THEORY OF DUCTED FAN. by Giacomo Sacchi. august, Theory of duct fan, by Giacomo Sacchi 1/10
|
|
- Hugh Lewis
- 6 years ago
- Views:
Transcription
1 THEORY OF DUCTED FAN by Giacomo Sacchi august, 2009 Theory of duct fan, by Giacomo Sacchi 1/10
2 DIFFERENCE BETWEEN FREE FAN END DUCTED FAN The air flow of fan is "ideal" if: is delimited by a clean boundary with the surrounding air with "quadratic" form; the air speeds up continuously along the way; the air has got a constant speed in every section of the flow; the density of the air is constant and equal to the surrounding one; For the principle of the conservation of the mass (with hypothesis of constant density) if the section halves, the speed doubles, since the area is function of the square of the radius as consequence the form of the border must be "quadratic". The real flow is less regular, since the depression that swallows the air in the propeller is attracted from every direction and this clearly does not allow Theory of duct fan, by Giacomo Sacchi 2/10
3 clear border between flow and surrounding air, therefore the accelerations and the speeds of the flow are disomogenee between center and peripheral zone. The air flow which comes form the propeller is pushed everywhere by the pressure. In particularly degenerated conditions, the same air tip comes newly inhaled by the propeller generating whirling rings that reduce the push drastically. The reason of this is in the sir properties such as: viscosity, frictions, molecular bonds, etc. The worsening of the flow is given above all for lowlands speed and small propellers in proportion to the applied power. In these cases it is useful to use a duct to address the flow in the propeller, as a consequence to reduce these aerodynamic inefficiencies. This brings to more weight and more construction complexity, moreover the dimensioning of the tube is optimized for a specific condition and far from this ideal condition, the wastes increase remarkably. Generally the employment of ducted propellers is necessary due by the lack of space for larger propellers or by the will to maximize the static thrust or for safety reasons because people must be protected form the propeller 's contact. Theory of duct fan, by Giacomo Sacchi 3/10
4 The most important parameters are: ρ0 = density of the air V0 = speed of the surrounding air Ain = in aera Av = fan area Aout = out area Vin = average speed of the air that enters Vv = air fan speed Vout = average speed of the air that exits Vmax = flow max speed Δp = variation of pressure between before and after the propeller ANALYSIS OF DUCTED FAN FLOW HUPOTHESIS CONSTANT DENSITY OF THE AIR (ρ) The first hypothesis to fix is that the density remains constant and equal to that of the surrounding air. This is a more legitimate approximation as well as the flow has a much minor speed of that of the sound (1200 KM/H). Moreover the pressure generated by the propeller does not have to reach the highest values, because it would cause accelerations of the air such to induce it to compress itself in order to win its inertia. MASS FLOW (m') Air amount that passes through the propeller (Av) in the unit of time (Kg/sec). TRUST (T) The push is exclusively given by the quantity of air which is accelerated T = mass x acceleration = m' (Vmax - Vo) = m' ΔV This formula refers to the push of the whole system propeller-tube, while the propeller generates a slightly advanced push that is lost in frictions between air and duct. Theory of duct fan, by Giacomo Sacchi 4/10
5 TRUST POWER (Pt) Pt = ½ m' (Vmax² - Vo²) = T Vo + ½ T (Vmax - Vo) Obviously the power increases with the push that has to be generated but it "uselessly" increases also with ΔV and Vo. The following considerations are drawn: 1. with constant ΔV and increasing m' I obtain same push with less power, this is obtained with large Av, this is always to maximize in the plan limits 2. with the increase of Vo we need more power; Air that goes into the tube must to be slow but if the air is slowed down by us, there is some wasted energy that is not completely regained, instead if the air is however slowed down (es. boundary layer on wings), it gives a greater output. AIR SPEED INTO DUCT The air speed in the conduct is only given by the principle of conservation of the mass: ρin Ain Vin = ρv Av Vv = ρout Aout Vout but with ρ constant: Ain Vin = Av Vv = Aout Vout Vin = (m'/ρ)/ain; Vv = (m'/ρ)/av; Vout = (m'/ρ)/aout; Please notice that Vin is generally different from Vo and Vout does not have ties with Vmax; The Vin, Vv, Vout speed does not depend directly from the tube sections and from Vo and Vmax; Moreover please remember that they are average speeds, for example the ideal flow could pass only through the central part of the section and the remaining air to be almost firm. In case of real flow are the resistances of sliding to give a bell distribution to the speed in the section. The speed in the section of propeller (Vv) is assumed to be exactly the same hardly before and hardly after and this is an acceptable approximation. For a good efficiency the speeds of the flow (in particular Vmax) are always more minor of the sound speed (approximately 1200 km/h). Theory of duct fan, by Giacomo Sacchi 5/10
6 PRESSURES IN THE CONDUCT The action of the propeller is to generate a depression hardly before (p.v1) that attracts the air in the conduct and a pressure hardly after (p.v2) such to accelerate the air in the getting out. Δp = p.v2 - p.v1, this difference of pressure generates the push of the propeller F (>T in order to satisfy the wastes for friction in the tube) F = Δp Av With high Δp more inefficiencies are generated and the air can be compressed, but we have to remember that we want to realize a ducted propeller not a compressor. The pressure in income to the tube (p.in) and the one in escape (p.out) can vary with the sections and the speeds of the air on the basis of Bernulli's equation that with constant ρ and with horizontal conduct (therefore without variations of potential energy) we have: ½ ρvin² + p.in = ½ ρvv² + p.v1 ½ ρvv² + p.v2 = ½ ρvout² + p.out The values of pressure in income and escape stretch to the external pressure (Po) but only if the sections of the conduct are correctly dimensioned to follow the flow and not to hinder it. SWIRL The spin of the propeller generates axial push (f) with a power (Pf), but also some vortices that are an undesired effect as they waste power (Ps). Total power applied to the propeller: Pt = Pf + Ps For the planning is supposed a distribution of the free vortices, that is to say that the speed of the vortices increases linearly moving away from the center of the propeller: Vs = K / r ωs = K / r² τs = m' K K = costant of swirl; it can be experimentally obtained by measuring the power Theory of duct fan, by Giacomo Sacchi 6/10
7 applied to the propeller and the effective obtained push; the values go from 1 to 6; The power of the vortices is obtained making the integral calculus on Av of (τs x ωs) and it obtains: Ps = 2 π (m' K² /Av) ln (Rv / Rhub) Rv = fan radius; Rhub = ogive propeller radius; CHARACTERISTICS OF THE DUCT The income culvert has the only aim to convey the air to the propeller in a regular way introducing less possibly frictions and maintaining the laminar flow. The income must be aerodynamically clean, streamlined. The surfaces must be smooth, regular and with course of the beam of the sections to be reduced in quadratic way. The length of the income culvert is determined by the optimization degree that we wanted to reach to a determined speed. That is to say that if the culvert is lenghtened until the income speed income and the movement speed are the same, to which we want to optimize the push, we obtain the maximum of the yield in that condition but the fast worsening of the efficiency in the others speed. The escape culvert has instead the task to transform the pressure in speed, as it happens in weapons where the pressure of the outbreak is transformed thanks to the cane in speed of the ogive. The escape culvert must be sufficiently long (some decimeters are enough) but not too long in order not to introduce resistances, moreover the section does not have to be increased. In order to have some advantages in the extreme circumstance of ducted propellers with very short ducts it is necessary to hinder the return of the air from the escape to the income (es. tail posts of some helicopters). Theory of duct fan, by Giacomo Sacchi 7/10
8 THE PLANNING OF THE DUCT Various approaches can be undertaken, beginning from various ties, but in any case it will be probably necessary to begin with estimated values and to proceed by trials and error in the direction of the aspects to optimize. The procedure chosen by me expects to decide: the propeller diameter: as large as possible; the Vo speed of the external air to which to optimize the push, it could be the cruise speed but it would penalize the takeoff; This is a choice to do estimating the aircraft and the installed power; to estimate the intentional push to Vo; Now the mass flow must be estimated (m') optimal, that is that it diminishes the total power which is necessary. The First method gives better results with low Vo or Ae small: Ptot = power for the push + swirl power (the other wastes as the resistance of the culvert can not be still estimated as the air flow speeds are still not known ) β = variable convenient; Ps = 2 π (m' K² /Av) ln (Rv / Rhub) = β m' T = m' ΔV Ptot = TVo + ½ TΔV + Ps replacing: Ptot = TVo + ½ T²/m' + β m' this formula links the necessary power to the mass flow, but it must diminish the power, therefore we derive in m' and we place equal to zero. m' = T / sqrt(2 β) Theory of duct fan, by Giacomo Sacchi 8/10
9 The second method gives better results with high Vo or Ae large m' = ρ Ae Vo Between the two methods it has to be used the mass flow which requires less power. Once m' is found, we can desume the several speeds : Vin = (m'/ρ)/ain; Vv = (m'/ρ)/av; Vout = (m'/ρ)/aout; Vmax = T/m' + Vo These speeds must be much lower of the sound speed (approximately 1200 km/h). Moreover it is possible to estimate the power wastes for the resistence (Pr) due to the friction of the air with the conduct that are depending on the speeds. Power to apply to the propeller: Pf = TVo + ½ T²/m' + Ps + Pr If it is excessive it is possible to increase the area of the impeller and/or diminishing the cruise speed (Vo). The fixed push (t) is the wished one, but the propeller must produce a greater push (f) in order to satisfy the wastes for friction (if considered). F = T ((Pf-Ps)/(Pf-Ps-Pr)) ((Vmax+Vo)/2)/Vv The swirl power has to be deducted as it does not contribute to the push. A parameter that will be useful for the planning of the propeller is: Δp = F / Av Theory of duct fan, by Giacomo Sacchi 9/10
10 THE PLANNING OF THE FAN Once the conduct is established, the speed of the air to impeller (Vv) is obtained, for the prefixed speed (Vo) and the push (r) that we want to obtained. We have to fix the speed of spin of the impeller (ω) according to the diagram of power/rpm of the engine to the necessary power (Pf), remember that the terminal velocity (Vt = ω R) must be lower of the sound speed (1200 km/h). The shovel must be divided in sections in order to gain for each one the values of chord and twisting angle. The relative speeds are obtained (Vi) and the angles of incidence (αi) of the air flow in the several blade sections. Now it can be decided to apply various choices, like for example to maintain a blade with constant chord (simplifying the propeller but not optimizing the result), or increase the number of the blades in order not to have too much large chord. Angles of twist and optimal chord From the diagram of the chosen profile for the shovels the angle of incidence is found (α') such for which 75% of (the Cp/Cr) maximum are had, so that the profile works as much as possible in good efficiency, but reducing the risk of stalls. We immediately desume the angle of twisting in the several sections = αi α' The width of the chord (ci) is desumed from Δp, Cp to α' and the formula of the lifting capacity P = ½ ρ Si Cp Vi². Si = surface of the shovel section Good job. Giacomo Sacchi Theory of duct fan, by Giacomo Sacchi 10/10
Performance. 5. More Aerodynamic Considerations
Performance 5. More Aerodynamic Considerations There is an alternative way of looking at aerodynamic flow problems that is useful for understanding certain phenomena. Rather than tracking a particle of
More informationRecap: Static Fluids
Recap: Static Fluids Archimedes principal states that the buoyant force acting on an object is equal to the weight of fluid displaced. If the average density of object is greater than density of fluid
More informationBlade Element Momentum Theory
Blade Element Theory has a number of assumptions. The biggest (and worst) assumption is that the inflow is uniform. In reality, the inflow is non-uniform. It may be shown that uniform inflow yields the
More informationDepartment of Energy Sciences, LTH
Department of Energy Sciences, LTH MMV11 Fluid Mechanics LABORATION 1 Flow Around Bodies OBJECTIVES (1) To understand how body shape and surface finish influence the flow-related forces () To understand
More informationQuiz 2 May 18, Statement True False 1. For a turbojet, a high. gives a high thermodynamic efficiency at any compression ratio.
Quiz 2 May 18, 2011 16.50 Propulsion Systems Spring 2011 Two hours, open book, open notes TRUE-FALSE QUESTIONS Justify your answer in no more than two lines. 4 points for correct answer and explanation
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 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 informationAE 2020: Low Speed Aerodynamics. I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson
AE 2020: Low Speed Aerodynamics I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson Text Book Anderson, Fundamentals of Aerodynamics, 4th Edition, McGraw-Hill, Inc.
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 informationChapter 10. Solids and Fluids
Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the
More informationBasic Information to Help Select the Correct Propeller
Propeller Performance Factors - Basic Information to Help Select the Correct Propeller The performance of a propeller in flight involves several complex subjects, and the high performance propellers we
More informationDefinitions. Temperature: Property of the atmosphere (τ). Function of altitude. Pressure: Property of the atmosphere (p). Function of altitude.
Definitions Chapter 3 Standard atmosphere: A model of the atmosphere based on the aerostatic equation, the perfect gas law, an assumed temperature distribution, and standard sea level conditions. Temperature:
More informationIntroduction to Turbomachinery
1. Coordinate System Introduction to Turbomachinery Since there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form, represented in three directions; 1. Axial 2. Radial
More informationJet Aircraft Propulsion Prof. Bhaskar Roy Prof A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay
Jet Aircraft Propulsion Prof. Bhaskar Roy Prof A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Module No. #01 Lecture No. # 07 Jet Engine Cycles For Aircraft propulsion
More informationPropeller theories. Blade element theory
30 1 Propeller theories Blade element theory The blade elements are assumed to be made up of airfoil shapes of known lift, C l and drag, C d characteristics. In practice a large number of different airfoils
More informationWritten in August 2017 during my holiday in Bulgaria, Sunny Coast
Electric ucted Fan Theory This paper describes a simple theory of a ducted fan. It is assumed that the reader knows what it is an electric ducted fan (EF), how it works, and what it is good for. When I
More informationequation 4.1 INTRODUCTION
4 The momentum equation 4.1 INTRODUCTION It is often important to determine the force produced on a solid body by fluid flowing steadily over or through it. For example, there is the force exerted on a
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 informationHeat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay
Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection
More informationAEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics
AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:
More informationFlight Vehicle Terminology
Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes
More informationIX. COMPRESSIBLE FLOW. ρ = P
IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.
More informationMasters in Mechanical Engineering Aerodynamics 1 st Semester 2015/16
Masters in Mechanical Engineering Aerodynamics st Semester 05/6 Exam st season, 8 January 06 Name : Time : 8:30 Number: Duration : 3 hours st Part : No textbooks/notes allowed nd Part : Textbooks allowed
More informationGiven the water behaves as shown above, which direction will the cylinder rotate?
water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0
More informationPrinciples of Rocketry
1-1 Principles of Rocketry 1-2 Water Rockets BASIC CONCEPTS 1-3 What is a Rocket? A chamber enclosing a gas under pressure. A balloon is a simple example of a rocket. Rubber walls compress the air inside.
More informationIntroduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Centrifugal Compressor Part I Good morning
More informationRotor reference axis
Rotor reference axis So far we have used the same reference axis: Z aligned with the rotor shaft Y perpendicular to Z and along the blade (in the rotor plane). X in the rotor plane and perpendicular do
More informationModel Rocketry. The Science Behind the Fun
Model Rocketry The Science Behind the Fun Topics History of Rockets Sir Isaac Newton Laws of Motion Rocket Principles Flight of a Model Rocket Rocket Propulsion Forces at Work History Rockets and rocket
More informationIn steady flow the velocity of the fluid particles at any point is constant as time passes.
Chapter 10 Fluids Fluids in Motion In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point
More informationFundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics
Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI (after: D.J. ACHESON s Elementary Fluid Dynamics ) bluebox.ippt.pan.pl/
More informationIn this lecture... Centrifugal compressors Thermodynamics of centrifugal compressors Components of a centrifugal compressor
Lect- 3 In this lecture... Centrifugal compressors Thermodynamics of centrifugal compressors Components of a centrifugal compressor Centrifugal compressors Centrifugal compressors were used in the first
More informationChapter 4 Force and Motion
Chapter 4 Force and Motion Units of Chapter 4 The Concepts of Force and Net Force Inertia and Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion More on Newton s Laws:
More information9. Pumps (compressors & turbines) Partly based on Chapter 10 of the De Nevers textbook.
Lecture Notes CHE 31 Fluid Mechanics (Fall 010) 9. Pumps (compressors & turbines) Partly based on Chapter 10 of the De Nevers textbook. Basics (pressure head, efficiency, working point, stability) Pumps
More informationHVAC Clinic. Duct Design
HVAC Clinic Duct Design Table Of Contents Introduction... 3 Fundamentals Of Duct Design... 3 Pressure Changes In A System... 8 Example 1... 13 Duct Design Methods... 15 Example 2... 15 Introduction The
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 informationChapter -5(Section-1) Friction in Solids and Liquids
Chapter -5(Section-1) Friction in Solids and Liquids Que 1: Define friction. What are its causes? Ans : Friction:- When two bodies are in contact with each other and if one body is made to move then the
More informationCHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES
Thermodynamics: An Engineering Approach 8th Edition in SI Units Yunus A. Çengel, Michael A. Boles McGraw-Hill, 2015 CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Lecture slides by Dr. Fawzi Elfghi
More informationLesson 37 Transmission Of Air In Air Conditioning Ducts
Lesson 37 Transmission Of Air In Air Conditioning Ducts Version 1 ME, IIT Kharagpur 1 The specific objectives of this chapter are to: 1. Describe an Air Handling Unit (AHU) and its functions (Section 37.1).
More informationP R E A M B L E. The module is run with the following pattern over 3 weeks. Introduction (1 hour) Facilitated Practical Class (2 hours)
CROSSWINDS ELECTROMAGNETIC INDU CTION - LABORATORY INVESTIGATION P R E A M B L E The original form of the problem is an Experimental Group Research Project, undertaken by students organised into small
More informationWhat s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube
PHYS 101 Lecture 29x - Viscosity 29x - 1 Lecture 29x Viscosity (extended version) What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube Viscosity We introduced
More informationNewton s Laws of Motion. I. Law of Inertia II. F=ma III. Action-Reaction
Newton s Laws of Motion I. Law of Inertia II. F=ma III. Action-Reaction While most people know what Newton's laws say, many people do not know what they mean (or simply do not believe what they mean).
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 2
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 2 WORK, POWER AND ENERGY TRANSFER IN DYNAMIC ENGINEERING SYSTEMS TUTORIAL 1 - LINEAR MOTION Be able to determine
More informationAAE 251 Formulas. Standard Atmosphere. Compiled Fall 2016 by Nicholas D. Turo-Shields, student at Purdue University. Gradient Layer.
AAE 51 Formulas Compiled Fall 016 by Nicholas D. Turo-Shields, student at Purdue University Standard Atmosphere p 0 = 1.0135 10 5 Pascals ρ 0 = 1.5 kg m 3 R = 87 J kg K γ = 1.4 for air p = ρrt ; Equation
More informationLABORATORY V PREDICTING NON-REPETITIVE MOTION
LABORATORY V PREDICTING NON-REPETITIVE MOTION In this section, you will continue working on problems in dynamics, the relationship of force and acceleration especially in complex situations that occur
More informationMECA-H-402: Turbomachinery course Axial compressors
MECA-H-40: Turbomachinery course Axial compressors Pr. Patrick Hendrick Aero-Thermo-Mecanics Year 013-014 Contents List of figures iii 1 Axial compressors 1 1.1 Introduction...............................
More informationFAN TERMINOLOGY. t = 1.2 kg/m 3 (Standard air density at 20 C and 1013mb. V = duct air velocity, m/s.
+7 (0)1 55 1077 +7 (0)1 55 797 FAN TERMINOLOGY These notes are designed to explain some of the terms that are used in describing the characteristics of fans and the relationship between the fan performance
More informationCircular Motion. I. Centripetal Impulse. The centripetal impulse was Sir Isaac Newton s favorite force.
Circular Motion I. Centripetal Impulse The centripetal impulse was Sir Isaac Newton s favorite force. The Polygon Approximation. Newton made a business of analyzing the motion of bodies in circular orbits,
More informationPropellers and Ducted Fans
Propellers and Ducted Fans Session delivered by: Prof. Q. H. Nagpurwala 1 To help protect your privacy, PowerPoint prevented this external picture from being automatically downloaded. To download and display
More informationFinal 1. (25) 2. (10) 3. (10) 4. (10) 5. (10) 6. (10) TOTAL = HW = % MIDTERM = % FINAL = % COURSE GRADE =
MAE101B: Advanced Fluid Mechanics Winter Quarter 2017 http://web.eng.ucsd.edu/~sgls/mae101b_2017/ Name: Final This is a three hour open-book exam. Please put your name on the top sheet of the exam. Answer
More informationDynamics of Machines. Prof. Amitabha Ghosh. Department of Mechanical Engineering. Indian Institute of Technology, Kanpur. Module No.
Dynamics of Machines Prof. Amitabha Ghosh Department of Mechanical Engineering Indian Institute of Technology, Kanpur Module No. # 07 Lecture No. # 01 In our previous lectures, you have noticed that we
More informationGeneral Physics I Spring Forces and Newton s Laws of Motion
General Physics I Spring 2011 Forces and Newton s Laws of Motion 1 Forces and Interactions The central concept in understanding why things move is force. If a tractor pushes or pulls a trailer, the tractor
More informationPART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG
1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity
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 informationPS113 Chapter 4 Forces and Newton s laws of motion
PS113 Chapter 4 Forces and Newton s laws of motion 1 The concepts of force and mass A force is described as the push or pull between two objects There are two kinds of forces 1. Contact forces where two
More informationContents. 2 Basic Components Aerofoils Force Generation Performance Parameters xvii
Contents 1 Working Principles... 1 1.1 Definition of a Turbomachine... 1 1.2 Examples of Axial Turbomachines... 2 1.2.1 Axial Hydraulic Turbine... 2 1.2.2 Axial Pump... 4 1.3 Mean Line Analysis... 5 1.4
More informationMOTION AND DESIGN VOCAB
MOTION AND DESIGN VOCAB Vocabulary Term acceleration Action/Reaction balanced Chemical Change Meaning/Definition rate of increase of speed or velocity (example: accelerator pedal on a car) Newton s 3rd
More informationTherefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V
When the mass m of the control volume remains nearly constant, the first term of the Eq. 6 8 simply becomes mass times acceleration since 39 CHAPTER 6 d(mv ) CV m dv CV CV (ma ) CV Therefore, the control
More informationSAIOH Tutorial Ventilation 1 pressures and basic air flow calculations
SAIOH Tutorial Ventilation 1 pressures and basic air flow calculations Acknowledgement This tutorial was provided by SAIOH as an assessment support aid for prospective candidates. The tutorial is free
More informationPropulsion Thermodynamics
Chapter 1 Propulsion Thermodynamics 1.1 Introduction The Figure below shows a cross-section of a Pratt and Whitney JT9D-7 high bypass ratio turbofan engine. The engine is depicted without any inlet, nacelle
More informationAEROSPACE ENGINEERING
AEROSPACE ENGINEERING Subject Code: AE Course Structure Sections/Units Topics Section A Engineering Mathematics Topics (Core) 1 Linear Algebra 2 Calculus 3 Differential Equations 1 Fourier Series Topics
More informationStator Blade Motor Motor Housing
The internal workings of a Ducted Fan The rotor velocity vectors and blade angles After looking at EDFs from a pure axial change of momentum position we must now address the question how the fan is shaped
More informationMECHANICAL PROPERTIES OF FLUIDS
CHAPTER-10 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 informationAircraft Structures Design Example
University of Liège Aerospace & Mechanical Engineering Aircraft Structures Design Example Ludovic Noels Computational & Multiscale Mechanics of Materials CM3 http://www.ltas-cm3.ulg.ac.be/ Chemin des Chevreuils
More informationexcept assume the parachute has diameter of 3.5 meters and calculate how long it takes to stop. (Must solve differential equation)
Homework 5 Due date: Thursday, Mar. 3 hapter 7 Problems 1. 7.88. 7.9 except assume the parachute has diameter of 3.5 meters and calculate how long it takes to stop. (Must solve differential equation) 3.
More informationSPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30
SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the
More informationPROBLEM 2 10 points. [ ] increases [ ] decreases [ ] stays the same. Briefly justify your answer:
PROBLEM 2 10 points A disk of mass m is tied to a block of mass 2m via a string that passes through a hole at the center of a rotating turntable. The disk rotates with the turntable at a distance R from
More informationChapter Four Hydraulic Machines
Contents 1- Introduction. 2- Pumps. Chapter Four Hydraulic Machines (لفرع الميكانيك العام فقط ( Turbines. -3 4- Cavitation in hydraulic machines. 5- Examples. 6- Problems; sheet No. 4 (Pumps) 7- Problems;
More informationChapter 4. Table of Contents. Section 1 Changes in Motion. Section 2 Newton's First Law. Section 3 Newton's Second and Third Laws
Forces and the Laws of Motion Table of Contents Section 1 Changes in Motion Section 2 Newton's First Law Section 3 Newton's Second and Third Laws Section 4 Everyday Forces Section 1 Changes in Motion Objectives
More informationFluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay
Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 35 Boundary Layer Theory and Applications Welcome back to the video course on fluid
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 informationPY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I
PY205N Spring 2013 Final exam, practice version MODIFIED This practice exam is to help students prepare for the final exam to be given at the end of the semester. Please note that while problems on this
More informationGyroRotor program : user manual
GyroRotor program : user manual Jean Fourcade January 18, 2016 1 1 Introduction This document is the user manual of the GyroRotor program and will provide you with description of
More informationAirfoils and Wings. Eugene M. Cliff
Airfoils and Wings Eugene M. Cliff 1 Introduction The primary purpose of these notes is to supplement the text material related to aerodynamic forces. We are mainly interested in the forces on wings and
More informationJet Aircraft Propulsion Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay
Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Lecture No. #03 Jet Engine Basic Performance Parameters We are talking
More informationCHAPTER EIGHT P U M P I N G O F L I Q U I D S
CHAPTER EIGHT P U M P I N G O F L I Q U I D S Pupmps are devices for supplying energy or head to a flowing liquid in order to overcome head losses due to friction and also if necessary, to raise liquid
More informationMestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 2012/13
Mestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 212/13 Exam 2ª época, 2 February 213 Name : Time : 8: Number: Duration : 3 hours 1 st Part : No textbooks/notes allowed 2 nd Part :
More informationFluid flow Pressure Bernoulli Principle Surface Tension
Lecture 9. Fluid flow Pressure Bernoulli Principle Surface Tension Fluid flow Speed of a fluid in a pipe is not the same as the flow rate Depends on the radius of the pipe. example: Low speed Large flow
More informationThe 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 3-D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider
More informationNewton s Laws of Motion. I. Law of Inertia II. F=ma III. Action-Reaction
Newton s Laws of Motion I. Law of Inertia II. F=ma III. Action-Reaction While most people know what Newton's laws say, many people do not know what they mean (or simply do not believe what they mean).
More informationExploring Motion. Introduction. Att. Number
Exploring Motion Introduction Newton s three laws of motion describe the interaction of forces that control movement. The first law states that a body in motion will remain in motion unless acted upon
More informationl Every object in a state of uniform motion tends to remain in that state of motion unless an
Motion and Machine Unit Notes DO NOT LOSE! Name: Energy Ability to do work To cause something to change move or directions Energy cannot be created or destroyed, but transferred from one form to another.
More informationJet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering
Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Indian Institute of Technology, IIT Bombay Module No. # 01 Lecture No. # 08 Cycle Components and Component
More informationChapter Four Holt Physics. Forces and the Laws of Motion
Chapter Four Holt Physics Forces and the Laws of Motion Physics Force and the study of dynamics 1.Forces - a. Force - a push or a pull. It can change the motion of an object; start or stop movement; and,
More informationLecture 4: Wind energy
ES427: The Natural Environment and Engineering Global warming and renewable energy Lecture 4: Wind energy Philip Davies Room A322 philip.davies@warwick.ac.uk 1 Overview of topic Wind resources Origin of
More informationBell Ringer: What is Newton s 3 rd Law? Which force acts downward? Which force acts upward when two bodies are in contact?
Bell Ringer: What is Newton s 3 rd Law? Which force acts downward? Which force acts upward when two bodies are in contact? Does the moon attract the Earth with the same force that the Earth attracts the
More informationReminder: HW #10 due Thursday, Dec 2, 11:59 p.m. (last HW that contributes to the final grade)
Reminder: HW #0 due Thursday, Dec, :59 p.m. (last HW that contributes to the final grade) Recitation Quiz # tomorrow (last Recitation Quiz) Formula Sheet for Final Exam posted on Bb Last Time: Pressure
More informationNewton s Laws.
Newton s Laws http://mathsforeurope.digibel.be/images Forces and Equilibrium If the net force on a body is zero, it is in equilibrium. dynamic equilibrium: moving relative to us static equilibrium: appears
More informationPractice Exam 2. Multiple Choice Identify the choice that best completes the statement or answers the question.
Practice Exam 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A roller-coaster car has a mass of 500.0 kg when fully loaded with passengers. At the bottom
More informationKinematics. v (m/s) ii. Plot the velocity as a function of time on the following graph.
Kinematics 1993B1 (modified) A student stands in an elevator and records his acceleration as a function of time. The data are shown in the graph above. At time t = 0, the elevator is at displacement x
More informationWS-CH-4 Motion and Force Show all your work and equations used. Isaac Newton ( )
AP PHYSICS 1 WS-CH-4 Motion and Force Show all your work and equations used. Isaac Newton (1643-1727) Isaac Newton was the greatest English mathematician of his generation. He laid the foundation for differential
More informationAssessment Schedule 2007 Physics: Demonstrate understanding of mechanics (90255)
NCEA Level Physics (9055) 007 page of 5 Assessment Schedule 007 Physics: Demonstrate understanding of mechanics (9055) Evidence Statement Q Evidence Achievement Achievement with Merit Achievement with
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationMechanical Engineering for Renewable Energy Systems. Dr. Digby Symons. Wind Turbine Blade Design
ENGINEERING TRIPOS PART IB PAPER 8 ELECTIVE () Mechanical Engineering for Renewable Energy Systems Dr. Digby Symons Wind Turbine Blade Design Student Handout CONTENTS 1 Introduction... 3 Wind Turbine Blade
More informationYear 11 Physics Tutorial 84C2 Newton s Laws of Motion
Year 11 Physics Tutorial 84C2 Newton s Laws of Motion Module Topic 8.4 Moving About 8.4.C Forces Name Date Set 1 Calculating net force 1 A trolley was moved to the right by a force applied to a cord attached
More informationPre-Comp Review Questions- 8 th Grade
Pre-Comp Review Questions- 8 th Grade Section 1- Units 1. Fill in the missing SI and English Units Measurement SI Unit SI Symbol English Unit English Symbol Time second s. Temperature K Fahrenheit Length
More informationNewton s Laws of Motion
Newton s Laws of Motion While most people know what Newton's Laws are, many people do not understand what they mean. Newton s Laws of Motion 1 st Law An object at rest will stay at rest, and an object
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 informationLecture 30 (Walker: ) Fluid Dynamics April 15, 2009
Physics 111 Lecture 30 (Walker: 15.6-7) Fluid Dynamics April 15, 2009 Midterm #2 - Monday April 20 Chap. 7,Chap. 8 (not 8.5) Chap. 9 (not 9.6, 9.8) Chap. 10, Chap. 11 (not 11.8-9) Chap. 13 (not 13.6-8)
More informationIntroduction to Aerospace Engineering
Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility
More informationContents. Preface... xvii
Contents Preface... xvii CHAPTER 1 Idealized Flow Machines...1 1.1 Conservation Equations... 1 1.1.1 Conservation of mass... 2 1.1.2 Conservation of momentum... 3 1.1.3 Conservation of energy... 3 1.2
More information