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82 Cards in this Set

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