# Fundamentals Of Fluid Mechanics - MIT OpenCourseWare

2y ago
55 Views
285.93 KB
13 Pages
Last View : 9d ago
Transcription

16.121 ANALYTICAL SUBSONIC AERODYNAMICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGYFundamentals of Fluid Mechanics1 F UNDAMENTALS OF F LUID M ECHANICS1.1 A SSUMPTIONS1. Fluid is a continuum2. Fluid is inviscid3. Fluid is adiabatic4. Fluid is a perfect gas5. Fluid is a constant-density ﬂuid6. Discontinuities (shocks, waves, vortex sheets) are treated as separate and serve as boundariesfor continuous portions of the ﬂow1.2 N OTATION0p pressure (static)ρ densityT temperature (absolute)Q velocity vector of ﬂuid particlesQ U i V j WkV control volume0S surface surrounding Vσ impermeable bodyn normal directed into the ﬂuidR gas constantF body force per unit massF ΩΩ potential of the force ﬁeldGravity ﬁeld: F g k; Ω g zph enthalpy per unit mass; h e ρc p speciﬁc heat at constant pressurec v speciﬁc heat at constant volumeγ c p /c ve internal energy per unit masss entropy per unit mass01.3 C ONTINUITY E QUATION ρ (ρQ) 0 tDρ ρ Q 0DtÑÓ ρρ(Qn)d s 0 0dV 0 V 0 tS 0 VÑ hi ρ (ρQ) dV 0 0V 0 t1

1.4 C ONSERVATION OF M OMENTUMXÑFi iV0DQ p F DtρÓ (ρQ)dV 0 ρQ(Qn)d s 0 tS 0 V1.5 C ONSERVATION OF T HERMODYNAMIC E NERGYD hQ2 i · (pQ)e F ·QDt2ρD hQ 2 i pρh ρF · QDt2 t1.6 E QUATION OF S TATEp RρT(thermally perfect gas)c p , c v constants (calorically perfect gas)2 P RESSURE DISTRIBUTION AND COMPRESSIBILITY2.1 A SSUMPTIONS1. Steady ﬂow2. Inviscid ﬂuid3. No discontinuities (shocks)4. Perfect gas5. One-dimensional motion6. Adiabatic ﬂow7. F 08. Isentropic2.2 N OTATION( )0 stagnation conditions, Q 0( ) free stream conditions, Q u c u c( ) conditions on body surface (airfoil)Q u 0 i u 0 j ωku 0 u γu2

2.3 E NERGY E QUATIONSh e pρih1d h Q2 02(Heat content plus kinetic energy is constant)2.4 P ERFECT G AS R ELATIONSp ρRTpV RTV 1ρCan show, without effort:ρV γ constant³ 1 γp constantρpa 2 γ , a speed of soundρr³ Q 2c p T0 Th³ p γ 1 iT iγ T0 1 T0 T T0 1 T0p0nh³ p γ 1 io 1γ2Q 2c p T0 1 p0h2.5 M ACH N UMBERM2 M2 22c p (T0 T ) 2c p (T0 T )Q p2aγRTγρ2c p³T0 1 2 ³ T0 1(γ 1) Tγ(c p c v ) TT0 hγ 1 2i 1 M β(γ, M )T2γγp 0 ³ T0 γ 1 β γ 1pT³1ρ0T0 γ 1 1 β γ 1ρT3

2.6 OTHER USEFUL FORMS , EXPRESSIONSQ 2 2c p (T0 T )p0 γRT0ρ0Q 2 2c p ³T 2 ³T 1 1 γRT0γ 1T0a 02³ Tγ 1 Q 2 1 2 a0T0γhpγ 1 ³ Q 2 i γ 1 1 2 a0p01ρ hγ 1 ³ Q 2 i γ 1 1 ρ02 a0a 02 γa 2 a 02 γ 1 2Q22.7 P RESSURE , VELOCITY RELATIONS IN ISENTROPIC FLOWWith some effort, one may show:γhpγ 1 2 ³Q 2 i γ 1 1 M 1 22u p Expanding the right-hand side:pγ³Q2 2 γ ³Q 2 2 4 γ(2 γ) ³Q 2 3 6 γ(2 γ)(3 2γ) ³Q 2 4 8 1 1 2 M 1 2 M 1 2 M 1 2 M .2u 8u 48u 384u p Obtain an expression forcp p p 122 ρ u LetQ u γV,γV¿1U Find c p and discuss its limitations.3 S IMILARITY OF FLOWS3.1 R EQUIREMENTS FOR SIMILARITY OF FLOWS1. Similarity in boundary geometryBoundary of one ﬂow can be made to coincide with that of another if its linear dimensions aremultiplied by a constant2. Dynamic constraintDependent variables of one ﬂow are proportional to those of another at the correspondingpoints.4

Example Problem - IllustrationConsider the dynamics of an incompressible ﬂuid ﬂow with constant.Equation of incompressibility:D p ρ ρ 0 uiDt t x iEquation of continuity: u i 0 x iIntroduce dimensionless variables:0ui ui

Fundamentals of Fluid Mechanics. 1 F. UNDAMENTALS OF . F. LUID . M. ECHANICS . 1.1 A. SSUMPTIONS . 1. Fluid is a continuum 2. Fluid is inviscid 3. Fluid is adiabatic 4. Fluid is a perfect gas 5. Fluid is a constant-density ﬂuid 6. Discontinuities (shocks, waves, vortex sheets) are treated as separate and serve as boundaries for continuous .

Related Documents:

Fluid Mechanics Fluid Engineers basic tools Experimental testing Computational Fluid Theoretical estimates Dynamics Fluid Mechanics, SG2214 Fluid Mechanics Definition of fluid F solid F fluid A fluid deforms continuously under the action of a s

Fluid Mechanics 63 Chapter 6 Fluid Mechanics _ 6.0 Introduction Fluid mechanics is a branch of applied mechanics concerned with the static and dynamics of fluid - both liquids and gases. . Solution The relative density of fluid is defined as the rate of its density to the density of water. Thus, the relative density of oil is 850/1000 0.85.

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 Bernoulli's Equation 7. General Energy Equation 8. Reynolds Number, Laminar Flow, Turbulent Flow and Energy Losses Due to Friction

Motion of a Fluid ElementMotion of a Fluid Element 1. 1. Fluid Fluid Translation: The element moves from one point to another. 3. 3. Fluid Fluid Rotation: The element rotates about any or all of the x,y,z axes. Fluid Deformation: 4. 4. Angular Deformation:The element's angles between the sides Angular Deformation:The element's angles between the sides

L M A B CVT Revision: December 2006 2007 Sentra CVT FLUID PFP:KLE50 Checking CVT Fluid UCS005XN FLUID LEVEL CHECK Fluid level should be checked with the fluid warmed up to 50 to 80 C (122 to 176 F). 1. Check for fluid leakage. 2. With the engine warmed up, drive the vehicle to warm up the CVT fluid. When ambient temperature is 20 C (68 F .

Continuum mechanics: fundamentals and applications Curriculum 5 1st semester (30 ECTS) rd Focus on basic competencies Mechanics and Thermodynamics of Continua (5 ECTS) Mechanics of Solids (6 ECTS): Elasticity, Plasticity Fluid Mechanics (5 ECTS) Computational Solid and Fluid Mechanics (4 ECTS) Mathematics in Natural Sciences

Chapter 06 Fluid Mechanics _ 6.0 Introduction Fluid mechanics is a branch of applied mechanics concerned with the static and dynamics of fluid - both liquids and gases. The analysis of the behavior of fluids is based on the fundamental laws of mechanics, which relate continuity of

Achieved a high qualification In Radiology such as American Board, ABRMI or equivalent. Has an experience of at least 3 years after the higher qualification. Of the rank of Consultant Radiologist. Is employed on a full time basis , in the selected training hospital/ center -6-4.2 - Responsibilities and Duties of the Trainer Responsible for the actual performance of the trainee. Look after the .