CHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.


 Allison Craig
 2 years ago
 Views:
Transcription
1 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
2 Dimensions, Dimensional homogeneity and Units Fluid has qualitative and quantitative characteristic. Qualitative : To identify the nature of fluid such as length, time, stress and velocity. Quantitative : Numerical measure of the characteristic. Quantitative requires both a number and a standard. Such standards are called unit. 2
3 Primary quantity : L : Length T : Time M : Mass θ: Temperature Secondary quantity : L 2 : Area LT 1 : Velocity ML 3 : Density 3
4 All theoretically derived equations are dimensionally homogeneous. The dimension of the left side of the equation must be the same as those on the right side, and all additive separate terms must have the same dimensions. Example : V LT = V o = + at LT + LT
5 5
6 UNIT 3 major systems that are commonly used in engineering. 1. British Gravitational (BG) System Length foot (ft) Time second (s) Force pound (lb) Temperature Fahrenheit (ºF) 2. International System (SI) Length meter (m) Time second (s) Mass kilogram (kg) Temperature Kelvin (K) The relation of Kelvin and Celsius is; K = C
7 3. English Engineering (EE) System Length foot (ft) Time second (s) Mass pound mass (lbm) Force pound (lb or lbf) Temperature Rankine (ºR) 7
8 8
9 Density MEASURES OF FLUID MASS AND WEIGHT Designated by the Greek symbol ρ (rho). Defined as its mass per unit volume. ρ = mass = volume kg 3 m Specific volume, is the volume per unit mass. This property is not commonly used in fluid mechanics but is used widely in thermodynamics. volume υ = mass = 1 ρ 9
10 10
11 11
12 Specific weight Designated by the Greek symbol γ (gamma). Defined as its weight per unit volume. weight mg kg g γ = = = = ρg 3 volume volume m Specific gravity Designated as SG. Defined as the ratio of the density of the fluid to the density of water at some specified temperature. Usually the specified temperature is taken as 4ºC. SG = ρ H 2 ρ C 12
13 Ideal gas law Gases are highly compressible in comparison to liquids, with changes in gas density directly related to changes in pressure and temperature through the equation ; P = ρrt P : pressure ρ : density R : gas constant T : temperature 13
14 The pressure in the ideal gas law must be expressed as an absolute pressure (abs), which means that it is measured relative to absolute zero pressure (a pressure that would only occur in a perfect vacuum) Standard sealevel atmospheric pressure is 14.7 psi and 101 kpa, respectively. 14
15 VISCOSITY The property of viscosity is described the fluidity of the fluid. To resist the applied force, P, a shearing stress, τ, would be developed at the platematerial interface. The equilibrium is ; P = τa It revealed that as the shearing stress, τ, is increased by increasing P. 15
16 We can say that shear stress, τ, has direct proportion with the velocity gradient that is ; τ du dy The shearing stress and velocity gradient can be related with a relationship of the form ; τ = µ (mu) is dynamic viscosity. µ du dy 16
17 Fluids for which the shearing stress is linearly related to the rate of shearing strain are designated as Newtonian fluids. Fluids for which the shearing stress is not linearly related to the rate of shearing strain are designated as nonnewtonian fluids. 17
18 18
19 19
20 BULK MODULUS A property that is commonly used to characterize compressibility is the bulk modulus. Defined as ; dp E = = dp υ dv dρ V ρ we conclude that liquids can be considered as incompressible for most practical engineering applications. 20
21 COMPRESSION & EXPANSION OF GAS When gases are compressed (or expanded) the relationship between pressure and density depends on the nature of the process. If the compression or expansion takes place under constant temperature conditions (isothermal process), then ; P = constant ρ If the compression or expansion is frictionless and no heat is exchanged with the surroundings (isentropic process), then ; P k ρ = constant 21
22 k is the ratio of the specific heat at constant pressure, c p, to the specific heat at constant volume, c v. k = c p c v 22
23 SURFACE TENSION The intensity of the molecular attraction per unit length along any line in the surface is called the surface tension. Designated by the Greek symbol, σ (sigma) Unit is N/m. The forces balance of halfcut spherical is shown as ; 2 2πRσ = PπR 23
24 The forces balance of capillary action is shown as ; 2 2π Rσ cosθ = ρghπr 24
25 Chapter 2  Pressure INTRODUCTION PRESSURE In this chapter we will consider an important class of problems in which the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. In both instances there will be no shearing stresses in the fluid, and the only forces that develop on the surfaces of the particles will be due to the pressure. The absence of shearing stresses greatly simplifies the analysis There are no shearing stresses present in a fluid at rest. 1
26 Chapter 2  Pressure PRESSURE The term pressure is used to indicate the normal force per unit area at a given point acting on a given plane within the fluid mass of interest. The equations of motion (Newton's second law, (F=ma) in the y and z directions are, respectively. y s y y a z y x s x p z x p F 2 sin δ δ δ ρ θ δ δ δ δ = = Σ z s z z a z y x z y x g s x p y x p F 2 2 cos δ δ δ ρ δ δ δ ρ θ δ δ δ δ = = Σ 2
27 Chapter 2  Pressure where p s, p y, and p z are the average pressures on the faces, γ and ρ are the fluid specific weight and density, respectively, and a y, a z the accelerations. Note that a pressure must be multiplied by an appropriate area to obtain the force generated by the pressure. Since we are really interested in what is happening at a point, we take the limit as δx, δy, and δz approach zero (while maintaining the angle θ), and it follows that p = p = y z p s The pressure at a point in a fluid at rest is independent of direction. We can conclude that the pressure at a point in a fluid at rest, or in motion, is independent of direction as long as there are no shearing stresses present. This important result is known as Pascal's law named in honor of Blaise Pascal ( ), 3
28 Chapter 2  Pressure BASIC EQUATION FOR PRESSURE FIELD For liquids or gases at rest the pressure gradient in the vertical direction at any point in a fluid depends only on the specific weight of the fluid at that point. dp dx = 0 dp dy = 0 dp dz = γ 4
29 Chapter 2  Pressure INCOMPRESSIBLE FLOW h = p 1 ρg p 2 5
30 Chapter 2  Pressure Pascal s Paradox 6
31 Chapter 2  Pressure STANDARD ATMOSPHERE 7
32 Chapter 2  Pressure MEASUREMENT OF PRESSURE The pressure at a point within a fluid mass will be designated as either an absolute pressure or a gage pressure. Absolute pressure is measured relative to a perfect vacuum (absolute zero pressure), whereas gage pressure is measured relative to the local atmospheric pressure. 8
33 Chapter 2  Pressure A barometer is used to measure atmospheric pressure. mercury barometer p = ρ gh + atm p vapor 9
34 Chapter 2  Pressure MANOMETRY A standard technique for measuring pressure involves the use of liquid columns in vertical or inclined tubes. Pressure measuring devices based on this technique are called manometers. The mercury barometer is an example of one type of manometer, but there are many other configurations possible, depending on the particular application. Three common types of manometers include the piezometer tube, the Utube manometer, and the inclinedtube manometer. 10
35 Chapter 2  Pressure PIEZOMETER TUBE p = ρ gh + p o p A = γ = 1h1 ρ1gh1 11
36 Chapter 2  Pressure UTUBE MANOMETER p A = ρ 2gh2 ρ1gh1 12
37 Chapter 2  Pressure INCLINEDTUBE MANOMETER p A p = ρ l B 2g 2 sinθ + ρ3gh3 ρ1gh1 13
38 Chapter 2  Pressure MECHANICAL AND ELECTRONIC PRESSURE DEVICES A Bourdon tube pressure gage uses a hollow, elastic, and curved tube to measure pressure. 14
39 PASCAL S LAW FOR PRESSURE AT A POINT By considering the equilibrium of a small fluid element in the form of a triangular prism surrounding a point in the fluid, as shown below, a relationship can be established between the pressure p x in the xdirection, p y in the ydirection and p s normal to any plane inclined at any angle to the horizontal at this point. If the fluid is at rest, p x will act at right angles to the plane ABFE, p y at right angles to CDEF and p s at right angle to ABCD. Since the fluid is at rest, there will be no shearing forces on the faces of the element and the element will not be accelerating. The sum of the forces in any direction must, therefore, be zero. 1
40 Considering the xdirection : Force due to p x = p x area ABFE = p x δyδz Component of force due to p s = = ( p areaabcd) sinθ s δy = psδsδz δs = p δyδz s δy sin θ = δs As p y has no compound in the xdirection, the element will be in equilibrium if : p δyδz + ( p δyδz) = 0 p x x = p s s 2
41 similarly in ydirection : Force due to p y = p y area CDEF = p y δxδz Component of force due to p s = = ( p areaabcd) cosθ s δx = psδsδz δs = p δxδz s δx cos θ = δs Weight of element = = specific weight Volume 1 = ρg δ xδyδz 2 As p x has no component in the ydirection, the element will be in equilibrium if ; p δ xδz + p δxδz) + ( ρg 1 δxδyδz ) = 0 y ( s 2 3
42 Since δx, δy and δz are all very small quantities, δxδyδz is negligible in comparison with the other two terms, and the equation reduces to p y = p s Now, we can conclude that ; p = p = x y p s 4
43 THE INFLUENCE OF HEIGHT IN PRESSURE For static equilibrium the sum of the horizontal forces must be zero : p1 A = p2a In mathematical term, if (x, y) is the horizontal plane: p p = 0 x and = 0 y 5
44 The sum of all vertical forces must be zero : ) ( z z g A p A p mg A p A p = = ρ We can conclude as : ( 1) z z g p p = ρ Thus, in any fluid under gravitational attraction, pressure decrease with increase of height z. 6
45 Chapter 3  Hydrostatic force on a submerged plane surface HYDROSTATIC FORCE ON A SUBMERGED PLANE SURFACE When a surface is submerged in a fluid, forces develop on the surface due to the fluid. The determination of these forces is important in the design of storage tanks, ships, dams, and other hydraulic structures. For fluids at rest we know that the force must be perpendicular to the surface since there are no shearing stresses present. We also know that the pressure will vary linearly with depth as shown in Figure 1 if the fluid is incompressible. Figure 1 1
46 Chapter 3  Hydrostatic force on a submerged plane surface The magnitude of the resultant fluid force is equal to the pressure acting at the centroid of the area multiplied by the total area. F R = ρ gh A (equation 1) c Figure 2 2
47 Chapter 3  Hydrostatic force on a submerged plane surface Note that the magnitude of the force is independent of the angle θ and depends only on the specific weight of the fluid, the total area, and the depth of the centroid of the area below the surface. In effect, Equation 1 indicates that the magnitude of the resultant force is equal to the pressure at the centroid of the area multiplied by the total area. Since all the differential forces that were summed to obtain F R are perpendicular to the surface, the resultant F R must also be perpendicular to the surface. The point through which the resultant force acts is called the center of pressure. 3
48 Chapter 3  Hydrostatic force on a submerged plane surface Coordinate for center of pressure (y R, x R ) : I xc y R = + yc A y c I xyc x R = + y A c x c 4
49 Chapter 3  Hydrostatic force on a submerged plane surface Centroidal coordinates and moments of inertia for some common areas are given in Figure 3. Figure 3 5
50 Chapter 3 Pressure prism for rectangular shape PRESSURE PRISM An informative and useful graphical interpretation can be made for the force developed by a fluid acting on a plane area. Consider the pressure distribution along a vertical wall of a tank of width b, which contains a liquid having a specific weight γ(=ρg). Since the pressure must vary linearly with depth, we can represent the variation as is shown in Figure 4, where the pressure is equal to zero at the upper surface and equal to γh(=ρgh) at the bottom. Figure 4 1
51 Chapter 3 Pressure prism for rectangular shape The base of this volume in pressurearea space is the plane surface of interest, and its altitude at each point is the pressure. This volume is called the pressure prism, and it is clear that the magnitude of the resultant force acting on the surface is equal to the volume of the pressure prism. The magnitude of the resultant fluid force is equal to the volume of the pressure prism and passes through its centroid 2
52 Chapter 3 Pressure prism for rectangular shape Specific values can be obtained by decomposing the pressure prism into two parts, ABDE and BCD, as shown in Figure 5. Thus, F R = F 1 + F 2 1 h FR = volume = ρ gh)( bh) = ρg( ) A 2 ( 2 The location of F R can be determined by summing moments about some convenient axis, such as one passing through A. In this instance F R y A = F1 y1 + F2 y2 Figure 5 3
53 Chapter 3 Pressure prism for rectangular shape Figure 6 For inclined plane surfaces the pressure prism can still be developed, and the cross section of the prism will generally be trapezoidal as is shown in Figure 6. The use of pressure prisms for determining the force on submerged plane areas is convenient if the area is rectangular so the volume and centroid can be easily determined. 4
54 Chapter 3 Pressure prism for rectangular shape However, for other nonrectangular shapes, integration would generally be needed to determine the volume and centroid. In these circumstances it is more convenient to use the equations developed in the previous section, in which the necessary integrations have been made and the results presented in a convenient and compact form that is applicable to submerged plane areas of any shape. 5
55 Chapter 3 Pressure prism for rectangular shape We note that in this case the force on one side of the wall now consists of F R as a result of the hydrostatic pressure distribution, plus the contribution of the atmospheric pressure, p atm A, where A is the area of the surface. However, if we are going to include the effect of atmospheric pressure on one side of the wall we must realize that this same pressure acts on the outside surface (assuming it is exposed to the atmosphere), so that an equal and opposite force will be developed as illustrated in the figure 7. Thus, we conclude that the resultant fluid force on the surface is that due only to the gage pressure contribution of the liquid in contact with the surface the atmospheric pressure does not contribute to this resultant. Figure 7 6
56 HYDROSTATIC FORCES ON A SUBMERGED CURVED PLANE The equations developed in previous lesson for the magnitude and location of the resultant force acting on a submerged surface only apply to plane surfaces. However, many surfaces of interest (such as those associated with dams, pipes, and tanks) are nonplanar. We will consider the equilibrium of the fluid volume enclosed by the curved surface of interest and the horizontal and vertical projections of this surface. 1
57 Horizontal Force ; F H = ρ gh c A Vertical Force ; F V = ρgv Resultant Force ; F = F + R 2 H F 2 V 2
58 Example 1 The 6mdiameter drainage conduit of Figure 1 is half full of water at rest. Determine the magnitude and line of action of the resultant force that the water exerts on a 1m length of the curved section BC of the conduit wall. Figure 1 3
59 Example 2 A 4mlong curved gate is located in the side of a reservoir containing water as shown in Figure 2. Determine the magnitude of the horizontal and vertical components of the force of the water on the gate. Will this force pass through point A? Explain. Figure 2 4
60 Example 3 Determine the magnitude of the horizontal and vertical components of the force (per unit length) of the water on the concrete seawall of Figure 3. Figure 3 5
61 Chapter 4 Buoyancy, Floatation and Stability BUOYANCY, FLOATATION AND STABILITY Archimedes Principle When a stationary body is completely submerged in a fluid, or floating so that it is only partially submerged, the resultant fluid force acting on the body is called the buoyant force. Note that the forces F 1, F 2, F 3, and F 4 are simply the forces exerted on the plane surfaces, W(=mg) is the weight of the shaded fluid volume, and F B is the force the body is exerting on the fluid. The forces on the vertical surfaces, such as F 3 and F 4, are all equal and cancel, so the equilibrium equation of interest is in the z direction and can be expressed as F F mg F B = 2 1 If the specific weight of the fluid is constant, then ; F F = ρ g h h ) A (1) 2 1 ( 2 1 where A is the horizontal area of the upper (or lower) surface, and Equation (1) can be written as ; = ρ g h h ) A g ( h h ) A V F B [ ] ( 2 1 ρ 2 1 1
62 Chapter 4 Buoyancy, Floatation and Stability Simplifying, we arrive at the desired expression for the buoyant force ; F B = ρgv Figure 1 2
63 Chapter 4 Buoyancy, Floatation and Stability Archimedes' principle states that the buoyant force has a magnitude equal to the weight of the fluid displaced by the body and is directed vertically upward. Thus, we conclude that the buoyant force passes through the centroid of the displaced volume as shown in Figure 1(c). The point through which the buoyant force acts is called the center of buoyancy. 3
64 Chapter 4 Buoyancy, Floatation and Stability Example A spherical buoy has a diameter of 1.5 m, weighs 8.50 kn, and is anchored to the seafloor with a cable as is shown in Figure 2(a). Although the buoy normally floats on the surface, at certain times the water depth increases so that the buoy is completely immersed as illustrated. For this condition what is the tension of the cable? Figure 2 4
65 Chapter 4 Buoyancy, Floatation and Stability Stability As illustrated by the Figure 3, a body is said to be in a stable equilibrium position if, when displaced, it returns to its equilibrium position. Conversely, it is in an unstable equilibrium position if, when displaced (even slightly), it moves to a new equilibrium position. Stability considerations are particularly important for submerged or floating bodies since the centers of buoyancy and gravity do not necessarily coincide. Figure 3 5
66 Chapter 4 Buoyancy, Floatation and Stability A small rotation can result in either a restoring or overturning couple. For example, for the completely submerged body shown in Figure 4, which has a center of gravity below the center of buoyancy, a rotation from its equilibrium position will create a restoring couple formed by the weight, W, and the buoyant force, F B, which causes the body to rotate back to its original position. Thus, for this configuration the body is stable. It is to be noted that as long as the center of gravity falls below the center of buoyancy, this will always be true; that is, the body is in a stable equilibrium position with respect to small rotations. Figure 4 6
67 Chapter 4 Buoyancy, Floatation and Stability However, as is illustrated in Figure 5, if the center of gravity of the completely submerged body is above the center of buoyancy, the resulting couple formed by the weight and the buoyant force will cause the body to overturn and move to a new equilibrium position. Thus, a completely submerged body with its center of gravity above its center of buoyancy is in an unstable equilibrium position. Figure 5 7
68 Chapter 4 Buoyancy, Floatation and Stability For floating bodies the stability problem is more complicated, since as the body rotates the location of the center of buoyancy (which passes through the centroid of the displaced volume) may change. As is shown in Figure 6, a floating body such as a barge that rides low in the water can be stable even though the center of gravity lies above the center of buoyancy. This is true since as the body rotates the buoyant force, F B, shifts to pass through the centroid of the newly formed displaced volume and, as illustrated, combines with the weight, W, to form a couple which will cause the body to return to its original equilibrium position. Figure 6 8
69 Chapter 4 Buoyancy, Floatation and Stability However, for the relatively tall, slender body shown in Figure 7, a small rotational displacement can cause the buoyant force and the weight to form an overturning couple as illustrated. Figure 7 9
CHARACTERISTIC 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 informationFluid Mechanics61341
AnNajah National University College of Engineering Fluid Mechanics61341 Chapter [2] Fluid Statics 1 Fluid Mechanics2nd Semester 2010 [2] Fluid Statics Fluid Statics Problems Fluid statics refers to
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 informationPressure in stationary and moving fluid Lab Lab On On Chip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: 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 informationFluid Mechanics Discussion. Prepared By: Dr.Khalil M. AlAstal Eng.Ahmed S. AlAgha Eng.Ruba M. Awad
Discussion Prepared By: Dr.Khalil M. AlAstal Eng.Ahmed S. AlAgha Eng.Ruba M. Awad 20142015 Chapter (1) Fluids and their Properties Fluids and their Properties Fluids (Liquids or gases) which a substance
More informationPressure in stationary and moving fluid. LabOnChip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: 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 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 informationFluid Mechanics. du dy
FLUID MECHANICS Technical English  I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's
More informationstorage tank, or the hull of a ship at rest, is subjected to fluid pressure distributed over its surface.
Hydrostatic Forces on Submerged Plane Surfaces Hydrostatic forces mean forces exerted by fluid at rest.  A plate exposed to a liquid, such as a gate valve in a dam, the wall of a liquid storage tank,
More informationFluid Mechanics Introduction
Fluid Mechanics Introduction Fluid mechanics study the fluid under all conditions of rest and motion. Its approach is analytical, mathematical, and empirical (experimental and observation). Fluid can be
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 informationChapter 1 INTRODUCTION
Chapter 1 INTRODUCTION 11 The Fluid. 12 Dimensions. 13 Units. 14 Fluid Properties. 1 11 The Fluid: It is the substance that deforms continuously when subjected to a shear stress. Matter Solid Fluid
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 informationChapter 9: Solids and Fluids
Chapter 9: Solids and Fluids State of matters: Solid, Liquid, Gas and Plasma. Solids Has definite volume and shape Can be crystalline or amorphous Molecules are held in specific locations by electrical
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 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 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 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 informationDIMENSIONS AND UNITS
DIMENSIONS AND UNITS A dimension is the measure by which a physical variable is expressed quantitatively. A unit is a particular way of attaching a number to the quantitative dimension. Primary Dimension
More informationSteven Burian Civil & Environmental Engineering September 25, 2013
Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session
More informationCHAPTER 13. Liquids FLUIDS FLUIDS. Gases. Density! Bulk modulus! Compressibility. To begin with... some important definitions...
CHAPTER 13 FLUIDS Density! Bulk modulus! Compressibility Pressure in a fluid! Hydraulic lift! Hydrostatic paradox Measurement of pressure! Manometers and barometers Buoyancy and Archimedes Principle! Upthrust!
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 informationWe may have a general idea that a solid is hard and a fluid is soft. This is not satisfactory from
Chapter 1. Introduction 1.1 Some Characteristics of Fluids We may have a general idea that a solid is hard and a fluid is soft. This is not satisfactory from scientific or engineering point of view. In
More informations and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I
Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum
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 informationFluid Mechanics Abdusselam Altunkaynak
Fluid Mechanics Abdusselam Altunkaynak 1. Unit systems 1.1 Introduction Natural events are independent on units. The unit to be used in a certain variable is related to the advantage that we get from it.
More informationTOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant ForcesArchimedes Principle
Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant ForcesArchimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation
More informationME3250 Fluid Dynamics I
ME3250 Fluid Dynamics I Section I, Fall 2012 Instructor: Prof. Zhuyin Ren Department of Mechanical Engineering University of Connecticut Course Information Website: http://www.engr.uconn.edu/~rzr11001/me3250_f12/
More informationMULTIPLECHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)
MULTIPLECHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.
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 informationPart II Fundamentals of Fluid Mechanics By Munson, Young, and Okiishi
Part II Fundamentals of Fluid Mechanics By Munson, Young, and Okiishi WHAT we will learn I. Characterization of Fluids  What is the fluid? (Physical properties of Fluid) II. Behavior of fluids  Fluid
More informationChapter 1 Fluid Proper2es. CE Fluid Mechanics Diogo Bolster
Chapter 1 Fluid Proper2es CE30460  Fluid Mechanics Diogo Bolster What is a Fluid? A substance that deforms con2nuously when acted on by a shearing stress A solid will deform to a certain point for a given
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 nonnewtonian fluids, Bernoulli equation, Macroscopic friction factors, energy balance, dimensional analysis,
More informationLiquids CHAPTER 13 FLUIDS FLUIDS. Gases. Density! Bulk modulus! Compressibility. To begin with... some important definitions...
CHAPTER 13 FLUIDS FLUIDS Liquids Gases Density! Bulk modulus! Compressibility Pressure in a fluid! Hydraulic lift! Hydrostatic paradox Measurement of pressure! Manometers and barometers Buoyancy and Archimedes
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 informationThermodynamics1. S. M. Hosseini Sarvari Chapter 1 Introduction & Basic Concepts
Mechanical Engineering Dept. Shahid Bahonar University of Kerman Thermodynamics1 S. M. Hosseini Sarvari Chapter 1 Introduction & Basic Concepts Mechanical Engineering Dept. Shahid Bahonar University of
More informationMEB41 Lab 1: Hydrostatics. Experimental Procedures
MEB41 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 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 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 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 information1 Fluid Statics. 1.1 Fluid Properties. Fluid
1 Fluid Statics 1.1 Fluid Properties Fluid A fluid is a substance, which deforms when subjected to a force. A fluid can offer no permanent resistance to any force causing change of shape. Fluid flow under
More informationCHAPTER 1 Fluids and their Properties
FLUID MECHANICS Gaza CHAPTER 1 Fluids and their Properties Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Define the nature of a fluid. Show where fluid mechanics concepts are common with those
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 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 informationMECHANICAL PROPERTIES OF FLUIDS:
Important Definitions: MECHANICAL PROPERTIES OF FLUIDS: Fluid: A substance that can flow is called Fluid Both liquids and gases are fluids Pressure: The normal force acting per unit area of a surface is
More informationNonNewtonian fluids is the fluids in which shear stress is not directly proportional to deformation rate, such as toothpaste,
CHAPTER1: Basic Definitions, Zeroth, First, and Second Laws of Thermodynamics 1.1. Definitions What does thermodynamic mean? It is a Greeks word which means a motion of the heat. Water is a liquid substance
More informationMULTIPLECHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)
Test Midterm 1 F2013 MULTIPLECHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct nswer in the Questions Below.) 1. The absolute viscosity µ of a fluid is primarily a function
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 informationENGR 292 Fluids and Thermodynamics
ENGR 292 Fluids and Thermodynamics Scott Li, Ph.D., P.Eng. Mechanical Engineering Technology Camosun College Jan.13, 2017 Review of Last Class Course Outline Class Information Contact Information, Website
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 informationFluid Mechanics. If deformation is small, the stress in a body is proportional to the corresponding
Fluid Mechanics HOOKE'S LAW If deformation is small, the stress in a body is proportional to the corresponding strain. In the elasticity limit stress and strain Stress/strain = Const. = Modulus of elasticity.
More informationFluid Mechanics61341
AnNajah National University College of Engineering Fluid Mechanics61341 Chapter [1] Fundamentals 1 The Book (Elementary Fluid Mechanics by Street, Watters and Vennard) Each chapter includes: Concepts
More informationStatic Forces on SurfacesBuoyancy. Fluid Mechanics. There are two cases: Case I: if the fluid is above the curved surface:
Force on a Curved Surface due to Hydrostatic Pressure If the surface is curved, the forces on each element of the surface will not be parallel (normal to the surface at each point) and must be combined
More informationReview of Fluid Mechanics
Chapter 3 Review of Fluid Mechanics 3.1 Units and Basic Definitions Newton s Second law forms the basis of all units of measurement. For a particle of mass m subjected to a resultant force F the law may
More informationFE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)
Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.
More informationChapter 15: Fluid Mechanics Dynamics Using Pascal s Law = F 1 = F 2 2 = F 2 A 2
Lecture 24: Archimedes Principle and Bernoulli s Law 1 Chapter 15: Fluid Mechanics Dynamics Using Pascal s Law Example 15.1 The hydraulic lift A hydraulic lift consists of a small diameter piston of radius
More informationFluid Mechanics. The atmosphere is a fluid!
Fluid Mechanics The atmosphere is a fluid! Some definitions A fluid is any substance which can flow Liquids, gases, and plasmas Fluid statics studies fluids in equilibrium Density, pressure, buoyancy Fluid
More informationThe online of midtermtests of Fluid Mechanics 1
The online of midtermtests of Fluid Mechanics 1 1) The information on a can of pop indicates that the can contains 460 ml. The mass of a full can of pop is 3.75 lbm while an empty can weights 80.5 lbf.
More informationM E 320 Professor John M. Cimbala Lecture 05
M E 320 Professor John M. Cimbala Lecture 05 Today, we will: Continue Chapter 3 Pressure and Fluid Statics Discuss applications of fluid statics (barometers and Utube manometers) Do some example problems
More informationStates of matter. Density high > high >> low (pressure dependent)
Fluids States of matter Solids Fluids crystalline amorphous liquids gasses Interatomic forces strong > strong >> very weak Density high > high >> low (pressure dependent) Density is an important material
More informationP = 1 3 (σ xx + σ yy + σ zz ) = F A. It is created by the bombardment of the surface by molecules of fluid.
CEE 3310 Thermodynamic Properties, Aug. 27, 2010 11 1.4 Review A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container
More informationINTRODUCTION AND BASIC CONCEPTS. Chapter 1. Mehmet Kanoglu. Thermodynamics: An Engineering Approach, 6 th Edition. Yunus A. Cengel, Michael A.
Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGrawHill, 2008 Chapter 1 INTRODUCTION AND BASIC CONCEPTS Mehmet Kanoglu Copyright The McGrawHill Companies, Inc.
More informationFormulae that you may or may not find useful. E v = V. dy dx = v u. y cp y = I xc/a y. Volume of an entire sphere = 4πr3 = πd3
CE30 Test 1 Solution Key Date: 26 Sept. 2017 COVER PAGE Write your name on each sheet of paper that you hand in. Read all questions very carefully. If the problem statement is not clear, you should ask
More informationHYDRAULICS STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL HYDRAULICS
1 STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL Syllabus Hydraulics ( Fluid Mechanics ) Fluid properties, hydrostatics, measurements of flow, Bernoulli's theorem and its application, flow
More informationFluid Dynamics Exam #1: Introduction, fluid statics, and the Bernoulli equation March 2, 2016, 7:00 p.m. 8:40 p.m. in CE 118
CVEN 311501 (Socolofsky) Fluid Dynamics Exam #1: Introduction, fluid statics, and the Bernoulli equation March 2, 2016, 7:00 p.m. 8:40 p.m. in CE 118 Name: : UIN: : Instructions: Fill in your name and
More informationThermodynamics INTRODUCTION AND BASIC CONCEPTS. Copyright The McGrawHill Companies, Inc. Permission required for reproduction or display.
Thermodynamics INTRODUCTION AND BASIC CONCEPTS Copyright The McGrawHill Companies, Inc. Permission required for reproduction or display. THERMODYNAMICS AND ENERGY Thermodynamics: The science of energy.
More informationFRIDAYS 14:00 to 15:40. FRIDAYS 16:10 to 17:50
Brad Peterson, P.E. FRIDAYS 14:00 to 15:40 FRIDAYS 16:10 to 17:50 BRAD PETERSON, P.E., PTOE Brigham Young University, 1975 Highway and Bridge Design Montana, Utah, Idaho, Wyoming Worked 27 Years in Helena,
More informationMECHANICAL PROPERTIES OF FLUIDS
CHAPTER10 MECHANICAL PROPERTIES OF FLUIDS QUESTIONS 1 marks questions 1. What are fluids? 2. How are fluids different from solids? 3. Define thrust of a liquid. 4. Define liquid pressure. 5. Is pressure
More informationCHAPTER 2 Fluid Statics
Chapter / Fluid Statics CHPTER Fluid Statics FEtype 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 informationPhy 212: General Physics II. Daniel Bernoulli ( )
Phy 1: General Physics II Chapter 14: Fluids Lecture Notes Daniel Bernoulli (1700178) Swiss merchant, doctor & mathematician Worked on: Vibrating strings Ocean tides Kinetic theory Demonstrated that as
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 Testbank By David Admiraal
Fluid Mechanics Testbank By David Admiraal This testbank was created for an introductory fluid mechanics class. The primary intentions of the testbank are to help students improve their performance on
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 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 informationPetroleum Engineering Dept. Fluid Mechanics Second Stage Dr. Ahmed K. Alshara
Continents Chapter 1. Fluid Mechanics Properties of fluids Density, specific gravity, specific volume and Viscosity Newtonian and non Newtonian fluids Surface tension Compressibility Pressure Cavitations
More informationCivil 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 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 informationFluid Properties and Units
Fluid Properties and Units CVEN 311 Continuum Continuum All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion. However, in dealing with fluidflow flow relations
More informationCHAPTER 28 PRESSURE IN FLUIDS
CHAPTER 8 PRESSURE IN FLUIDS EXERCISE 18, Page 81 1. A force of 80 N is applied to a piston of a hydraulic system of crosssectional area 0.010 m. Determine the pressure produced by the piston in the hydraulic
More informationChapter 14  Fluids. Archimedes, On Floating Bodies. David J. Starling Penn State Hazleton PHYS 213. Chapter 14  Fluids. Objectives (Ch 14)
Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced. Archimedes, On Floating Bodies David J.
More informationEnergy: The ability to cause changes. thermodynamics stems from therme (heat) and dynamis (power).
Energy: The ability to cause changes. thermodynamics stems from therme (heat) and dynamis (power). Thermodynamics: The science of energy. Conservation of energy principle: During an interaction, energy
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) 8000 A 679 B or A/B 346 C or B/C 933 marginal 98 D Physics 07: Lecture 8,
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 informationUniversity of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING. ME Fluid Mechanics Lecture notes. Chapter 1
University of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING ME 311  Fluid Mechanics Lecture notes Chapter 1 Introduction and fluid properties Prepared by : Dr. N. Ait Messaoudene Based
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 informationLecture 8 Equilibrium and Elasticity
Lecture 8 Equilibrium and Elasticity July 19 EQUILIBRIUM AND ELASTICITY CHAPTER 12 Give a sharp blow one end of a stick on the table. Find center of percussion. Baseball bat center of percussion Equilibrium
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 informationA Physical Introduction to Fluid Mechanics. Study Guide and Practice Problems Spring 2017
A Physical Introduction to Fluid Mechanics Study Guide and Practice Problems Spring 2017 A Physical Introduction to Fluid Mechanics Study Guide and Practice Problems Spring 2017 by Alexander J. Smits
More informationClass Notes Fall 2014
57:020 Fluid Mechanics Class Notes Fall 2014 Prepared by: Professor Fred Stern Typed by: Stephanie Schrader (Fall 1999) Corrected by: Jun Shao (Fall 2003, Fall 2005) Corrected by: Jun Shao, Tao Xing (Fall
More informationFluid Mechanics. Chapter 14. Modified by P. Lam 6_7_2012
Chapter 14 Fluid Mechanics PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 6_7_2012 Goals for Chapter 14 To study
More informationDimensions represent classes of units we use to describe a physical quantity. Most fluid problems involve four primary dimensions
BEE 5330 Fluids FE Review, Feb 24, 2010 1 A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container will form a free
More informationME3560 Tentative Schedule Fall 2018
ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read
More information10  FLUID MECHANICS Page 1
0  FLUID MECHANICS Page Introduction Fluid is a matter in a state which can flow. Liquids, gases, molten metal and tar are examples of fluids. Fluid mechanics is studied in two parts: ( i ) Fluid statics
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 informationME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 4. (Buoyancy and Viscosity of water)
ME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 4 (Buoyancy and Viscosity of water) 16. BUOYANCY Whenever an object is floating in a fluid or when it is completely submerged in
More informationCivil Engineering Hydraulics. Pressure and Fluid Statics
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
More informationch01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows
ch01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows ch01.qxd 8/4/04 2:33 PM Page 3 Introduction 1 Summary The introduction chapter reviews briefly the basic fluid properties
More informationChapter 1 Fluid Characteristics
Chapter 1 Fluid Characteristics 1.1 Introduction 1.1.1 Phases Solid increasing increasing spacing and intermolecular liquid latitude of cohesive Fluid gas (vapor) molecular force plasma motion 1.1.2 Fluidity
More informationME3560 Tentative Schedule Spring 2019
ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to
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 information