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82 Cards in this Set
- Front
- Back
continuum
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where there are enough particles in a fluid so that the mean free path is extremely short
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where does continuum fail?
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in the outer edges of the rarefied atmosphere and during reentry from space
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mean free path
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average distance a molecule travels before colliding with another
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compressible v incompressible
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fluids are usually incompressible, air is usually compressible
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incompressible flow
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flow with a constant density
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laws of conservation
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mass, newton's 2nd law: F=ma (d(mv)/dt)), and energy
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Pressure
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Force normal to the surface per unit area due to random molecular motion (aka static pressure)
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rarefied/noncontinuous flow
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where there arent enough particles in the flow to consider it continuous
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knudsen number
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how to tell if a flow is continuous, if Kn <0.2
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Continuous Flow
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Flows which contain many, many particles: dont need to follow individual particles for fluctuations in density or pressure
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mass flow rate
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the net rate at which mass passed through a control surface over time
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uniform flow
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a flow in which all velo vectors are equal in a given plane
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volume flow rate
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net rate at which volume pases through a given C.S. over time
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C.V. approach
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volume fixed in space (stationary) through which flow is observed. Eulerian approach utilizes this approach
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Eulerian approach
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apply conserv. laws to finite and infinite C.V.'s to develop fluid dynamic equations
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C.M. approach
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a system that always contains the same amount of particles and which moves with the fluid. Lagrangian approach utilizes this approach.
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Lagrangian approach
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apply conserv. laws to finite and infinite C.M.'s to develop fluid dynamic equations
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conservation of mass
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mass can't be created/destroyed
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What conditions are the continuity equation valid for?
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1. Steady/Unsteady
2. Incompressible/Compressible 3. Viscous/Inviscid 4. BUT MUST BE A CONTINUOUS FLOW |
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What does steady mean in terms of equations?
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that all d/dt equations go to zero
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Viscous Forces
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shear and normal frictional forces acting on the c.s.
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Incompressible flow
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flow in which density is constant
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Body Forces
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Forces which act on a flow from great distances- Grav, E&M forces
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Surface Forces
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Forces which affect the surface of the flow: Pressure and Viscous
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Pressure Forces
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always acts normal to the c.s. C.s. may be real like the wall or imaginary.
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Reaction Force
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the force at which the object acts on the fluid (may contain both shear and pressure forces)
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rake
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measures flow velo, pres, and or other quantities
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wake
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region of flow downstream of the body which has been disturbed by it
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streamline
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curve along which the flow velo is tangent. For steady flow: streamline=pathline. Streamline is the "snapshot"
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What is the pressure of a flow in the atmosphere?
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The same as the press of the atmosphere
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Surface Tension
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interaction b/t one liquid and a 2nd or a gas. Molecules deep in the liquid are close-packed and want to repel where as the ones at the surface attract because they are not dense.
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vapor pressure
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pressure at which a liquid boils and is at equilibrium
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psia
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absolute press
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psig
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gauge press (usually measured from standard pressure of sea-lvl)
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Substantial deriv
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expresses time rate of change or a property as we follow a single moving fluid element (aka material deriv)
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streamtube
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area between 2 streamlinea
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pathline
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the total path of a fluid element, much like the "long exposure" of a camera
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boundary layer
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thin region of fluid adjacent to surface, dominated by the viscous effects
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vorticity
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when the fluid element spins b/c it is dragged faster by viscous forces at the top than at the bottom
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stagnation pressure
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total pressure= P +0.5(p)(V^2)
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what is circulation due to?
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vorticity (vortex sheets)
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why is circulation important?
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Because it is directly related to lift
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Assumptions for Bernoulli
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Inviscid, steady, and incompressible
@ rotational flow- holds for streamline only @ irrotational flow- holds everywhere |
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What does the Laplace allow us to do?
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Allows us to superimpose the P.D.E's of flows in order to simplify them (due to its linearity)
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Doublet
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source-sink flow, strength is constant, and has a distance of delta (lowercase)
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Adverse P.G.
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region of flow in which pressure increases along streamline
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favorable P.G.
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region of flow in which the pressure decreases along the streamline
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What does an Adverse P.G. do to a B.L?
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in viscous flow, causes it to go unstable and separate. Can also cause it to transition to turbulence quicker.
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D'alembert's paradox
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a body w/ constant velocity in incompressible, inviscid flow created zero drag, however this is not the case in real life because flow is viscid and tends to seperate
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What must be generated for lift to exist?
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circulation
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spinning cylinder
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surface friction on cylinder causes fluid to speed up faster on upper surface rather than lower
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Kutta condition
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for a body with a sharp T.E. The circulation value must be one that keeps the flow from going around the T.E.
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Why do most airfoils have sharp T.E?
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The kutta condition, which causes the circulation to be greater and gives the airfoil a greater lift efficiency
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Kelvins Circulation Theorem
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circulation around a closed path is constant
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When to vorticies start?
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When circulation changes
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mean camber line
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locus of points midway b/t upper/lower surfaces
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Drag
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forces in the streamwise direction
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Lift
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forces in the perpendicular direction
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Assumptions for thin airfoil theory
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1. Inviscid
2. Irrotational 3. Must be "thin" thickness ratio <10% 4. must be an airfoil (2-D) 5. incompressible 6. steady 7. continuous flow 8. assumes angle of atk is small 9. max camber is small |
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What is the lift-curve slope?
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2 pi
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what happens at a high angle of atk
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flow seperates and pressure distribution changes drastically, causing plane to stall
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pitching moment
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tendency to rotate at a given point
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at what angle of attack does stall occur?
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around 15 degrees
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What is pitching moment considered when nose-up?
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positive
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at the center of pressure, what is the moment?
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Moment at center of pressure is ZERO because the forces balance, therefore Cm is also zero
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aerodynamic center
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location where the moment is independent of the angle of atk
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angle of attack (lo)
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angle of attack of zero lift
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What does viscosity help predict?
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Drag, and onset of seperation and stall
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Viscocity
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Molecular diffusion of energy and momentum across streamlines
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no-slip boundary
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where the fluid velocity is zero right along the wall
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Laminar Flow
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Involves molecular transverse exchange of momentum
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Turbulent Flow
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Involves macroscopic transverse exchange of momentum
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Transitional Flow
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flow which is transitioning from laminar to turbulent
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Navier-Stokes Eqns
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set of eqns that describe continuous flows - inc the conserv, eqns
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reynolds #
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nondimensional # related to viscosity, lower-thick, higher- thin
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delta
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thickness of BL
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delta*
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distance through which the external inviscid flow is displaced by the B.L.
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Blasius assumptions
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1. laminar
2. flat plate 3. no press gradient 4. viscosity is constant 5. incompressible 6. steady 7. high Reynolds # |
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Transition factors
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1. Location of flow
2. Geometry 3. Pressure Gradient 4. Surface Roughness 5. Freestream level of turbulence 6. Heating 7. Mach # 8. Wall section |
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Falkner-Skan eqns
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analysis of flat plate B.L. with P.G's, describes only laminar flow flow
- no separated regions either |
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Laminar Flow Characteristics
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1. Laminar is easier to seperate
2. Lower Rn 3. lower skin friction /skn fric drag 4. thinner B.L. 5. Microscopic transfer of momentum |
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Turbulent Flow Characteristics
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1. harder to seperate
2. higher Rn 3. higher skin friction /skn fric drag 4. thicker B.L. 5. macroscopic transfer of momentum |