Unit C1: List of Subjects


 Anastasia Morton
 1 years ago
 Views:
Transcription
1 Unit C: List of Subjects The elocity Field The Acceleration Field The Material or Substantial Derivative Steady Flow and Streamlines Fluid Particle in a Flow Field F=ma along a Streamline Bernoulli s Equation F=ma across a Streamline Basic Equations of Fluid
2 Page of Unit C The elocity Field u x, y, z, tˆi v x, y, z, tˆj w x, y, z, t kˆ The infinitesimal particles of a fluid are tightly packed together continuum assumption At a given instant in time, a description of any fluid property such as density, pressure, velocity, and acceleration may be given as a function of the fluid s location in 3D space This representation of fluid parameters as functions of the spatial coordinates is called a field representation of the flow The velocity field in 3D Cartesian coordinates: u x, y, z, tˆi v x, y, z, tˆj w x, y, z, t kˆ The Convection of a Flow Field The presence of the velocity field is often called the CONECTION of the flow field: the flow field properties mass, momentum, energy, etc. are CONECTED transported from one location to another, within the flow field.
3 Page of Unit C The Acceleration Field a A t d dt A t A x y z Taking the time derivative of velocity using the chain rule: da A A dxa A dya A dz A a A t dt t x dt y dt z dt The particle velocity components are given: u dx dt v dy dt w dz dt A A A A A A Hence, the acceleration of particle A is: A A A A aa t ua va wa t x y z A dx dt A A dy dt A A dz dt A
4 Unit C Page 3 of The Material or Substantial Derivative u v w t x y z a a t Dt D k j i ˆ ˆ ˆ z y x z w y v x u t Dt D The shorthand notation called material or substantial derivative: Using the gradient or del operator: Operator definition Dot Product: Dt D a z w y v x u t Dt D where, t Dt D k j i ˆ ˆ ˆ z y x where, The acceleration field: Components in x, y, z coordinates: z w y v x u t t a z u w y u v x u u t u a x z v w y v v x v u t v a y z w w y w v x w u t w a z UNIT D UNIT D SLIDE SLIDE 5 The Material Derivative The Material Derivative 4 4 The shorthand notation called material or substantial derivative: Using the gradient or del operator: Operator definition Dot Product: Hence, the acceleration field is: Dt D a z w y v x u t Dt D where, t Dt D k j i ˆ ˆ ˆ z y x z w y v x u a t Dt D where,
5 Page 4 of Unit C Steady Flow and Streamlines sˆ a a ˆ ˆ ˆ ˆ ss ann s n s If the velocity does not change with time at a given location in the flow field: Steady Flow For steady flows, each particle slides along its path and its velocity vector is everywhere tangent to the path the lines that are tangent to the velocity vectors throughout the flow field are called: streamlines Let us define a D coordinate system that is attached to and moving with a fluid particle along a streamline: the Streamline Coordinate system This is the coordinate system, defined at a specific location on a streamline. If a particle is moving steadily along a streamline, the streamline coordinate system is the coordinate that is attached to this particle and moving together with this particle. The direction along the streamline tangential direction: ŝ The direction across the streamline normal direction: ˆn The normal direction is taken toward the center of radius of curvature.
6 Page 5 of Unit C Fluid Particle in a Flow Field Unit C Consider the freebody diagram of a small fluid particle in a flow field along a streamline: nd Streamlines The important forces are those due to pressure and gravity in aerodynamics, gravity forces are often ignored a this is steady flow, so acceleration is only convective sˆ a a ˆ ˆ ˆ ˆ ss ann s n s as Tangential Acceleration s a ˆ ˆ aˆ n ˆ ss ann s ncentrifugal Acceleration s
7 Page 6 of Unit C F=ma along a Streamline sin p s s a s Consider a small fluid particle of size: s n Apply Newton s Second Law along a streamline: p sin s s Equation of Motion a s Euler s Equation A change in fluid particle speed is accomplished by the appropriate combination of pressure gradient and particle weight along the streamline Textbook Munson, Young, and Okiishi, page 97 In tangential ŝ direction, F = ma becomes, W sin p ps n y p ps n y mas W sin ps ps n y mas note that: ps ps p Dividing by the volume of the particle s n y and taking the limit: s 0, n 0, y 0, also note that W olume specific weight p sin lim as sin p as s0 s s
8 Page 7 of Unit C Bernoulli s Equation p z constant along a streamline Equation of motion can be rearranged p sin a s s s Along the streamline: p p p dp dp ds dn dn 0 s n s ds dz d d Also, sin ds s ds ds Hence, along a streamline: dz dp d ds ds ds dp d dz 0 dp Divide by the density, d gdz 0 Assuming constant acceleration of gravity: dp gz constant With additional assumption of constant density incompressible fluid: p z constant along a streamline Bernoulli s Equation
9 Page 8 of Unit C Bernoulli s Equation Static Pressure, Dynamic Pressure, Hydrostatic Pressure Each term in the Bernoulli s equation can be interpreted as a form of pressure p z constant along a streamline Static Pressure Dynamic Pressure Hydrostatic Pressure Static Pressure: actual thermodynamic pressure of the fluid as it flows Dynamic Pressure: pressure due to the energy stored in moving fluid Hydrostatic Pressure: pressure due to gravitational effects Recall, UNIT B Bernoulli s equation in conservation of pressure form: p z constant Static Pressure + Dynamic Pressure + Hydrostatic Pressure = Total Pressure Bernoulli s equation in conservation of energy form: p gz constant Flow Energy + Kinetic Energy + Potential Energy = Total Energy Bernoulli s equation in conservation of head form: p z constant 3 g Static Head + Dynamic Head + Head = Total Head
10 Page 9 of EXAMPLE 3. Textbook Munson, Young, and Okiishi, page 0 Unit C The Bernoulli Equation Applying the Bernoulli s equation along the same streamline: between point and, p z p z For aerodynamics, usually the hydrostatic pressure is not considered z z. Thus, p p Note that: 0 equal to the velocity of bicycle itself: called the freestream 0 velocity is zero: called the stagnation point Therefore, p p 0
11 Page 0 of Unit C F=ma across a Streamline dz dn p n Consider a small fluid particle of size: s n Apply Newton s Second Law Normal to a streamline: dz dn p n Equation of Motion A change in the direction of flow of a fluid particle is accomplished by the appropriate combination of pressure gradient and particle weight normal to the streamline Textbook Munson, Young, and Okiishi, page 97 This is Euler s equation across the streamline the direction normal: ˆn
12 Page of Class Example Problem Related Subjects... F=ma across a Streamline Unit C Unit CC Streamline s a Streamline Unit CC Applying the equation of motion across the streamline: dz dz p p dn dn n n z where, dz p dz dn, p dp dn, nand = 6 n n dn dp Hence, dn 6 n Integrating this equation yields: n dn n n n n dp ln 6 n 0 dn dn 6 dn dn 6 n 0 n n n dn ln 6 n ln 6 n ln 6 0 p p n 6 n 6 0 ln 6 ln 6 n ln 6 6 n p p n ln 6 n For point : p 40 kpa and n m => p.0 kpa For point 3: p 40 kpa and n m => p3 0. kpa
13 Page of Unit C Basic Equations of Fluid p z constant along a streamline p dnz constant across the streamline Normal to a streamline: dz p dn n Assuming constant acceleration of gravity: dp dn gz constant With additional assumption of constant density incompressible fluid: p dn z constant across the streamline This is Bernoulli s equation across the streamline the direction normal: ˆn The following assumptions were made: The flow is steady The fluid is inviscid The fluid is incompressible A violation of one or more of the above assumptions is a common cause for obtaining an incorrect match between the real world and solutions obtained by use of these equations
14 ES06 Fluid Mechanics Unit C: List of Subjects Static and Dynamic Pressure Stagnation Point PitotStatic Tube Directional Finding PitotStatic Tube
15 Page of 7 Unit C Static and Dynamic Pressure Each term in the Bernoulli s equation can be interpreted as a form of pressure If we apply Bernoulli s equation between points and, assuming = 0 and z = z p p Stagnation Pressure Static Pressure Dynamic Pressure If elevation effects are neglected, stagnation pressure is the largest pressure obtainable along a given streamlinecalled, the total pressure
16 Page of 7 Unit C Stagnation Point A point in a flow where the velocity is zero, where any streamline touches a solid surface at an angle: stagnation point p z pt constant along a streamline Bernoulli s equation Textbook Munson, Young, and Okiishi, page 08 NOTE: for aerodynamics, usually the hydrostatic pressure term can be ignored: p p T constant along a streamline PitotStatic Probe for Airspeed Measurement At the stagnation point, the flow is decelerated to zero speed. This deceleration process increases the pressure static pressure => total pressure by converting kinetic energy dynamic pressure. Hence, the total pressure can be considered as: Total Pressure = Static Pressure + Dynamic Pressure. This total pressure can be sensed at the tip stagnation point of a special device, called the PitotStatic probe. PitotStatic probe is also equipped with a side port, called the static port senses the static pressure of the flow. By taking the difference between total pressure and static pressure, the Pitot Static probe can be used to determine the airspeed of the flow.
17 Page 3 of 7 Unit C PitotStatic Tube Note that: p p3 center tube and p p4 outer tube The center tube measures the stagnation pressure at its open tip p 3 p The outer tube is made with several small holes so that they measure the static pressure p p p 4 Combining these two equations: p 3 p 4 p 3 p4 / Textbook Munson, Young, and Okiishi, page 09
18 Page 4 of 7 Unit C PitotStatic Tube PitotStatic Probe Pitotstatic probe can determine airspeed, by sensing the pressure difference between total and static pressures p pt ps: Usually this can be measured by differential Utube manometers. Then the airspeed can be determined by: p
19 Page 5 of 7 Directional Finding PitotStatic Tube Unit C p p / Three pressure taps are drilled into a small circular cylinder, fitted with small tube, and connected to three pressure transducers The side holes are located at a specific angle = 9.5 The speed is then obtained from: p p / Preview of aerodynamics Based on the ideal flow analysis aero, at the angle of β = 30º, the pressure on the surface of the circular cylinder becomes equal to the freestream static pressure hence, static ports can be established by making the holes at these locations. Some Important Points for PitotStatic Probe Design An accurate measurement of static pressure requires that none of the fluid s kinetic energy be converted into a pressure rise at the point of measurement This requires a smooth hole with absolutely no burrs or imperfections Textbook Munson, Young, and Okiishi, page It is important that the pressure taps be properly located to ensure that the pressure measured is actually the static pressure Textbook Munson, Young, and Okiishi, page
20 Page 6 of 7 EXAMPLE 3.6 Textbook Munson, Young, and Okiishi, page 0 Unit C PitotStatic Tube a The pressure at point far ahead of the airplane From the textbook table C. in Appendix C page 764: 3 3 p 0.08 lb/in psi slugs/ft b The pressure at the stagnation point on the nose of the airplane, point Applying Bernoulli s equation assuming steady, incompressible, and inviscid flow with no elevation change: p p 88 ft/s where, 00 mph ft/s 60 mph and 0 stagnation point 3 3 in.7560 slugs/ft ft/s Hence, p p 0.08 lb/in ft =, lb/ft 3 = 0.39 psi c The pressure difference indicated by a Pitotstatic probe attached to the fuselage The pitotstatic tube measures the difference between freestream static pressure p and stagnation pressure p : p p 0.39 psi 0.08 psi = 0.3 psi
21 Page 7 of 7 Class Example Problem Related Subjects... PitotStatic Tube Unit C Pitotstatic tube measures the difference between static and stagnation pressure: At point, the tip of the probe: p p3 stagnation pressure At point, the static port of the probe: p p4 patm 0 gage pressure Applying Bernoulli s equation yields: p3 p4 or, p3 p4 For indicated also called, the equivalent airspeed e : SeaLevel p3 p4 e eqn. For true airspeed true : 0,000 fttrue p3 p4 eqn. Combining eqns. & for the same pressure difference p3 p4: SeaLevel 0,000 ft e true 3 3 SeaLevel slugs/ft Therefore, true e 0 knots = knots 3 3 0,000 ft.67 0 slugs/ft
22 ES06 Fluid Mechanics Unit C3: List of Subjects Bernoulli s Equation Free Jets Confined Flows Cavitation Flowrate Measurement
23 Page of 9 Unit C3 Bernoulli s Equation p z p z Between any two points, and, on a streamline in steady, inviscid, and incompressible flow ideal flow: p Free Jets z Confined Flows Flowrate Measurement p z Bernoulli s Equation in 3 Forms p z p z Pressure form p p gz gz Energy per unit mass form p p z z g g Head form
24 Page of 9 Unit C3 Free Jets p p4 0 Between and : h h gh g h H p p4 Textbook Munson, Young, and Okiishi, page 0 Free Jet elocity The magnitude of free jet velocity depends solely on the depth of liquid, relative to the location of the free jet flow. This can be seen as a velocity of falling baseball conversion of potential energy into kinetic energy.
25 Page 3 of 9 Unit C3 Confined Flows Nozzles and pipes of variable diameter for which the fluid velocity changes because the flow area is different from one section to another Need to use the concept of conservation of mass the continuity equation along with the Bernoulli s equation The rate at which the fluid flows into the volume must equal the rate at which it flows out of the volume otherwise, mass would not be conserved The mass flowrate: The volume flowrate: m Q Q To conserve mass, the inflow rate must be equal to the outflow rate: m m The continuity equation: If the density is constant incompressible fluid: A A Q Q A A A
26 Page 4 of 9 EXAMPLE 3.7 Textbook Munson, Young, and Okiishi, page 5 Unit C3 Flow from a Tank Gravity Assuming a steady, incompressible, and inviscid flow, the Bernoulli s equation can be applied between points and : p z p z where, p p patm 0 gage pressure with z h and z 0 Hence, h => gh eqn. In order to maintain constant water depth h.0 m, the flowrate in and out of the tank must be equal: Q Q. Since the flowrate is defined as: Q A, A A this is called, the conservation of mass. d Hence, D d => eqn. 4 4 D Combining eqns. & yields: gh 9.8 m/s.0 m 4 4 = 6.6 m/s dd 0. m m Q A d 0.0 m 6.6 m/s = m 3 /s 4 4
27 Page 5 of 9 Class Example Problem Related Subjects... Confined Flows Unit C3 Assuming a steady, incompressible, and inviscid flow, the Bernoulli s equation can be applied between points 0 and 4 as: 0 4 p0 z0 p4 z4 where, p0 p4 patm 0 gage pressure with z0 5 ft and z4 0. Also, Therefore, z0 => 4 z0 gz0 3. ft/s 5 ft = 7.94 ft/s The flowrate can be determined as: Q A ft 7.94 ft/s = 0.4 ft 3 /s 4 Pressure at point can be determined by applying the Bernoulli s equation as: 4 p z p4 z4 where, p4 patm 0 gage pressure with z 8 ft and z4 0. Also, Q constant conservation of mass, so: 4 since A A4 3 Hence, p z 6.4 lb/ft 8 ft = 499 lb/ft gage pressure 3 Similarly, p p3 z z3 6.4 lb/ft 5 ft = 3 lb/ft gage pressure
28 Page 6 of 9 Unit C3 Cavitation Cavitation occurs when the pressure is reduced to the vapor pressure Textbook Munson, Young, and Okiishi, page 9 Cavitation at Siphon During a siphon, it is possible to establish a cavitation, when the lowest pressure at highest elevation during the siphon becomes vapor pressure of the liquid under the given temperature.
29 Page 7 of 9 EXAMPLE 3.0 Textbook Munson, Young, and Okiishi, page 0 Unit C3 Siphon and Cavitation Assuming a steady, incompressible, and inviscid flow, the Bernoulli s equation can be 3 applied between points and 3 as: p z p3 z3 where, p p3 patm 0 gage pressure with z 5 ft and z3 5 ft. Also, 0 Therefore, z 3 z3 or, 3 z z3 g z z3 3. ft/s 5 ft 5 ft = 35.9 ft/s Also, Q constant conservation of mass, so: 3 since A A3 Now, let us apply the Bernoulli s equation between points and as: p z p z where, p patm 0 gage pressure with z 5 ft and z H. Also, 0 and ft/s. At incipient of cavitation, p pvapor =.60 psi absolute =.60 in 4.7 = 4.47 lb/in, lb/ft gage ft Therefore, z p z 3.94 slugs/ft 35.9 ft/s 3 3 or, 6.4 lb/ft 5 ft, lb/ft 6.4 lb/ft H Hence, H 8.36 ft
30 Page 8 of 9 Unit C3 Flowrate Measurement Assuming horizontal z = z, steady, inviscid, and incompressible flow between points and : p p If velocity profiles are assumed to be uniform at sections and : Q A A Combining these equations: Q A p [ A p A ] Textbook Munson, Young, and Okiishi, page
31 Page 9 of 9 EXAMPLE 3. Textbook Munson, Young, and Okiishi, page Unit C3 enturi Meter Combining the Bernoulli s equation and conservation of mass: p p Q A A A Rearranging this equation provides: Q A A p p A 3 where, Q m /s A A D D 0.06 m 0.0 m = Also, from SG 0.85, SG HO 0.85,000 kg/m = 850 kg/m 3 3 Therefore, for Q m /s : 0.36 p 3 3 p m /s 850 kg/m =,60 N/m.6 kpa m 3 For Q 0.05 m /s : 0.36 p 3 3 p 0.05 m /s 850 kg/m = 60 3 N/m 6 kpa m
The Bernoulli Equation
The Bernoulli Equation The most used and the most abused equation in fluid mechanics. Newton s Second Law: F = ma In general, most real flows are 3D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider
More informationFLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation
FLUID MECHANICS Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation CHAP 3. ELEMENTARY FLUID DYNAMICS  THE BERNOULLI EQUATION CONTENTS 3. Newton s Second Law 3. F = ma along a Streamline 3.3
More informationChapter 3 Bernoulli Equation
1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around
More information5 ENERGY EQUATION OF FLUID MOTION
5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws
More informationROAD MAP... D0: Reynolds Transport Theorem D1: Conservation of Mass D2: Conservation of Momentum D3: Conservation of Energy
ES06 Fluid Mechani UNIT D: Flow Field Analysis ROAD MAP... D0: Reynolds Transport Theorem D1: Conservation of Mass D: Conservation of Momentum D3: Conservation of Energy ES06 Fluid Mechani Unit D0:
More informationMass of fluid leaving per unit time
5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.
More informationAerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)
Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation
More information2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.
CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise
More informationCHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD
CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.
More information3.8 The First Law of Thermodynamics and the Energy Equation
CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1D form ( r F )ext = [ˆ ] ( r v)d + ( r v) out ṁ out ( r v) in ṁ in t CV 3.8 The First Law of Thermodynamics and
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 informationChapter 4 DYNAMICS OF FLUID FLOW
Faculty Of Engineering at Shobra nd Year Civil  016 Chapter 4 DYNAMICS OF FLUID FLOW 41 Types of Energy 4 Euler s Equation 43 Bernoulli s Equation 44 Total Energy Line (TEL) and Hydraulic Grade Line
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 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 informationChapter Four fluid flow mass, energy, Bernoulli and momentum
41Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (41). Figure (41): the differential control volume and differential control volume (Total mass entering
More informationRate of Flow Quantity of fluid passing through any section (area) per unit time
Kinematics of Fluid Flow Kinematics is the science which deals with study of motion of liquids without considering the forces causing the motion. Rate of Flow Quantity of fluid passing through any section
More informationfor what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?
1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first
More informationCEE 3310 Control Volume Analysis, Oct. 10, = dt. sys
CEE 3310 Control Volume Analysis, Oct. 10, 2018 77 3.16 Review First Law of Thermodynamics ( ) de = dt Q Ẇ sys Sign convention: Work done by the surroundings on the system < 0, example, a pump! Work done
More informationME 3560 Fluid Mechanics
Sring 018 ME 3560 Fluid Mechanic Chater III. Elementary Fluid Dynamic The Bernoulli Equation 1 Sring 018 3.1 Newton Second Law A fluid article can exerience acceleration or deceleration a it move from
More informationCEE 3310 Control Volume Analysis, Oct. 7, D Steady State Head Form of the Energy Equation P. P 2g + z h f + h p h s.
CEE 3310 Control Volume Analysis, Oct. 7, 2015 81 3.21 Review 1D Steady State Head Form of the Energy Equation ( ) ( ) 2g + z = 2g + z h f + h p h s out where h f is the friction head loss (which combines
More information!! +! 2!! +!"!! =!! +! 2!! +!"!! +!!"!"!"
Homework 4 Solutions 1. (15 points) Bernoulli s equation can be adapted for use in evaluating unsteady flow conditions, such as those encountered during start up processes. For example, consider the large
More informationHOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION
AMEE 0 Introduction to Fluid Mechanics Instructor: Marios M. Fyrillas Email: m.fyrillas@frederick.ac.cy HOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION. Conventional sprayguns operate by achieving a low pressure
More informationIsentropic Flow. Gas Dynamics
Isentropic Flow Agenda Introduction Derivation Stagnation properties IF in a converging and convergingdiverging nozzle Application Introduction Consider a gas in horizontal sealed cylinder with a piston
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 information6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s
Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an
More information3.25 Pressure form of Bernoulli Equation
CEE 3310 Control Volume Analysis, Oct 3, 2012 83 3.24 Review The Energy Equation Q Ẇshaft = d dt CV ) (û + v2 2 + gz ρ d + (û + v2 CS 2 + gz + ) ρ( v n) da ρ where Q is the heat energy transfer rate, Ẇ
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 informationObjectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation
Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved
More informationEGN 3353C Fluid Mechanics
Lecture 8 Bernoulli s Equation: Limitations and Applications Last time, we derived the steady form of Bernoulli s Equation along a streamline p + ρv + ρgz = P t static hydrostatic total pressure q = dynamic
More informationBERNOULLI EQUATION. The motion of a fluid is usually extremely complex.
BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over
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 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 PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 4. ELEMENTARY FLUID DYNAMICS THE BERNOULLI EQUATION
More informationExam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118
CVEN 311501 (Socolofsky) Fluid Dynamics Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118 Name: : UIN: : Instructions: Fill in your name and UIN in the space
More informationAE301 Aerodynamics I UNIT A: Fundamental Concepts
AE3 Aerodynamics I UNIT A: Fundamental Concets ROAD MAP... A: Engineering Fundamentals Review A: Standard Atmoshere A3: Governing Equations of Aerodynamics A4: Airseed Measurements A5: Aerodynamic
More informationLab Section Date. ME4751 Air Flow Rate Measurement
Name Lab Section Date ME4751 Air Flow Rate Measurement Objective The objective of this experiment is to determine the volumetric flow rate of air flowing through a pipe using a Pitotstatic tube and a
More informationMAE 3130: Fluid Mechanics Lecture 7: Differential Analysis/Part 1 Spring Dr. Jason Roney Mechanical and Aerospace Engineering
MAE 3130: Fluid Mechanics Lecture 7: Differential Analysis/Part 1 Spring 2003 Dr. Jason Roney Mechanical and Aerospace Engineering Outline Introduction Kinematics Review Conservation of Mass Stream Function
More informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationCHEN 3200 Fluid Mechanics Spring Homework 3 solutions
Homework 3 solutions 1. An artery with an inner diameter of 15 mm contains blood flowing at a rate of 5000 ml/min. Further along the artery, arterial plaque has partially clogged the artery, reducing the
More 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 informationMeasurements using Bernoulli s equation
An Internet Book on Fluid Dynamics Measurements using Bernoulli s equation Many fluid measurement devices and techniques are based on Bernoulli s equation and we list them here with analysis and discussion.
More informationAEROSPACE ENGINEERING DEPARTMENT. Second Year  Second Term ( ) Fluid Mechanics & Gas Dynamics
AEROSPACE ENGINEERING DEPARTMENT Second Year  Second Term (20082009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:
More informationAE/ME 339. K. M. Isaac. 9/22/2005 Topic 6 FluidFlowEquations_Introduction. Computational Fluid Dynamics (AE/ME 339) MAEEM Dept.
AE/ME 339 Computational Fluid Dynamics (CFD) 1...in the phrase computational fluid dynamics the word computational is simply an adjective to fluid dynamics.... John D. Anderson 2 1 Equations of Fluid
More informationUseful concepts associated with the Bernoulli equation. Dynamic
Useful concets associated with the Bernoulli equation  Static, Stagnation, and Dynamic Pressures Bernoulli eq. along a streamline + ρ v + γ z = constant (Unit of Pressure Static (Thermodynamic Dynamic
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 informationMASS, MOMENTUM, AND ENERGY EQUATIONS
MASS, MOMENTUM, AND ENERGY EQUATIONS This chapter deals with four equations commonly used in fluid mechanics: the mass, Bernoulli, Momentum and energy equations. The mass equation is an expression of the
More informationBasic equations of motion in fluid mechanics
1 Annex 1 Basic equations of motion in fluid mechanics 1.1 Introduction It is assumed that the reader of this book is familiar with the basic laws of fluid mechanics. Nevertheless some of these laws will
More information주요명칭 수직날개. Vertical Wing. Flap. Rudder. Elevator 수평날개
High Lift Devices 주요명칭 동체 Flap 수직날개 Vertical Wing Rudder Elevator 수평날개 방향전환 () Rolling Yawing Pitching 방향전환 () Rolling Yawing Pitching Potential Flow of Helicopter PNU ME CFD LAB. =0 o =60 o =90 o =0 o
More informationWhere does Bernoulli's Equation come from?
Where does Bernoulli's Equation come from? Introduction By now, you have seen the following equation many times, using it to solve simple fluid problems. P ρ + v + gz = constant (along a streamline) This
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 informationDetailed Outline, M E 320 Fluid Flow, Spring Semester 2015
Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous
More informationIran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics
1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation 1 5.1 Introduction In this chapter we will show that the equation of motion of a particle
More informationStream Tube. When density do not depend explicitly on time then from continuity equation, we have V 2 V 1. δa 2. δa 1 PH6L24 1
Stream Tube A region of the moving fluid bounded on the all sides by streamlines is called a tube of flow or stream tube. As streamline does not intersect each other, no fluid enters or leaves across the
More informationvector H. If O is the point about which moments are desired, the angular moment about O is given:
The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment
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 informationFluids. Fluid = Gas or Liquid. Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion
Chapter 14 Fluids Fluids Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion Fluid = Gas or Liquid MFMcGrawPHY45 Chap_14HaFluidsRevised 10/13/01 Densities MFMcGrawPHY45 Chap_14HaFluidsRevised
More informationIntroduction to Aerospace Engineering
4. Basic Fluid (Aero) Dynamics Introduction to Aerospace Engineering Here, we will try and look at a few basic ideas from the complicated field of fluid dynamics. The general area includes studies of incompressible,
More informationV (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
More informationCHAPTER 3 Introduction to Fluids in Motion
CHAPTER 3 Introduction to Fluids in Motion FEtpe Eam Review Problems: Problems 3 to 39 nˆ 0 ( n ˆi+ n ˆj) (3ˆi 4 ˆj) 0 or 3n 4n 0 3. (D) 3. (C) 3.3 (D) 3.4 (C) 3.5 (B) 3.6 (C) Also n n n + since ˆn
More informationAE301 Aerodynamics I UNIT B: Theory of Aerodynamics
AE301 Aerodynamics I UNIT B: Theory of Aerodynamics ROAD MAP... B1: Mathematics for Aerodynamics B: Flow Field Representations B3: Potential Flow Analysis B4: Applications of Potential Flow Analysis
More informationQ1 Give answers to all of the following questions (5 marks each):
FLUID MECHANICS First Year Exam Solutions 03 Q Give answers to all of the following questions (5 marks each): (a) A cylinder of m in diameter is made with material of relative density 0.5. It is moored
More informationIn this section, mathematical description of the motion of fluid elements moving in a flow field is
Jun. 05, 015 Chapter 6. Differential Analysis of Fluid Flow 6.1 Fluid Element Kinematics In this section, mathematical description of the motion of fluid elements moving in a flow field is given. A small
More informationMAE 101A. Homework 7  Solutions 3/12/2018
MAE 101A Homework 7  Solutions 3/12/2018 Munson 6.31: The stream function for a twodimensional, nonviscous, incompressible flow field is given by the expression ψ = 2(x y) where the stream function has
More information2.25 Advanced Fluid Mechanics
MIT Department of Mechanical Engineering.5 Advanced Fluid Mechanics Problem 4.05 This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin Consider the frictionless, steady
More informationLecture 3 The energy equation
Lecture 3 The energy equation Dr Tim Gough: t.gough@bradford.ac.uk General information Lab groups now assigned Timetable up to week 6 published Is there anyone not yet on the list? Week 3 Week 4 Week 5
More informationBERNOULLI EQUATION. The motion of a fluid is usually extremely complex.
Chapter 5 Fluid in Motion The Bernoulli Equation BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence
More informationIf a stream of uniform velocity flows into a blunt body, the stream lines take a pattern similar to this: Streamlines around a blunt body
Venturimeter & Orificemeter ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 5 Applications of the Bernoulli Equation The Bernoulli equation can be applied to a great
More informationMechanical Engineering Programme of Study
Mechanical Engineering Programme of Study Fluid Mechanics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy SOLVED EXAMPLES ON VISCOUS FLOW 1. Consider steady, laminar flow between two fixed parallel
More informationAE301 Aerodynamics I UNIT A: Fundamental Concepts
AE301 Aerodynamics I UNIT A: Fundamental Concets ROAD MAP... A1: Engineering Fundamentals Reiew A: Standard Atmoshere A3: Goerning Equations of Aerodynamics A4: Airseed Measurements A5: Aerodynamic
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 informationChapter 5 Flow in Pipelines
For updated ersion, please click on http://kalam.ump.edu.my Chapter 5 Flow in ipelines by Dr. Nor Azlina binti Alias Faculty of Ciil and Earth Resources Enineerin azlina@ump.edu.my 5.4 Flowrate and Velocity
More information2 Internal Fluid Flow
Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.
More informationFLUID MECHANICS EQUATIONS
FLUID MECHANIC EQUATION M. Ragheb 11/2/2017 INTRODUCTION The early part of the 18 th century saw the burgeoning of the field of theoretical fluid mechanics pioneered by Leonhard Euler and the father and
More informationProject TOUCAN. A Study of a TwoCan System. Prof. R.G. Longoria Update Fall ME 144L Prof. R.G. Longoria Dynamic Systems and Controls Laboratory
Project TOUCAN A Study of a TwoCan System Prof. R.G. Longoria Update Fall 2009 Laboratory Goals Gain familiarity with building models that reflect reality. Show how a model can be used to guide physical
More informationSignature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
More informationChapter 5: Mass, Bernoulli, and Energy Equations
Chapter 5: Mass, Bernoulli, and Energy Equations Introduction This chapter deals with 3 equations commonly used in fluid mechanics The mass equation is an expression of the conservation of mass principle.
More informationFor example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then:
Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing
More informationPART II. Fluid Mechanics Pressure. Fluid Mechanics Pressure. Fluid Mechanics Specific Gravity. Some applications of fluid mechanics
ART II Some applications of fluid mechanics Fluid Mechanics ressure ressure = F/A Units: Newton's per square meter, Nm , kgm  s  The same unit is also known as a ascal, a, i.e. a = Nm  ) English units:
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 information1.060 Engineering Mechanics II Spring Problem Set 3
1.060 Engineering Mechanics II Spring 2006 Due on Monday, March 6th Problem Set 3 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More information1.060 Engineering Mechanics II Spring Problem Set 1
1.060 Engineering Mechanics II Spring 2006 Due on Tuesday, February 21st Problem Set 1 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group
More informationME 3560 Fluid Mechanics
ME 3560 Fluid Mechanics 1 4.1 The Velocity Field One of the most important parameters that need to be monitored when a fluid is flowing is the velocity. In general the flow parameters are described in
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 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 informationV/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0
UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and nonuniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and irrotational
More information4 Mechanics of Fluids (I)
1. The x and y components of velocity for a twodimensional flow are u = 3.0 ft/s and v = 9.0x ft/s where x is in feet. Determine the equation for the streamlines and graph representative streamlines in
More informationPhysics 123 Unit #1 Review
Physics 123 Unit #1 Review I. Definitions & Facts Density Specific gravity (= material / water) Pressure Atmosphere, bar, Pascal Barometer Streamline, laminar flow Turbulence Gauge pressure II. Mathematics
More informationUNIT I FLUID PROPERTIES AND STATICS
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: IIB.Tech & ISem Course & Branch:
More informationFLOW MEASUREMENT IN PIPES EXPERIMENT
University of Leicester Engineering Department FLOW MEASUREMENT IN PIPES EXPERIMENT Page 1 FORMAL LABORATORY REPORT Name of the experiment: FLOW MEASUREMENT IN PIPES Author: Apollin nana chaazou Partner
More informationBasics of fluid flow. Types of flow. Fluid Ideal/Real Compressible/Incompressible
Basics of fluid flow Types of flow Fluid Ideal/Real Compressible/Incompressible Flow Steady/Unsteady Uniform/Nonuniform Laminar/Turbulent Pressure/Gravity (free surface) 1 Basics of fluid flow (Chapter
More informationVelocity Measurement in Free Surface Flows
Velocity Measurement in Free Surface Flows Generally, the flow is assumed as one dimensional and standard. Pitot tube is used for measurement of velocity using either an inclined manometer or other type
More informationE80. Fluid Measurement The Wind Tunnel Lab. Experimental Engineering.
Fluid Measurement The Wind Tunnel Lab http://twistedsifter.com/2012/10/redbullstratosspacejumpphotos/ Feb. 13, 2014 Outline Wind Tunnel Lab Objectives Why run wind tunnel experiments? How can we use
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 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 informationi.e. the conservation of mass, the conservation of linear momentum, the conservation of energy.
04/04/2017 LECTURE 33 Geometric Interpretation of Stream Function: In the last class, you came to know about the different types of boundary conditions that needs to be applied to solve the governing equations
More informationPart A: 1 pts each, 10 pts total, no partial credit.
Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: 3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,
More informationLECTURE NOTES  III. Prof. Dr. Atıl BULU
LECTURE NOTES  III «FLUID MECHANICS» Istanbul Technical University College of Civil Engineering Civil Engineering Department Hydraulics Division CHAPTER KINEMATICS OF FLUIDS.. FLUID IN MOTION Fluid motion
More informationChapter 5 Mass, Bernoulli, and Energy Equations Chapter 5 MASS, BERNOULLI, AND ENERGY EQUATIONS
Chapter 5 MASS, BERNOULLI, AND ENERGY EQUATIONS Conservation of Mass 5C Mass, energy, momentum, and electric charge are conserved, and volume and entropy are not conserved during a process. 5C Mass flow
More informationThe E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012
The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel
More information