Fluid Mechanics 101 A Skeleton Guide-Books Pdf

Fluid Mechanics 101 A Skeleton Guide
06 Jun 2020 | 28 views | 0 downloads | 76 Pages | 568.71 KB

Share Pdf : Fluid Mechanics 101 A Skeleton Guide

Download and Preview : Fluid Mechanics 101 A Skeleton Guide


Report CopyRight/DMCA Form For : Fluid Mechanics 101 A Skeleton Guide



Transcription

This is guide is intended for students in Ae101 Fluid Mechanics the class on the fundamentals of fluid. mechanics that all first year graduate students take in Aeronautics and Mechanical Engineering at Caltech. It contains all the essential formulas grouped into sections roughly corresponding to the order in which the. material is taught when I give the course I have done this now five times beginning in 1995 This is not a. text book on the subject or even a set of lecture notes The document is incomplete as description of fluid. mechanics and entire subject areas such as free surface flows buoyancy turbulent flows etc are missing. some of these elements are in Brad Sturtevant s class notes which cover much of the same ground but are. more expository It is simply a collection of what I view as essential formulas for most of the class The. need for this typeset formulary grew out of my poor chalk board work and the many mistakes that happen. when I lecture Several generations of students have chased the errors out but please bring any that remain. to my attention,JES December 16 2007,1 Fundamentals 1. 1 1 Control Volume Statements 1,1 2 Reynolds Transport Theorem 2. 1 3 Integral Equations 2,1 3 1 Simple Control Volumes 3. 1 3 2 Steady Momentum Balance 3,1 4 Vector Calculus 3. 1 4 1 Vector Identities 3,1 4 2 Curvilinear Coordinates 3.
1 4 3 Gauss Divergence Theorem 4,1 4 4 Stokes Theorem 4. 1 4 5 Div Grad and Curl 4,1 4 6 Specific Coordinates 5. 1 5 Differential Relations 5,1 5 1 Conservation form 5. 1 6 Convective Form 6,1 7 Divergence of Viscous Stress 7. 1 8 Euler Equations 7,1 9 Bernoulli Equation 7,1 10 Vorticity 8.
1 11 Dimensional Analysis 9,2 Thermodynamics 11, 2 1 Thermodynamic potentials and fundamental relations 11. 2 2 Maxwell relations 11,2 3 Various defined quantities 12. 2 4 v P s relation 13,2 5 Equation of State Construction 13. 3 Compressible Flow 15,3 1 Steady Flow 15,3 1 1 Streamlines and Total Properties 15. 3 2 Quasi One Dimensional Flow 15,3 2 1 Isentropic Flow 16.
3 3 Heat and Friction 18,3 3 1 Fanno Flow 18,3 3 2 Rayleigh Flow 18. 3 4 Shock Jump Conditions 19,3 4 1 Lab frame moving shock versions 19. 3 5 Perfect Gas Results 20,3 6 Reflected Shock Waves 20. 3 7 Detonation Waves 22,3 8 Perfect Gas 2 Model 22. 3 8 1 2 Solution 23,3 8 2 High Explosives 23,3 9 Weak shock waves 25.
3 10 Acoustics 26,3 11 Multipole Expansion 27,3 12 Baffled surface source 28. 3 13 1 D Unsteady Flow 29,3 14 2 D Steady Flow 31,3 14 1 Oblique Shock Waves 31. 3 14 2 Weak Oblique Waves 31,3 14 3 Prandtl Meyer Expansion 32. 3 14 4 Inviscid Flow 32,3 14 5 Potential Flow 32,3 14 6 Natural Coordinates 33. 3 14 7 Method of Characteristics 33,4 Incompressible Inviscid Flow 34.
4 1 Velocity Field Decomposition 34,4 2 Solutions of Laplace s Equation 34. 4 3 Boundary Conditions 35,4 4 Streamfunction 35,4 4 1 2 D Cartesian Flows 36. 4 4 2 Cylindrical Polar Coordinates 37,4 4 3 Spherical Polar Coordinates 38. 4 5 Simple Flows 38,4 6 Vorticity 40,4 7 Key Ideas about Vorticity 41. 4 8 Unsteady Potential Flow 42,4 9 Complex Variable Methods 42.
4 9 1 Mapping Methods 44,4 10 Airfoil Theory 44,4 11 Thin Wing Theory 45. 4 11 1 Thickness Solution 46,4 11 2 Camber Case 48. 4 12 Axisymmetric Slender Bodies 49,4 13 Wing Theory 50. 5 Viscous Flow 52,5 1 Scaling 52,5 2 Two Dimensional Flow 53. 5 3 Parallel Flow 53,5 3 1 Steady Flows 54,5 3 2 Poiseuille Flow 56.
5 3 3 Rayleigh Problem 57,5 4 Boundary Layers 57,5 4 1 Blasius Flow 59. 5 4 2 Falkner Skan Flow 59,5 5 Ka rma n Integral Relations 60. 5 6 Thwaites Method 60,5 7 Laminar Separation 61,5 8 Compressible Boundary Layers 61. 5 8 1 Transformations and Approximations 61,5 8 2 Energy Equation 62. 5 8 3 Moving Shock Waves 64,5 8 4 Weak Shock Wave Structure 64.
5 9 Creeping Flow 66,A Famous Numbers 69,B Books on Fluid Mechanics 71. 1 FUNDAMENTALS 1,1 Fundamentals,1 1 Control Volume Statements. is a material volume V is an arbitrary control volume indicates the surface of the volume. mass conservation,Momentum conservation,Forces Z Z. F G dV T dA 3,Surface traction forces,T P n n T n 4. Stress tensor T,T P I or Tik P ik ik 5, where I is the unit tensor which in cartesian coordinates is.
Viscous stress tensor shear viscosity bulk viscosity v. ik 2 Dik ik Djj v ik Djj implicit sum on j 7,Deformation tensor. Energy conservation,e dV Q W 9,W G u dV T u dA 10,Q q n dA 11. heat flux q thermal conductivity k and thermal radiation qr. q k T qr 12,Entropy inequality 2nd Law of Thermodynamics. s dV dA 13,1 FUNDAMENTALS 2,1 2 Reynolds Transport Theorem. The multi dimensional analog of Leibniz s theorem,x t dV dV uV n dA 14.
dt V t V t t V, The transport theorem proper Material volume arbitrary volume V. dV dV u uV n dA 15,1 3 Integral Equations, The equations of motions can be rewritten with Reynolds Transport Theorem to apply to an almost arbi. trary moving control volume Beware of noninertial reference frames and the apparent forces or accelerations. that such systems will introduce,Moving control volume. dV u uV n dA 0 16,udV u u uV n dA G dV T dA 17,dt V V V V. e dV e u uV n dA,dt V 2 V 2,G u dV T u dA q n dA 18.
sdV s u uV n dA n dA 0 19,dt V V V T,Stationary control volume. dV u n dA 0 20,udV uu n dA G dV T dA 21,dt V V V V. e dV e u n dA,dt V 2 V 2,G u dV T u dA q n dA 22,sdV su n dA n dA 0 23. dt V V V T,1 FUNDAMENTALS 3,1 3 1 Simple Control Volumes. Consider a stationary control volume V with i 1 2 I connections or openings through which there is. fluid flowing in and j 1 2 J connections through which the fluid is following out At the inflow and. outflow stations further suppose that we can define average or effective uniform properties hi i ui of the. fluid Then the mass conservation equation is,dV Ai m i Aj m j 24.
dt dt V i 1 j 1, where Ai is the cross sectional area of the ith connection and m i i ui is the mass flow rate per unit area. through this connection The energy equation for this same situation is. e gz dV Ai m i hi gzi,dt dt V 2 i 1,Aj m j hj gzj Q W 25. where Q is the thermal energy heat transferred into the control volume and W is the mechanical work. done on the fluid inside the control volume,1 3 2 Steady Momentum Balance. For a stationary control volume the steady momentum equation can be written as. uu n dA P n dA G dV n dA Fext 26, where Fext are the external forces required to keep objects in contact with the flow in force equilibrium. These reaction forces are only needed if the control volume includes stationary objects or surfaces For a. control volume completely within the fluid Fext 0,1 4 Vector Calculus.
1 4 1 Vector Identities, If A and B are two differentiable vector fields A x B x and is a differentiable scalar field x then. the following identities hold,A B B A A B A B B A 27. A B B A A B B A A B 28,A A 2 A 31,1 4 2 Curvilinear Coordinates. Scale factors Consider an orthogonal curvilinear coordinate system x1 x2 x3 defined by a triad of unit. vectors e1 e2 e3 which satisfy the orthogonality condition. ei ek ik 33,1 FUNDAMENTALS 4,and form a right handed coordinate system. e3 e1 e2 34,The scale factors hi are defined by,dr h1 dx1 e1 h2 dx2 e2 h3 dx3 e3 35.
The unit of arc length in this coordinate system is ds2 dr dr. ds2 h21 dx21 h22 dx22 h23 dx23 37,The unit of differential volume is. dV h1 h2 h3 dx1 dx2 dx3 38,1 4 3 Gauss Divergence Theorem. For a vector or tensor field F the following relationship holds. F dV F n dA 39, This leads to the simple interpretation of the divergence as the following limit. F lim F n dA 40,A useful variation on the divergence theorem is. F dV n F dA 41, This leads to the simple interpretation of the curl as.
F lim n F dA 42,1 4 4 Stokes Theorem, For a vector or tensor field F the following relationship holds on an open two sided surface S bounded by. a closed non intersecting curve S,F n dA F dr 43,1 4 5 Div Grad and Curl. The gradient operator or grad for a scalar field is. e1 e2 e3 44,h1 x1 h2 x2 h3 x3, A simple interpretation of the gradient operator is in terms of the differential of a function in a direction a. da lim x da x da 45,1 FUNDAMENTALS 5,The divergence operator or div is. F h2 h3 F1 h3 h1 F2 h1 h2 F3 46,h1 h2 h3 x1 x2 x3,The curl operator or curl is.
h 1 e1 h 2 e2 h3 e3,h1 h2 h3 h 1 F1 h 2 F2 h3 F3,The components of the curl are. F h3 F3 h2 F2,h2 h3 x2 x3,h1 F1 h3 F3,h3 h1 x3 x1,h2 F2 h1 F1 48. h1 h2 x1 x2,The Laplacian operator 2 for a scalar field is. 2 1 h2 h3 h3 h1 h1 h2,h1 h2 h3 x1 h1 x1 x2 h2 x2 x3 h3 x3. 1 4 6 Specific Coordinates,x1 x2 x3 x y z h1 h2 h3.
x y z x y z 1 1 1,Cylindrical,r z r sin r cos z 1 r 1. r r sin cos r sin sin r cos 1 r r sin,Parabolic Cylindrical. u2 v 2 uv z u2 v 2 h1 1,Paraboloidal,u v uv cos uv sin 2. u2 v2 u2 v 2 h1 uv,Elliptic Cylindrical p, u v z a cosh u cos v a sinh u sin v z a sinh2 u sin2 v h1 1. Prolate Spheroidal p, a sinh sin cos a sinh sin sin a cosh cos a sinh2 sin2 h1 a sinh sin.
1 5 Differential Relations,1 5 1 Conservation form. The equations are first written in conservation form. density flux source 50,1 FUNDAMENTALS 6, for a fixed Eulerian control volume in an inertial reference frame by using the divergence theorem. u uu T G 52,e u e T u q G u 53,1 6 Convective Form. This form uses the convective or material derivative. e T u q G u 58,Alternate forms of the energy equation. e P u u q G u 60,Formulation using enthalpy h e P,h u q G u 61.
Mechanical energy equation,u P u G u 62,Thermal energy equation. P v u v q 63,Dissipation,u ik sum on i and k 64,1 FUNDAMENTALS 7. 1 7 Divergence of Viscous Stress, For a fluid with constant and v the divergence of the viscous stress in Cartesian coordinates can be. reduced to,2 u v u 66,1 8 Euler Equations,Inviscid no heat transfer no body forces. 1 9 Bernoulli Equation,Consider the unsteady energy equation in the form.
h u q G u 71, and further suppose that the external force field G is conservative and can be derived from a potential as. then if x only we have,The Bernoulli constant is, In the absence of unsteadiness viscous forces and heat transfer we have. H constant on streamlines, For the ordinary case of isentropic flow of an incompressible fluid dh dP in a uniform gravitational. field g z z we have the standard result,P gz constant 76. 1 FUNDAMENTALS 8,1 10 Vorticity,Vorticity is defined as.
and the vector identities can be used to obtain,u u u u 78. The momentum equation can be reformulated to read,H h u T s 79. 1 FUNDAMENTALS 9,1 11 Dimensional Analysis,Fundamental Dimensions. L length meter m,M mass kilogram kg,T time second s. temperature Kelvin K,I current Ampere A,Some derived dimensional units.
force Newton N M LT 2,pressure Pascal Pa M L 1 T 2. bar 105 Pa,energy Joule J M L2 T 2,frequency Hertz Hz T 1. power Watt W M L2 T 3,viscosity Poise P M L 1 T 1, Pi Theorem Given n dimensional variables X1 X2 Xn and f independent fundamental dimensions. at most 5 involved in the problem, 1 The number of dimensionally independent variables r is. 2 The number p n r of dimensionless variables i,that can be formed is.
Conventional Dimensionless Numbers,Reynolds Re U L. Mach Ma U c,Prandtl Pr cP k,Strouhal St L U T,Knudsen Kn L. Peclet Pe U L,Schmidt Sc D,Lewis Le D, Reference conditions U velocity vicosity D mass diffusivity k thermal conductivity L length scale. T time scale c sound speed mean free path cP specific heat at constant pressure. Parameters for Air and Water Values given for nominal standard conditions 20 C and 1 bar. 1 FUNDAMENTALS 10,shear viscosity kg ms 1 8 10 5 1 00 10 3. kinematic viscosity m2 s 1 5 10 5 1 0 10 6,thermal conductivity k W mK 2 54 10 2 0 589.
thermal diffusivity m2 s 2 1 10 5 1 4 10 7,specific heat cp J kgK 1004 4182. sound speed c m s 343 3 1484,density kg m3 1 2 998. gas constant R m2 s2 K 287 462,thermal expansion K 1 3 3 10 4 2 1 10 4. isentropic compressibility s Pa 1 7 01 10 6 4 5 10 10. Prandtl number Pr 72 7 1,Fundamental derivative 1 205 4 4. ratio of specific heats 1 4 1 007,Gru neisen coefficient G 0 40 0 11.
2 THERMODYNAMICS 11,2 Thermodynamics, 2 1 Thermodynamic potentials and fundamental relations. de T ds P dv 80,enthalpy h s P e Pv,dh T ds v dP 81. Helmholtz f T v e Ts,df s dT P dv 82,Gibbs g T P e Ts Pv. dg s dT v dP 83,2 2 Maxwell relations,Calculus identities. Fluid Mechanics 101 A Skeleton Guide J E Shepherd Aeronautics and Mechanical Engineering California Institute of Technology Pasadena CA USA 91125

Related Books

2007 Buick Rendezvous Owner Manual M

2007 Buick Rendezvous Owner Manual M

Buick Motor Division whenever it appears in this manual This manual describes features that may be available in this model but your vehicle may not have all of them For example more than one entertainment system may be offered or your vehicle may have been ordered without a front passenger or rear seats

Baseball Division Event Hosting Manual

Baseball Division Event Hosting Manual

Page 2 of 17 Appendix 2 Event Hosting Manual Women s Baseball World Cup BIDDING PROCEDURES FOR WBSC BD EVENT In order to bid to host an WBSC BD Event formal documents need to be submitted to the WBSC BD office 3 years before the proposed Event year WBSC BD office will then review the submitted applications and will bring to the WBSC BD Executive Board for final approval The final

DocuSign Envelope ID 32F281CD 0E00 41A3 A0E9 2F89DAA47812

DocuSign Envelope ID 32F281CD 0E00 41A3 A0E9 2F89DAA47812

2 1 Roles of the Parties The parWie acknoledge and agree haW Zih regard Wo he ProceVing of PerVonal Daa CVomer i he Conroller SFDC i he ProceVor and haW SFDC or memberV of Whe SFDC Grop Zill engage SXb proceorV pXranW o he reqXiremen VeW forh in Secion 2 2 CXVomer Vhall in iV Xe of Whe SericeV ProceVV Peronal Daa in accordance

The ISV Business Case For Building SaaS on Amazon Web

The ISV Business Case For Building SaaS on Amazon Web

Amazon Project Directors Sarah Musto August 2016 The ISV Business Case For Building SaaS on Amazon Web Services AWS A SaaS sales growth rates are 100 in Year 2 90 in Year 3 60 in Year 4 and 50 in Year 5 The annual average revenue churn rate is 5 The composite ISV develops new and complementary products for cross and upsell purposes TABLE 1 Five Year Pro Forma

Watches Style Guide Amazon S3

Watches Style Guide Amazon S3

help in driving traffic and sales but also inspire a customer to spend more time shopping for your products to discover a selection matching his style latest trends and preferences The standard amazon product detail pages have various components which directly impact the customer s online buying experience These key features have been

Getting started with in the U S marketplace

Getting started with in the U S marketplace

Getting started with FBA Create an FBA shipment from converted inventory If you have converted a listing to FBA but not yet created a shipment or if you are already using FBA and need to replenish your inventory you can use this step to create a shipment so you can send your items to a U S Amazon fulfillment center 1

Appendix 2 Sales Page Amazon S3

Appendix 2 Sales Page Amazon S3

Appendix 2 Sales Page Sales Page Copy Example The MOST Complete Facebook Marketing Training Created To Date Giving You The A Z of Social Marketing Coupled With Powerful Strategies To Increase Your Client Base by 100 So You Can Finally Generate thousands of leads Tons of traffic or make 100 MORE Money selling digital and physical items over Facebook Click PLAY to watch how this

ACI Hebdo diktio kapa dos gr

ACI Hebdo diktio kapa dos gr

anniversaire de l ACI Europe comme une r gion part enti re Cependant ce ne fut pas le moment de regarder en arri re mais plut t de se projeter vers le futur Les d l gu s ont approuv la strat gie d une plate forme unique d activit s pour l ACI Europe et le Comit de Coordination des Associations Coop ratives Europ ennes CCACE Cette plate forme connue sous la d n

Conf rence de presse aeroport fr

Conf rence de presse aeroport fr

ACI Europe En 2016 les a roports r gionaux voient leur trafic fret augmenter significativement par rapport 2015 9 9 tandis que les a roports parisiens ont une hausse plus modeste 1 8 Il est vrai que les a roports en r gion partent de loin La baisse continue pour les a roports d outre mer 1 Les a roports parisiens concentrent 86 1 du fret m tropolitain contre

ACI EUROPE Airport Exchange Airport IT Seminar

ACI EUROPE Airport Exchange Airport IT Seminar

ACI Airport Service Quality amp Facilitation Conference 2 Contents 1 Facts on Narita Airport 2 Big change in Narita Alliance partners under One Roof 100 EDS Inline Screening system Departure lobbies renewal 3 e Airport project Government IT Strategy HQ Decision e Airport Concept at Narita Overview of e Check in Trials in 2004 Results of e Check in Trials from 02 to 04

OUTLINE SPEECH AT ACI WORLD AND ACI EUROPE

OUTLINE SPEECH AT ACI WORLD AND ACI EUROPE

ACI WORLD AND ACI EUROPE AIRPORT ECONOMICS AND FINANCE CONFERENCE 10 February 2009 ERRATIC TIMES THE NEW CONSTANT Angel Gittens Director General Airports Council International When we began planning this conference some six months ago we thought that the new constant for our industry was high energy and commodity prices That almost seems like a golden era now In 2008 we watched the