14-1. Fluids in Motion There are two types of fluid motion called laminar flow and turbulent flow.
|
|
- Dwain Hubbard
- 7 years ago
- Views:
Transcription
1 Fluid Dynamics Sections Covered in the Text: Chapter 15, except 15.6 To complete our study of fluids we now examine fluids in motion. For the most part the study of fluids in motion was put into an organized state by scientists working a generation after Pascal and Torricelli. We shall see here that much of the physics of fluids is encapsulated in the statement of Bernoulli s principle. The study of fluid flow was driven by the demands of the industrial revolution. It was vital for progress and profit that the movement of water, steam and oil through pipes, and the movement of aerofoils through the air, were understood mathematically. Today, the physics of fluids in motion is of special interest in the various branches of the environmental and life sciences. Flow Rate When a fluid occupies a pipe of cross sectional area A and flows with average speed v, the rate of flow Q is given by Q = Av. [14-1] The units of Q are m 3.s 1. These are units of volume.s 1, so flow rate is the same as volume rate. The paths of particles in a fluid moving with laminar flow are called streamlines. Streamlines never cross one another (Figure 14-1). Fluids in Motion There are two types of fluid motion called laminar flow and turbulent flow. A fluid will execute laminar flow when it is moving at low velocity. The particles of the fluid follow smooth paths that do not cross, and the rate of fluid flow remains constant in time. This is the easiest type of flow to describe mathematically. A fluid will execute turbulent flow when it is moving above a certain critical velocity. Strings of vortices form in the fluid, resulting in highly irregular motion. A white water rapid is a good example. A system moving irregularly is difficult to describe mathematically, so we shall not be concerned with turbulent flow here. An Ideal Fluid Since a fluid is in general a complicated medium to describe mathematically, even in laminar flow, we shall assume for simplicity that the fluid is ideal. By ideal we mean 1 The fluid is moving in laminar flow; viscous forces between adjacent layers are negligible. The flow is steady, that is, the flow rate does not change with time. 3 The fluid has a uniform density and is thus incompressible. 4 The flow is irrotational, that is, the angular momentum about any point is zero; in common parlance the fluid does not swirl. Figure Particles in a fluid moving with laminar flow follow streamlines that do not cross. The Equation of Continuity A fluid moving in laminar flow in a flow tube (that may be a pipe) can be shown to satisfy a simple relationship. Consider an ideal fluid flowing through a tube of variable cross-section (Figure 14-). In an elapsed time t, a volume A 1 v 1 t of fluid crosses area A 1, and a volume A v t crosses area A. Since the fluid is incompressible and the streamlines do not cross the volume of fluid crossing A 1 must equal the volume of fluid crossing A, so A 1 v 1 t = A v t, from which it follows that A 1 v 1 = A v or Q 1 = Q. This means that the flow rate Q = Av = const. [14-] An important consequence of eq[14-] is that if the cross sectional area of the flow tube is reduced at some point, then the flow speed increases. Eq[14-] is 14-1
2 known as the equation of continuity. 1 Example Problem 14-1 Speed of Blood Flow in Capillaries The radius of the aorta is about 1.0 cm and the blood flowing through it has a speed of about 30.0 cm.s 1. Calculate the average speed of the blood in the capillaries using the fact that although each capillary has a diameter of about 8.0 x 10 4 cm, there are literally billions of them so that their total cross section is about 000 cm. From the equation of continuity the speed of blood in the capillaries is v = v A 1 1 = 0.30(m.s 1 ) 3.14 (0.010) (m ) A (m ) = 5.0 x 10 4 m.s 1 or about 0.5 mm.s 1. This is a very low speed. Figure 14-. Illustration of the equation of continuity. The flow tube of a fluid is shown at two positions 1 and. At no time does fluid enter or leave the flow tube. The equation of continuity can be applied to explain the various rates of blood flow in the body. Blood flows from the heart into the aorta from which it passes into the major arteries; these branch into the small arteries (arterioles), which in turn branch into myriads of tiny capillaries. The blood then returns to the heart via the veins. Blood flow is fast in the aorta, but quite slow in capillaries. When you cut a finger (capillary) the blood oozes, or flows very slowly. We can show this by means of a numerical example. 1 The equation of continuity can be thought of as a statement of the conservation of fluid. As the fluid flows through the pipe the volume of fluid remains constant; it neither increases nor decreases. 14- Bernoulli s Equation Daniel Bernoulli ( ), a Swiss mathematician and scientist, lived a generation after Pascal and Torricelli. The equation he derived is a more general statement of the laws and principles of fluids we have examined thus far. Bernoulli allowed for the flow tube to undergo a possible change in height (Figure 14-3). Consider points 1 and. Let point 1 be at a height y 1 and let v 1, A 1 and p 1 be the speed of the fluid, cross sectional area of the tube and pressure of the fluid at that point. Similarly let v, A and p be the same variables at point. The actual system is the volume of fluid in the flow tube. In an elapsed time t the amount of fluid crossing A 1 is V 1 = A 1 v 1 t and the amount of fluid crossing A is V = A v t. But from the equation of continuity, A 1 v 1 = A v. So the volume of fluid crossing either area is the same; let us simply write it as ΔV = AvΔt. Fluid is moved in the flow tube as the result of the work done on the fluid by the surrounding fluid (the environment). The net work W done on the fluid in the elapsed time t is
3 p v + ρgy = const. Note 14 [14-6] Many of the principles and laws we have seen can be shown to be special cases of Bernoulli s equation. We shall consider a number of them. Many homes and buildings in the colder climates are heated by the circulation of hot water in pipes. Even if they are not explicitly aware of it, architects must ensure that their designs conform to Bernoulli s principle in order to avoid system failure. Let us consider an example. Figure Illustration of Bernoulli s equation. W = ( F F 1 )Δx = ( F F 1 ) ΔV A = ( p p 1)ΔV. This work goes into achieving two things: 1 changing the kinetic energy of the fluid between the two points by the amount: ΔK = ρδv v v 1 ( ). [14-3] changing the gravitational potential energy of the fluid between the two points by the amount mg h or ΔU = ρδvg( y y 1 ). [14-4] Since W = ( p p 1 )ΔV = ΔK + ΔU, we have, by substituting eqs[14-3] and [14-4]: ( p 1 p )ΔV = ρδv v v 1 ( ) + ρδvg y y 1 ( ). Dividing through by V we obtain the general form of Bernoulli s equation: p 1 v + ρgy = p + ρ 1 1 v + ρgy. We can put this equation into the simpler form: [14-5] Example Problem 14- Application of Bernoulli s Principle Water circulates throughout a house in a hot water heating system. If the water is pumped at a speed of 0.50 m.s 1 through a pipe of diameter 4.0 cm in the basement under a pressure of 3.0 atm, what will be the flow speed and pressure in a pipe of diameter.6 cm on the second floor 5.0 m above? Let the basement be level 1 and the second floor be level. We can obtain the flow speed by applying the equation of continuity, eq[14-]: v = v 1 A 1 A = 0.50(m.s 1 ) π(0.00m) π(0.013m) = 1. m.s 1. To find the pressure p we use Bernoulli s equation, eq[14-5]: p = p 1 + ρg( y 1 y ) + 1 ρ v ( 1 v ). Substituting p 1 = 3.0 x 10 5 Pa, ρ water = 1000 kg.m 3, g = 9.8 m.s, y 1 = 0, y = 5.0 m, v 1 = 0.50 m.s 1, v = 1. m.s 1 we get p =.5 x 10 5 Pa. Thus p < p 1. Obviously, the pipe on the second floor of the house must be able to withstand less pressure than the pipe in the basement. Eqs[14-5] and [14-6] have the look of conservation of energy expressions including work, because that, in effect, is what they are. 14-3
4 1 Torricelli s Theorem Consider the container filled with fluid in Figure A distance h below the surface of the fluid a small hole allows fluid to escape. What is the velocity of the outflowing fluid? h Example Problem 14-3 Applying Torricelli s Theorem A glass container of height 1.0 m is full of water. A small hole appears on the side of the container at the bottom (as shown in Figure 14-4). What is the speed of the water flowing out the hole? This is a straightforward application of Torricelli s theorem and eq[14-7]. The speed of the water is Figure A container of fluid with a small hole a distance h below the surface allowing fluid to escape. Applying Bernoulli s equation we have p v + ρgy = const. Assuming a container of normal laboratory size, the atmospheric pressure p is essentially the same at its top and bottom, so we can cancel p and write to a good approximation ρ v + ρgy = const. But if the container is not vanishingly small then the fluid velocity is essentially zero at the top (at y = 0). So the velocity v of the outflowing fluid (at y = h) is given by ρ v + ρg( h) = 0, from which it follows that v = gh. [14-7] This is what is known as Torricelli s theorem. Note that the velocity is independent of the fluid density. Note too that our treatment here neglects the effect of fluid viscosity (that would otherwise reduce the speed). v = gh = 9.80(m.s 1 ) 1.0(m) = 4.43 m.s 1 The value measured would be less than this if the fluid (for example, shampoo) had a significant viscosity. A Fluid at Rest For a fluid at rest (static fluid) the speed v in eq[14-6] is zero. Bernoulli s equation then reduces to p + ρgy = const. This is just Pascal s law; see eq[13-3] in Note 13. The point to be made here is that Bernoulli s equation is a more general statement of the physics of fluids than is Pascal s law. 3 Pressure in a Flowing Fluid We studied hydrostatic pressure in Note 13. We can show that in a moving fluid the pressure is dependent on velocity. A fluid flowing along a horizontal level experiences a constant gravitational potential (y = constant). Bernoulli s equation therefore becomes p v = const. [14-8] This means that as the speed v of the fluid increases the pressure p must fall. This result forms the principle of operation of many practical devices. One is the Venturi tube, which we consider next. Eq[14-5] is the same expression as obtained for the final velocity of an object dropped from rest at a height h (Note 09). 14-4
5 The Venturi Tube The Venturi tube (Figure 14-5) is a device that is used to measure the flow rate Q of a fluid. It consists of two sections of different cross sectional areas A 1 and A that are known with good precision. The difference in pressure in the fluid in the two sections (p 1 p ) is measured with a built-in manometer. Example Problem 14-4 Using a Venturi Tube Note 14 A Venturi tube is used to measure the flow of water. It has a main diameter of 3.0 cm tapering down to a throat diameter of 1.0 cm. The pressure difference p 1 p is measured to be 18 mm Hg. Calculate the velocity v 1 of the fluid input and the flow rate Q. The pressure difference in Pa is, using the conversion expression eq[13-4]: p 1 p = 18 mm Hg x 10 5 (Pa.m 1 )x18x10 3 (m) = 4.0 x 10 Pa. Therefore from eq[14-9] the speed of the input fluid is ( ) p v 1 = A 1 p ρ A 1 A ( ) = 4.6 cm.s 1. Multiplying by A 1 we obtain the flow rate Q: Q = π(1.5cm) 4.6(cm.s 1 ) =174 cm 3.s 1 Figure The Venturi tube. From Bernoulli s equation with y = y 1 we have p 1 p = ρ v v 1 ( ). Substituting the equation of continuity to eliminate v we can rearrange and solve for v 1. The flow rate Q is therefore given by ( ) p Q = A 1 v 1 = A 1 A 1 p ρ A 1 A ( ). [14-9] Since the density of the fluid ρ is also known, as are the areas A 1 and A, Q can be calculated once (p 1 p ) is measured with the manometer. These results, too, would be quite in error if the fluid had a non-negligible viscosity. The viscosity of water has a negligible effect in this example. The Aerofoil Bernoulli s equation helps to explain why an airplane is equipped with wings to help it stay in the air. An airplane wing is an example of an aerofoil (Figure 14-6). In a moving stream of air, the air travels more quickly over the top surface of an aerofoil than over the bottom surface. According to Bernoulli s principle the pressure on the top surface is less than the pressure on the bottom surface, contributing to a net upward force called aerodynamic lift. When an airplane is flying at constant altitude and speed, the upward aerodynamic lift balances the downward gravitational force and prevents the plane from falling. This is sometimes called the Bernoulli effect. A glider moving on an air track is a kind of aerofoil. On the top surface of a glider the pressure is atmospheric pressure. In the space between the bottom 14-5
6 surface and the surface of the air track the pressure of the air is higher than atmospheric. The difference in pressure accounts for the aerodynamic lift that keeps the glider from contacting the air track surface and grinding to a halt. wing. From eq[14-5] we can write p above air v above = p below air v below [14-10] where above and below refer to the airplane wing. The difference in pressure accounts for the aerodynamic lift, that is, the difference in pressure is equal to the resultant force per unit area on the wing. The magnitude of force must just equal the weight of the airplane. Thus p below p above = F A = (kg) 9.80(m.s ) 100(m ) = 16,300 Pa. Rearranging eq[14-10] we can write Figure Streamlines around an aerofoil. Example Problem 14-5 Aerodynamic Lift An airplane has a mass of.0 x 10 6 kg and the air flows past the lower surface of the wings at 100 m.s 1. If the wings have a surface area of 100 m, how fast must the air flow over the upper surface of the wing if the plane is to stay in the air? Consider only the Bernoulli effect. The wing is a surface moving horizontally through the air. The effect is the same as if the wing were stationary and the air were flowing horizontally over the v above = p p below above + v below. ρ / Taking the density of air as the value at the Earth s surface, i.e., 1.9 kg.m 3 we have v above = (1.9 /) Evaluating and taking the square root we have finally v above = 190 m.s 1. Thus the air must flow over the upper surface of the wing nearly twice as fast as past the lower surface. 14-6
7 To Be Mastered Note 14 Definitions: laminar flow, turbulent flow, equation of continuity Physics of: Bernoulli s Equation p 1 v + ρgy = p + ρ 1 1 v + ρgy Physics of: the Venturi tube Physics of: the aerofoil Typical Quiz/Test/Exam Questions 1. State Benoulli s law relating pressure p, velocity v and density ρ in a moving fluid.. Sketch a Venturi tube, labelling the important features. 3. Explain briefly what a Venturi tube is used for, and how it is used
Chapter 28 Fluid Dynamics
Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example
More informationoil liquid water water liquid Answer, Key Homework 2 David McIntyre 1
Answer, Key Homework 2 David McIntyre 1 This print-out should have 14 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making
More informationFluid Dynamics. AP Physics B
Fluid Dynamics AP Physics B Fluid Flow Up till now, we hae pretty much focused on fluids at rest. Now let's look at fluids in motion It is important that you understand that an IDEAL FLUID: Is non iscous
More informationSo if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold.
Name: MULTIPLE CHOICE: Questions 1-11 are 5 points each. 1. A safety device brings the blade of a power mower from an angular speed of ω 1 to rest in 1.00 revolution. At the same constant angular acceleration,
More informationLecture 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
More informationWhen 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
More informationXI / 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
More informationFLUID 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
More informationMercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional
Chapter 14 Fluid Mechanics. Solutions of Selected Problems 14.1 Problem 14.18 (In the text book) Mercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional area
More informationDensity (r) Chapter 10 Fluids. Pressure 1/13/2015
1/13/015 Density (r) Chapter 10 Fluids r = mass/volume Rho ( r) Greek letter for density Units - kg/m 3 Specific Gravity = Density of substance Density of water (4 o C) Unitless ratio Ex: Lead has a sp.
More informationChapter 13 - Solutions
= Chapter 13 - Solutions Description: Find the weight of a cylindrical iron rod given its area and length and the density of iron. Part A On a part-time job you are asked to bring a cylindrical iron rod
More informationFluids and Solids: Fundamentals
Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.
More informationdu 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:
More informationPhysics 1114: Unit 6 Homework: Answers
Physics 1114: Unit 6 Homework: Answers Problem set 1 1. A rod 4.2 m long and 0.50 cm 2 in cross-sectional area is stretched 0.20 cm under a tension of 12,000 N. a) The stress is the Force (1.2 10 4 N)
More informationDifferential 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
More informationAids needed for demonstrations: viscous fluid (water), tubes (pipes), injections, paper, stopwatches, vessels,, weights
1 Viscous and turbulent flow Level: high school (16-17 years) hours (2 hours class teaching, 2 hours practical excercises) Content: 1. Viscous flow 2. Poiseuille s law 3. Passing from laminar to turbulent
More informationPOURING THE MOLTEN METAL
HEATING AND POURING To perform a casting operation, the metal must be heated to a temperature somewhat above its melting point and then poured into the mold cavity to solidify. In this section, we consider
More informationPressure. Pressure. Atmospheric pressure. Conceptual example 1: Blood pressure. Pressure is force per unit area:
Pressure Pressure is force per unit area: F P = A Pressure Te direction of te force exerted on an object by a fluid is toward te object and perpendicular to its surface. At a microscopic level, te force
More informationChapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS
Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright
More informationPractice 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 =
More informationNUMERICAL 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
More informationSwissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to:
I. OBJECTIVE OF THE EXPERIMENT. Swissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to: 1) Viscosity of gas (cf. "Viscosity of gas" experiment)
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationCHAPTER 3: FORCES AND PRESSURE
CHAPTER 3: FORCES AND PRESSURE 3.1 UNDERSTANDING PRESSURE 1. The pressure acting on a surface is defined as.. force per unit. area on the surface. 2. Pressure, P = F A 3. Unit for pressure is. Nm -2 or
More informationCE 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
More informationAgoraLink Agora for Life Science Technologies Linköpings Universitet Kurs i Fysiologisk mätteknik Biofluidflöden
AgoraLink Agora for Life Science Technologies Linköpings Universitet Kurs i Fysiologisk mätteknik Biofluidflöden Fysiologisk mätteknik Anatomy of the heart The complex myocardium structure right ventricle
More informationFLUID FLOW Introduction General Description
FLUID FLOW Introduction Fluid flow is an important part of many processes, including transporting materials from one point to another, mixing of materials, and chemical reactions. In this experiment, you
More informationForces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy
Forces Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Definition of Force Force = a push or pull that causes a change
More informationA small volume of fluid speeds up as it moves into a constriction (position A) and then slows down as it moves out of the constriction (position B).
9.8 BERNOULLI'S EQUATION The continuity equation relates the flow velocities of an ideal fluid at two different points, based on the change in cross-sectional area of the pipe. According to the continuity
More information2.2.1 Pressure and flow rate along a pipe: a few fundamental concepts
1.1 INTRODUCTION Single-cell organisms live in direct contact with the environment from where they derive nutrients and into where they dispose of their waste. For living systems containing multiple cells,
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationChapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations
Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationMEASUREMENT OF VISCOSITY OF LIQUIDS BY THE STOKE S METHOD
130 Experiment-366 F MEASUREMENT OF VISCOSITY OF LIQUIDS BY THE STOKE S METHOD Jeethendra Kumar P K, Ajeya PadmaJeeth and Santhosh K KamalJeeth Instrumentation & Service Unit, No-610, Tata Nagar, Bengaluru-560092.
More informationINTRODUCTION 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
More informationFor 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
More informationChapter 6 Work and Energy
Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationp 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
More informationGrade 8 Science Chapter 9 Notes
Grade 8 Science Chapter 9 Notes Force Force - Anything that causes a change in the motion of an object. - usually a push or a pull. - the unit for force is the Newton (N). Balanced Forces - forces that
More informationPhysics 125 Practice Exam #3 Chapters 6-7 Professor Siegel
Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More informationPractice Test SHM with Answers
Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one
More informationHead Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids
Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness
More informationFluid 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
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
More informationFundamentals of Fluid Mechanics
Sixth Edition. Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department
More informationCEE 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:
More informationPractice final for Basic Physics spring 2005 answers on the last page Name: Date:
Practice final for Basic Physics spring 2005 answers on the last page Name: Date: 1. A 12 ohm resistor and a 24 ohm resistor are connected in series in a circuit with a 6.0 volt battery. Assuming negligible
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 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
More informationCurso2012-2013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationFLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions
FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or
More informationChapter 27 Static Fluids
Chapter 27 Static Fluids 27.1 Introduction... 1 27.2 Density... 1 27.3 Pressure in a Fluid... 2 27.4 Pascal s Law: Pressure as a Function of Depth in a Fluid of Uniform Density in a Uniform Gravitational
More informationChapter 15. FLUIDS. 15.1. What volume does 0.4 kg of alcohol occupy? What is the weight of this volume? m m 0.4 kg. ρ = = ; ρ = 5.
Chapter 15. FLUIDS Density 15.1. What volume does 0.4 kg of alcohol occupy? What is the weight of this volume? m m 0.4 kg ρ = ; = = ; = 5.06 x 10-4 m ρ 790 kg/m W = D = ρg = 790 kg/m )(9.8 m/s )(5.06 x
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationExperiment (13): Flow channel
Introduction: An open channel is a duct in which the liquid flows with a free surface exposed to atmospheric pressure. Along the length of the duct, the pressure at the surface is therefore constant and
More informationAOE 3104 Aircraft Performance Problem Sheet 2 (ans) Find the Pressure ratio in a constant temperature atmosphere:
AOE 3104 Aircraft Performance Problem Sheet 2 (ans) 6. The atmosphere of Jupiter is essentially made up of hydrogen, H 2. For Hydrogen, the specific gas constant is 4157 Joules/(kg)(K). The acceleration
More informationThis chapter deals with three equations commonly used in fluid mechanics:
MASS, BERNOULLI, AND ENERGY EQUATIONS CHAPTER 5 This chapter deals with three equations commonly used in fluid mechanics: the mass, Bernoulli, and energy equations. The mass equation is an expression of
More informationVISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries?
VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW VISCOSITY POISEUILLE'S LAW? Why do cars need different oils in hot and cold countries? Why does the engine runs more freely as
More informationOUTCOME 1 STATIC FLUID SYSTEMS TUTORIAL 1 - HYDROSTATICS
Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 1 STATIC FLUID SYSTEMS TUTORIAL 1 - HYDROSTATICS 1. Be able to determine the behavioural characteristics and parameters
More informationPhysics 11 Assignment KEY Dynamics Chapters 4 & 5
Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problem-solving questions, draw appropriate free body diagrams and use the aforementioned problem-solving method.. Define the following
More informationFluid Dynamics Basics
Fluid Dynamics Basics Bernoulli s Equation A very important equation in fluid dynamics is the Bernoulli equation. This equation has four variables: velocity ( ), elevation ( ), pressure ( ), and density
More informationExperiment 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
More informationMillikan Oil Drop Experiment Matthew Norton, Jurasits Christopher, Heyduck William, Nick Chumbley. Norton 0
Millikan Oil Drop Experiment Matthew Norton, Jurasits Christopher, Heyduck William, Nick Chumbley Norton 0 Norton 1 Abstract The charge of an electron can be experimentally measured by observing an oil
More informationPhysics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE
1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object
More informationTHE KINETIC THEORY OF GASES
Chapter 19: THE KINETIC THEORY OF GASES 1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure
More informationPhysics 181- Summer 2011 - Experiment #8 1 Experiment #8, Measurement of Density and Archimedes' Principle
Physics 181- Summer 2011 - Experiment #8 1 Experiment #8, Measurement of Density and Archimedes' Principle 1 Purpose 1. To determine the density of a fluid, such as water, by measurement of its mass when
More informationCO 2 41.2 MPa (abs) 20 C
comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle
More informationLecture 24 - Surface tension, viscous flow, thermodynamics
Lecture 24 - Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms
More informationProving the Law of Conservation of Energy
Table of Contents List of Tables & Figures: Table 1: Data/6 Figure 1: Example Diagram/4 Figure 2: Setup Diagram/8 1. Abstract/2 2. Introduction & Discussion/3 3. Procedure/5 4. Results/6 5. Summary/6 Proving
More informationViscous 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...........................
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationMagnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.
Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.
More informationWork, Energy and Power
Work, Energy and Power In this section of the Transport unit, we will look at the energy changes that take place when a force acts upon an object. Energy can t be created or destroyed, it can only be changed
More informationWork, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions
Work, Power, Energy Multiple Choice PSI Physics Name Multiple Choice Questions 1. A block of mass m is pulled over a distance d by an applied force F which is directed in parallel to the displacement.
More informationChapter 8: Flow in Pipes
Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks
More informationSURFACE 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
More informationChapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any
Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass
More informationKinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same.
1. A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall
More informationPhysical Quantities and Units
Physical Quantities and Units 1 Revision Objectives This chapter will explain the SI system of units used for measuring physical quantities and will distinguish between vector and scalar quantities. You
More informationLAB 6: GRAVITATIONAL AND PASSIVE FORCES
55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction
More informationTurn off all electronic devices
Balloons 1 Balloons 2 Observations about Balloons Balloons Balloons are held taut by the gases inside Some balloon float in air while others don t Hot-air balloons don t have to be sealed Helium balloons
More informationPrelab Exercises: Hooke's Law and the Behavior of Springs
59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically
More informationLAB 6 - GRAVITATIONAL AND PASSIVE FORCES
L06-1 Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies
More informationChapter 4: Newton s Laws: Explaining Motion
Chapter 4: Newton s Laws: Explaining Motion 1. All except one of the following require the application of a net force. Which one is the exception? A. to change an object from a state of rest to a state
More informationPhysics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationKinetic Theory of Gases. Chapter 33. Kinetic Theory of Gases
Kinetic Theory of Gases Kinetic Theory of Gases Chapter 33 Kinetic theory of gases envisions gases as a collection of atoms or molecules. Atoms or molecules are considered as particles. This is based on
More information8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential
8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential energy, e.g. a ball in your hand has more potential energy
More informationLab 7: Rotational Motion
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125
More informationChapter 3 Falling Objects and Projectile Motion
Chapter 3 Falling Objects and Projectile Motion Gravity influences motion in a particular way. How does a dropped object behave?!does the object accelerate, or is the speed constant?!do two objects behave
More informationPhysics of the Atmosphere I
Physics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uni-heidelberg.de heidelberg.de Last week The conservation of mass implies the continuity equation:
More informationWORK DONE BY A CONSTANT FORCE
WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newton-meter (Nm) = Joule, J If you exert a force of
More informationUnit 1 INTRODUCTION 1.1.Introduction 1.2.Objectives
Structure 1.1.Introduction 1.2.Objectives 1.3.Properties of Fluids 1.4.Viscosity 1.5.Types of Fluids. 1.6.Thermodynamic Properties 1.7.Compressibility 1.8.Surface Tension and Capillarity 1.9.Capillarity
More informationG U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M
G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD
More informationChapter 9. particle is increased.
Chapter 9 9. Figure 9-36 shows a three particle system. What are (a) the x coordinate and (b) the y coordinate of the center of mass of the three particle system. (c) What happens to the center of mass
More information