the fluid did not enter into our calculation at the end. W At any point in a fluid, the magnitude of the pressure is the same in all 0 = P2 - P3 directions. P1 = P3 P2 = P3 = P1 25 at a point Note that this statement is made about any point, it not made about any two points having the same pressure. That is a different problem and not covered by the assumptions that we just made. W 0 = P2 - P3 P1 = P3 P2 = P3 = P
14 Variation with Depth Consider a fluid with a constant density over a depth We can start by remembering that pressure is the force exerted per unit of area. 27 Variation with Depth We can start with a cylinder of diameter d and find the pressure at some depth h in the cylinder. d The fluid has a mass density of ρ and the pressure at the top of the cylinder is patm (atmospheric pressure). h The pressure at the depth h is going to be the sum of the patm and the pressure exerted by the weight of the fluid above the depth h
15 Variation with Depth The weight of the fluid can be determined by taking the volume of the fluid and multiplying that by the product of the mass density ρ and the gravitational constant g. d h V= π d2 4 h F = Vρ g = 29 π d2 4 hρ g Variation with Depth The area that the force is acting normal to is the cross sectional area of the cylinder. d V= h π d2 4 h F = Vρ g = A= 30 π d2 4 hρ g π d2 4 15
16 Variation with Depth So the added pressure of the fluid is the force exerted by the fluid divided by the area it is acting over. d F = Vρg = h A= The development in the text uses z for the depth of the fluid rather than h. 31 π d2 hρ g 4 π d2 4 π d2 hρ g F p = = 4 2 = hρ g πd A 4 Variation with Depth We can check for dimensional consistency. d p = hρ g h 32 mass length mass length time 2 = length 2 length length 3 time 2 16
17 Variation with Depth The pressure is not dependent on the area. d If we assume that density remains constant with depth and that the gravitational constant also remains constant with depth the pressure becomes a linear function of depth. h As you go deeper in a fluid, the pressure increases linearly. p = hρ g 33 Variation with Depth p = hρ g In your text, the symbol z is used for depth because h is often also used as a variable in thermodynamics. We may use both depending on the problem. The important thing is to take the variable as measuring the depth below the surface in the fluid
18 Variation with Depth p = hρ g In the previous slide, we made two assumptions The first was that we were starting from 0 gage pressure at the top of the fluid which was the reference for our depth measurement l The second was that the density of the fluid did not change with depth l 35 Variation with Depth A more formal expression for change of pressure with changing depth would be z2 h2 z2 h2 z1 h1 z1 h1 p2 p1 = ρ g dz = ρ g dh = γ dz = γ dh 36 18
19 Variation with Depth This would allow for a fluid which might change density as a function of depth z2 h2 z2 h2 z1 h1 z1 h1 p2 p1 = ρ g dz = ρ g dh = γ dz = γ dh 37 Problem 38 pressure increases downward in a given fluid and decreases upward 19
20 Problem 39 pressure increases downward in a given fluid and decreases upward Reading 40 Sections 2-2 and
21 Homework Problem Homework Problem
22 Homework Problem
Civil Engineering Hydraulics Mechanics of Fluids. Pressure and Fluid Statics. The fastest healing part of the body is the tongue.
Civil Engineering Hydraulics Mechanics of Fluids and Fluid Statics The fastest healing part of the body is the tongue. Common Units 2 In order to be able to discuss and analyze fluid problems we need to
More informationCHAPTER 2 Pressure and Head
FLUID MECHANICS Gaza, Sep. 2012 CHAPTER 2 Pressure and Head Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Introduce the concept of pressure. Prove it has a unique value at any particular elevation.
More information! =!"#$% exerted by a fluid (liquid or gas) !"#$ =!"# FUNDAMENTAL AND MEASURABLE INTENSIVE PROPERTIES PRESSURE, TEMPERATURE AND SPECIFIC VOLUME
FUNDAMENTAL AND MEASURABLE INTENSIVE PROPERTIES PRESSURE, TEMPERATURE AND SPECIFIC VOLUME PRESSURE, P! =!"#$%!"#! exerted by a fluid (liquid or gas) Thermodynamic importance of pressure One of two independent
More informationThermodynamic Systems
Thermodynamic Systems For purposes of analysis we consider two types of Thermodynamic Systems: Closed System - usually referred to as a System or a Control Mass. This type of system is separated from its
More informationEric G. Paterson. Spring 2005
Eric G. Paterson Department of Mechanical and Nuclear Engineering Pennsylvania State University Spring 2005 Reading and Homework Read Chapter 3. Homework Set #2 has been posted. Due date: Friday 21 January.
More informationCHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.
CHARACTERISTIC OF FLUIDS A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. 1 Dimensions,
More informationHydrostatic. Pressure distribution in a static fluid and its effects on solid surfaces and on floating and submerged bodies.
Hydrostatic Pressure distribution in a static fluid and its effects on solid surfaces and on floating and submerged bodies. M. Bahrami ENSC 283 Spring 2009 1 Fluid at rest hydrostatic condition: when a
More informationEngineering Thermodynamics. Chapter 1. Introductory Concepts and Definition
1.1 Introduction Chapter 1 Introductory Concepts and Definition Thermodynamics may be defined as follows : Thermodynamics is an axiomatic science which deals with the relations among heat, work and properties
More informationFluid Mechanics-61341
An-Najah National University College of Engineering Fluid Mechanics-61341 Chapter [2] Fluid Statics 1 Fluid Mechanics-2nd Semester 2010- [2] Fluid Statics Fluid Statics Problems Fluid statics refers to
More informationCHAPTER 2 Fluid Statics
Chapter / Fluid Statics CHPTER Fluid Statics FE-type Eam Review Problems: Problems - to -9. (C). (D). (C).4 ().5 () The pressure can be calculated using: p = γ h were h is the height of mercury. p= γ h=
More informationApplied 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
More informationFluid Statics. Pressure. Pressure
Pressure Fluid Statics Variation of Pressure with Position in a Fluid Measurement of Pressure Hydrostatic Thrusts on Submerged Surfaces Plane Surfaces Curved Surfaces ddendum First and Second Moment of
More informationThe general rules of statics (as applied in solid mechanics) apply to fluids at rest. From earlier we know that:
ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 2 Pressure This section will study the forces acting on or generated by fluids at rest. Objectives Introduce the concept
More informationStates of matter. Density high > high >> low (pressure dependent)
Fluids States of matter Solids Fluids crystalline amorphous liquids gasses Inter-atomic forces strong > strong >> very weak Density high > high >> low (pressure dependent) Density is an important material
More informationNicholas 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
More informationChapter 3 Fluid Statics
Chapter 3 Fluid Statics 3.1 Pressure Pressure : The ratio of normal force to area at a point. Pressure often varies from point to point. Pressure is a scalar quantity; it has magnitude only It produces
More informationPhysics 220: Classical Mechanics
Lecture 10 1/34 Phys 220 Physics 220: Classical Mechanics Lecture: MWF 8:40 am 9:40 am (Phys 114) Michael Meier mdmeier@purdue.edu Office: Phys Room 381 Help Room: Phys Room 11 schedule on course webpage
More informationFluid Mechanics Indian Institute of Technology, Kanpur Prof. Viswanathan Shankar Department of chemical Engineering. Lecture No.
Fluid Mechanics Indian Institute of Technology, Kanpur Prof. Viswanathan Shankar Department of chemical Engineering. Lecture No. # 05 Welcome to this fifth lecture on this nptel course on fluid mechanics
More informationChapter 12: Gravity, Friction, & Pressure Physical Science, McDougal-Littell, 2008
SECTION 1 (PP. 381-388): GRAVITY IS A FORCE EXERTED BY MASSES. Georgia Standards: S8P3b Demonstrate the effect of balanced and unbalanced forces on an object in terms of gravity, inertia, and friction;
More informationIntroduction to Marine Hydrodynamics
1896 1920 1987 2006 Introduction to Marine Hydrodynamics (NA235) Department of Naval Architecture and Ocean Engineering School of Naval Architecture, Ocean & Civil Engineering Shanghai Jiao Tong University
More informationME-B41 Lab 1: Hydrostatics. Experimental Procedures
ME-B41 Lab 1: Hydrostatics In this lab you will do four brief experiments related to the following topics: manometry, buoyancy, forces on submerged planes, and hydraulics (a hydraulic jack). Each experiment
More informationLagrangian description from the perspective of a parcel moving within the flow. Streamline Eulerian, tangent line to instantaneous velocity field.
Chapter 2 Hydrostatics 2.1 Review Eulerian description from the perspective of fixed points within a reference frame. Lagrangian description from the perspective of a parcel moving within the flow. Streamline
More information11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an
Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior
More informationStates of Matter. Physics 201, Lecture 25. Density ρ. Fluids
Physics 201, Lecture 25 Today s Topics n Fluid Mechanics (chapter 14) n Solids, Liquids, Gases, Plasmas n Pressure (14.1) n Pascal s Principle, Pressure Variation with Depth (14.2) n Pressure Measurement
More informationAMME2261: Fluid Mechanics 1 Course Notes
Module 1 Introduction and Fluid Properties Introduction Matter can be one of two states: solid or fluid. A fluid is a substance that deforms continuously under the application of a shear stress, no matter
More informationM o d u l e B a s i c A e r o d y n a m i c s
Category A B1 B2 B3 Level 1 2 3 M o d u l e 0 8-0 1 B a s i c A e r o d y n a m i c s P h y s i c s o f t h e A t m o s p h e r e 08-01- 1 Category A B1 B2 B3 Level 1 2 3 T a b l e o f c o n t e n t s
More informationChapter 15 - Fluid Mechanics Thursday, March 24 th
Chapter 15 - Fluid Mechanics Thursday, March 24 th Fluids Static properties Density and pressure Hydrostatic equilibrium Archimedes principle and buoyancy Fluid Motion The continuity equation Bernoulli
More informationChapter 15: Fluids. Mass Density = Volume. note : Fluids: substances which flow
Fluids: substances which flow Chapter 5: Fluids Liquids: take the shape of their container but have a definite volume Gases: take the shape and volume of their container Density m ρ = V Mass Density =
More informationThe hydrostatic equilibrium
Chapter 10 The hydrostatic equilibrium 10.1 The force on the infinitesimal parcel Now we will compute the total force acting on an infinitesimal parcel of fluid at rest. Consider a rectangular parallelepiped
More informationFluid Mechanics Discussion. Prepared By: Dr.Khalil M. Al-Astal Eng.Ahmed S. Al-Agha Eng.Ruba M. Awad
Discussion Prepared By: Dr.Khalil M. Al-Astal Eng.Ahmed S. Al-Agha Eng.Ruba M. Awad 2014-2015 Chapter (1) Fluids and their Properties Fluids and their Properties Fluids (Liquids or gases) which a substance
More informationThermodynamics-1. S. M. Hosseini Sarvari Chapter 1 Introduction & Basic Concepts
Mechanical Engineering Dept. Shahid Bahonar University of Kerman Thermodynamics-1 S. M. Hosseini Sarvari Chapter 1 Introduction & Basic Concepts Mechanical Engineering Dept. Shahid Bahonar University of
More informationThe word thermodynamics is derived from two Greek words Therm which means heat Dynamis which means power
THERMODYNAMICS INTRODUCTION The word thermodynamics is derived from two Greek words Therm which means heat Dynamis which means power Together the spell heat power which fits the time when the forefathers
More informationProperties of plane surfaces I: First moment and centroid of area
Properties of plane surfaces I: First moment and centroid of area Having deal with trusses and frictional forces, we now change gears and go on to discuss some properties of surfaces mathematically. Of
More informationGATE PSU. Chemical Engineering. Fluid Mechanics. For. The Gate Coach 28, Jia Sarai, Near IIT Hauzkhas, New Delhi 16 (+91) ,
For GATE PSU Chemical Engineering Fluid Mechanics GATE Syllabus Fluid statics, Newtonian and non-newtonian fluids, Bernoulli equation, Macroscopic friction factors, energy balance, dimensional analysis,
More informationFluid Mechanics. Forces on Fluid Elements. Fluid Elements - Definition:
Fluid Mechanics Chapter 2: Fluid Statics Lecture 3 Forces on Fluid Elements Fluid Elements - Definition: Fluid element can be defined as an infinitesimal region of the fluid continuum in isolation from
More informationPhysics 123 Unit #1 Review
Physics 123 Unit #1 Review I. Definitions & Facts Density Specific gravity (= material / water) Pressure Atmosphere, bar, Pascal Barometer Streamline, laminar flow Turbulence Gauge pressure II. Mathematics
More informationCEE 342 Aut Homework #2 Solutions
CEE 4 Aut 005. Homework # Solutions.9. A free-body diagram of the lower hemisphere is shown below. This set of boundaries for the free body is chosen because it isolates the force on the bolts, which is
More information(Refer Slide Time: 0:28)
Engineering Thermodynamics Professor Jayant K Singh Department of Chemical Engineering Indian Institute of Technology Kanpur Lecture 08 Examples on basic concept & energy balance Welcome back! Myself Parul
More informationGeneral Physics I (aka PHYS 2013)
General Physics I (aka PHYS 2013) PROF. VANCHURIN (AKA VITALY) University of Minnesota, Duluth (aka UMD) OUTLINE CHAPTER 12 CHAPTER 19 REVIEW CHAPTER 12: FLUID MECHANICS Section 12.1: Density Section 12.2:
More informationChapter 1 INTRODUCTION
Chapter 1 INTRODUCTION 1-1 The Fluid. 1-2 Dimensions. 1-3 Units. 1-4 Fluid Properties. 1 1-1 The Fluid: It is the substance that deforms continuously when subjected to a shear stress. Matter Solid Fluid
More informationChapter 12. Fluid Mechanics. A. The density ρ of a substance of uniform composition is defined as its mass M divided by its volume V.
Chapter 12 Fluid Mechanics 12.1 Density A. The density ρ of a substance of uniform composition is defined as its mass M divided by its volume V. That is,! = M V The density of water at 4 o C is 1000 kg/m
More informationStatics : Rigid Bodies
Statics : Rigid Bodies The Moment of a Force The moment M (turning effect) of a force about a point O is the product of the magnitude of the force (F) and the perp. distance (x)to the point of application.
More informationLecture 23 Sound Beats Sound Solids and Fluids
Lecture 23 Sound Beats Sound Solids and Fluids To round out our discussion of interference and waves, we should talk about beats. When you combine two waves (sound is a good example), if the frequencies
More informationControl Volume Revisited
Civil Engineering Hydraulics Control Volume Revisited Previously, we considered developing a control volume so that we could isolate mass flowing into and out of the control volume Our goal in developing
More informationFluids. Fluid = Gas or Liquid. Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion
Chapter 14 Fluids Fluids Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion Fluid = Gas or Liquid MFMcGraw-PHY45 Chap_14Ha-Fluids-Revised 10/13/01 Densities MFMcGraw-PHY45 Chap_14Ha-Fluids-Revised
More informationChapter 2 Mechanical Equilibrium
Chapter 2 Mechanical Equilibrium I. Force (2.1) A. force is a push or pull 1. A force is needed to change an object s state of motion 2. State of motion may be one of two things a. At rest b. Moving uniformly
More informationch-01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows
ch-01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows ch-01.qxd 8/4/04 2:33 PM Page 3 Introduction 1 Summary The introduction chapter reviews briefly the basic fluid properties
More informationCourse: TDEC202 (Energy II) dflwww.ece.drexel.edu/tdec
Course: TDEC202 (Energy II) Thermodynamics: An Engineering Approach Course Director/Lecturer: Dr. Michael Carchidi Course Website URL dflwww.ece.drexel.edu/tdec 1 Course Textbook Cengel, Yunus A. and Michael
More informationPhysics 207 Lecture 18
Physics 07, Lecture 8, Nov. 6 MidTerm Mean 58.4 (64.6) Median 58 St. Dev. 6 (9) High 94 Low 9 Nominal curve: (conservative) 80-00 A 6-79 B or A/B 34-6 C or B/C 9-33 marginal 9-8 D Physics 07: Lecture 8,
More informationPhy 212: General Physics II. Daniel Bernoulli ( )
Phy 1: General Physics II Chapter 14: Fluids Lecture Notes Daniel Bernoulli (1700-178) Swiss merchant, doctor & mathematician Worked on: Vibrating strings Ocean tides Kinetic theory Demonstrated that as
More informationPhysics 1A Lecture 10B
Physics 1A Lecture 10B "Sometimes the world puts a spin on life. When our equilibrium returns to us, we understand more because we've seen the whole picture. --Davis Barton Cross Products Another way to
More informationTypes of Forces. Pressure Buoyant Force Friction Normal Force
Types of Forces Pressure Buoyant Force Friction Normal Force Pressure Ratio of Force Per Unit Area p = F A P = N/m 2 = 1 pascal (very small) P= lbs/in 2 = psi = pounds per square inch Example: Snow Shoes
More informationPhysics 106 Lecture 13. Fluid Mechanics
Physics 106 Lecture 13 Fluid Mechanics SJ 7 th Ed.: Chap 14.1 to 14.5 What is a fluid? Pressure Pressure varies with depth Pascal s principle Methods for measuring pressure Buoyant forces Archimedes principle
More informationP = ρ{ g a } + µ 2 V II. FLUID STATICS
II. FLUID STATICS From a force analysis on a triangular fluid element at rest, the following three concepts are easily developed: For a continuous, hydrostatic, shear free fluid: 1. Pressure is constant
More informationWhy do we need to study thermodynamics? Examples of practical thermodynamic devices:
Why do we need to study thermodynamics? Knowledge of thermodynamics is required to design any device involving the interchange between heat and work, or the conversion of material to produce heat (combustion).
More informationMechanics of Materials
Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics
More informationHydrostatics. ENGR 5961 Fluid Mechanics I: Dr. Y.S. Muzychka
1 Hydrostatics 2 Introduction In Fluid Mechanics hydrostatics considers fluids at rest: typically fluid pressure on stationary bodies and surfaces, pressure measurements, buoyancy and flotation, and fluid
More informationThe Laws of Motion. Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples
The Laws of Motion Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples Gravitational Force Gravitational force is a vector Expressed by Newton s Law of Universal
More informationRotational Equilibrium
Rotational Equilibrium In this laboratory, we study the conditions for static equilibrium. Axis Through the Center of Gravity Suspend the meter stick at its center of gravity, with its numbers increasing
More informationChapter 7 Applications of Integration
Chapter 7 Applications of Integration 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk Method 7.3 Volume: The Shell Method 7.4 Arc Length and Surfaces of Revolution 7.5 Work 7.6 Moments, Centers
More informationFinal Review, Day 1. Announcements: Web page:
Announcements: Final Review, Day 1 Final exam next Wednesday (5/9) at 7:30am in the Coors Event Center. Recitation tomorrow is a review. Please feel free to ask the TA any questions on the course material.
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 5 Equilibrium of a Rigid Body Chapter Objectives Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body
More informationGeneral Physics I Spring Applying Newton s Laws
General Physics I Spring 2011 Applying Newton s Laws 1 Equilibrium An object is in equilibrium if the net force acting on it is zero. According to Newton s first law, such an object will remain at rest
More informationMA 102 Mathematics II Lecture Feb, 2015
MA 102 Mathematics II Lecture 1 20 Feb, 2015 Differential Equations An equation containing derivatives is called a differential equation. The origin of differential equations Many of the laws of nature
More informationEQUILIBRIUM OBJECTIVES PRE-LECTURE
27 FE3 EQUILIBRIUM Aims OBJECTIVES In this chapter you will learn the concepts and principles needed to understand mechanical equilibrium. You should be able to demonstrate your understanding by analysing
More information9. Pumps (compressors & turbines) Partly based on Chapter 10 of the De Nevers textbook.
Lecture Notes CHE 31 Fluid Mechanics (Fall 010) 9. Pumps (compressors & turbines) Partly based on Chapter 10 of the De Nevers textbook. Basics (pressure head, efficiency, working point, stability) Pumps
More informationT H E R M O D Y N A M I C S M E
T H E R M O D Y N A M I C S M E THERMODYNAMICS CONTENTS 1 BASIC CONCEPTS IN THERMODYNAMICS 2 TEMPERATURE 3 WORK AND HEAT TRANSFER Thermodynamic system, surroundings, universe, system boundary Types of
More informationProperties of Gases. The perfect gas. States of gases Gas laws Kinetic model of gases (Ch th ed, th ed.) Real gases
Properties of Gases Chapter 1 of Physical Chemistry - 6th Edition P.W. Atkins. Chapter 1 and a little bit of Chapter 24 of 7th Edition. Chapter 1 and a little bit of Chapter 21 of 8th edition. The perfect
More informationENGG 3260: Thermodynamics. Home Assignment 1 (Chapter 1) (Answer)
ENGG 360: Thermodynamics Home Assignment 1 (Chapter 1) (Answer) 1. Why does a bicyclist pick up speed on a downhill road even when he is not pedaling? Does this violate the conservation of energy principle?
More informationStatic equilibrium. Objectives. Physics terms. Assessment. Brainstorm. Equations 6/3/14
Static equilibrium Objectives State the conditions of static equilibrium in terms of forces and torques. Draw a free-body diagram of a lever showing all forces. Use the condition of equilibrium to solve
More informationPHYSICS 220 Lecture 16 Fluids Textbook Sections
PHYSICS 220 Lecture 16 Fluids Textbook Sections 10.1-10.4 Lecture 16 Purdue University, Physics 220 1 States of Matter Fluids Solid Hold Volume Hold Shape Liquid Hold Volume Adapt Shape Gas Adapt Volume
More informationChapter 14. Fluid Mechanics
Chapter 14 Fluid Mechanics States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite volume nor shape All of these
More informationEQUATIONS OF MOTION: RECTANGULAR COORDINATES
EQUATIONS OF MOTION: RECTANGULAR COORDINATES Today s Objectives: Students will be able to: 1. Apply Newton s second law to determine forces and accelerations for particles in rectilinear motion. In-Class
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. APPLICATIONS
More informationPressure in stationary and moving fluid Lab- Lab On- On Chip: Lecture 2
Pressure in stationary and moving fluid Lab-On-Chip: Lecture Lecture plan what is pressure e and how it s distributed in static fluid water pressure in engineering problems buoyancy y and archimedes law;
More informationAn-Najah National University Civil Engineering Departemnt. Fluid Mechanics. Chapter [2] Fluid Statics
An-Najah National University Civil Engineering Deartemnt Fluid Mechanics Chater [2] Fluid Statics 1 Fluid Statics Problems Fluid statics refers to the study of fluids at rest or moving in such a manner
More informationPhysics 141 Rotational Motion 2 Page 1. Rotational Motion 2
Physics 141 Rotational Motion 2 Page 1 Rotational Motion 2 Right handers, go over there, left handers over here. The rest of you, come with me.! Yogi Berra Torque Motion of a rigid body, like motion of
More informationFluids, Thermodynamics, Waves, and Optics Fluids
Fluids, Thermodynamics, Waves, and Optics Fluids Lana Sheridan De Anza College April 10, 2018 Overview static fluids pressure liquid pressure Pascal s law Elastic Properties of Solids We are considering
More informationForces and Newton s Laws Reading Notes. Give an example of a force you have experienced continuously all your life.
Forces and Newton s Laws Reading Notes Name: Section 4-1: Force What is force? Give an example of a force you have experienced continuously all your life. Give an example of a situation where an object
More informationCONCEPTS AND DEFINITIONS. Prepared by Engr. John Paul Timola
CONCEPTS AND DEFINITIONS Prepared by Engr. John Paul Timola ENGINEERING THERMODYNAMICS Science that involves design and analysis of devices and systems for energy conversion Deals with heat and work and
More informationChapter 10. Solids & Liquids
Chapter 10 Solids & Liquids Next 6 chapters use all the concepts developed in the first 9 chapters, recasting them into a form ready to apply to specific physical systems. 10.1 Phases of Matter, Mass Density
More informationJurong Junior College 2014 J1 H1 Physics (8866) Tutorial 3: Forces (Solutions)
Jurong Junior College 2014 J1 H1 Physics (8866) Tutorial 3: Forces (Solutions) Take g = 9.81 m s -2, P atm = 1.0 x 10 5 Pa unless otherwise stated Learning Outcomes (a) Sub-Topic recall and apply Hooke
More informationHomework Assignment on Fluid Statics
AMEE 0 Introduction to Fluid Mecanics Instructor: Marios M. Fyrillas Email: m.fyrillas@fit.ac.cy Homework Assignment on Fluid Statics --------------------------------------------------------------------------------------------------------------
More informationPressure in stationary and moving fluid. Lab-On-Chip: Lecture 2
Pressure in stationary and moving fluid Lab-On-Chip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at
More informationReferences: Parcel Theory. Vertical Force Balance. ESCI Cloud Physics and Precipitation Processes Lesson 3 - Stability and Buoyancy Dr.
References: ESCI 340 - Cloud Physics and Precipitation Processes Lesson 3 - Stability and Buoyancy Dr. DeCaria Glossary of Meteorology, 2nd ed., American Meteorological Society A Short Course in Cloud
More informationME2320 Thermodynamics I. Summer I Instructor: Dr. William W. Liou
ME2320 Thermodynamics I Summer I 2016 Instructor: Dr. William W. Liou Syllabus http://homepages.wmich.edu/~liou/wp_course.htm Homework Solutions Format 3 How to get, and stay, ahead in this class? Preview
More informationT H E R M O D Y N A M I C S M T
T H E R M O D Y N A M I C S M T THERMODYNAMICS AND RATE PROCESSES CONTENTS CHAPTER DESCRIPTION PAGE NO 1 Thermodynamics NOTES 1.1. Definitions 1 1.2. Laws of Thermodynamics 3 1.2.1. Zeroth Law of Thermodynamics
More informationStudent Academic Learning Services Page 1 of 6 Laws about gases
Student Academic Learning Services Page 1 of 6 Laws about gases Charles law Volume is directly proportional to temperature. V = ct, where c > 0 is constant. French balloonist Jacque Charles noticed that
More informationChapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian
Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite
More informationFluid Mechanics Abdusselam Altunkaynak
Fluid Mechanics Abdusselam Altunkaynak 2.3.3 Pascal s Law Let s consider a closed container filled with gas. We have seen earlier that the pressure at a point can be determined in relation with the pressure
More informationGATE & PSUs CHEMICAL ENGINEERING
Postal Correspondence GATE & PSUs CHEMICAL ENGINEERING THERMODYNAMICS 1 T A B L E O F C O N T E N T S. No. Title Page no. 1. Introduction 3 2. Work and Heat Transfer 9 3. Second Law of Thermodynamics 27
More informationInstructions: (62 points) Answer the following questions. SHOW ALL OF YOUR WORK. A B = A x B x + A y B y + A z B z = ( 1) + ( 1) ( 4) = 5
AP Physics C Fall, 2016 Work-Energy Mock Exam Name: Answer Key Mr. Leonard Instructions: (62 points) Answer the following questions. SHOW ALL OF YOUR WORK. (12 pts ) 1. Consider the vectors A = 2 î + 3
More informationPhysics 101: Lecture 17 Fluids
Exam III Physics 101: Lecture 17 Fluids Exam 2 is Mon Nov. 4, 7pm Extra office hours on Fri. (see webpage!) Physics 101: Lecture 17, Pg 1 Homework 9 Help A block of mass M 1 = 3 kg rests on a table with
More informationShell 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
More informationCIV100: Mechanics. Lecture Notes. Module 1: Force & Moment in 2D. You Know What to Do!
CIV100: Mechanics Lecture Notes Module 1: Force & Moment in 2D By: Tamer El-Diraby, PhD, PEng. Associate Prof. & Director, I2C University of Toronto Acknowledgment: Hesham Osman, PhD and Jinyue Zhang,
More informationMAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics
MAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics S. H. Lam February 22, 1999 1 Reading and Homework Assignments The problems are due on Wednesday, March 3rd, 1999, 5PM. Please submit your
More information1.4 Perform the following unit conversions: (b) (c) s. g s. lb min. (d) (e) in. ft s. m 55 h. (f) ft s. km h. (g)
1.4 Perform the following unit conversions: 0.05 ft 1 in. (a) 1L 61in. 1L 1ft (b) 1kJ 650 J 10 J 1Btu 1.0551kJ 0.616 Btu (c) 41 Btu/h 0.15 kw 1kW 1h 600 s 778.17 ft lbf 1Btu ft lbf 99.596 s (d) g 78 s
More informationCHEN 3200 Fluid Mechanics Spring Homework 3 solutions
Homework 3 solutions 1. An artery with an inner diameter of 15 mm contains blood flowing at a rate of 5000 ml/min. Further along the artery, arterial plaque has partially clogged the artery, reducing the
More informationm V DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: SI Unit of Mass Density: kg/m 3
Chapter 11 Fluids 11.1 Mass Density DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: ρ m V SI Unit of Mass Density: kg/m 3 11.1 Mass Density
More informationLecture 13 An introduction to hydraulics
Lecture 3 An introduction to hydraulics Hydraulics is the branch of physics that handles the movement of water. In order to understand how sediment moves in a river, we re going to need to understand how
More information