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Transport phenomena
momentum, heat, mass, fluid mechanics
flux
rate of transfer or flow of a physical quantity per unit area per unit time
fluid
substance that deforms continuously under the action of a shear stress (gases/liquids)
continuum
continuous distribution of matter
The smallest volume of interest in a continuum is large enough _____
to make statistical averages meaningful
Continuum NOT applicable
for small volumes of gas at rest because time dependent
Continuum variation in properties is smooth
to make differential calculus useful for analysis
Density
mass/volume
Fluid property
density, specific heat, viscosity, surface tension
flow property
velocity, shear stress, concentration flux, temp flux
stress
force/area
2nd order tensor
an ordered array which is completely determined by specifying its 9 components
Surface forces
friction, pressing, shear stress
Body Forces
gravity, magnetism, electrical potential
compressible fluid
fluid where density varies under normal conditions
incompressible fluid
fluids where density is constant
surface tension
work associated with creating a new surface
capillary pressure
a pressure difference resulting from surface tension
Contact Angle is 0
for a clean glass tube
Newton's First Law
a body will remain at rest or in motion unless acted upon by an external force
Newton's Second Law
the sum of the forces on an object is equal to mass x acceleration
Newton's Third Law
to every action there is an equal and opposite reaction
Inertial reference frame
the coordinate system is fixed with respect to the earth
non-inertial reference frame
uniformly translating coordinate system
manometer
device for measuring pressure
Pascal's principle
the pressure in a fluid at rest must be the same at all points with the same elevation
Absolute pressure
gauge pressure + atmospheric pressure
buoyant force
vertical component of the pressure force integrated around the entire surface of a solid
Archimedes principle
a floating body displaces a volumes of fluid whose weight is equal to its own
field
a quantity defined as a function of position and time throughout a given region
steady flow
flow that is independent of time
unsteady flow
flow dependent on time
streamline
a line everywhere tangent to the velocity vector at a given instant in a flow field
pathline
the actual path of the fluid
Streamlines and pathlines
are exactly corresponding in steady flow
system
a collection of entities enclosed in a set of identifiable boundaries
control volume
region in space through which fluid flows
open system
allows mass transfer across boundaries
closed system
does not allow mass transfer across boundaries
extensive property
depends on an element of matter (mass, energy, momentum)
intensive property
independent of amount of matter (pressure, temperature, color)
Inertial Delta P =
rho g
Non intertial Delta P =
rho (g-a)
Inertial F=
0
Noninertial F=
ma
mass flow rate =
pho v A
volumetric flow rate
v A
Soap surface pressure delta P =
4 sigma / R
1st Law of Thermodynamics
Energy can neither be created nor destroyed
Positive Work
done by the system
Negative Work
done on the system
Bernoulli assumptions
Steady flow
incompressible
inviscid
isothermal
no change in internal energy
no shaft work
Toricelli eq conditions
small inlet, large outlet
head loss
change in internal energy
viscosity
property of a fluid to resist the rate at which deformation takes place when a fluid is acted upon by a shear stress
Newtonian fluid
constant viscosity, linear relationship between shear stress and shear rate
Non-newtonian fluid
does not obey Newton’s Law of viscosity, shear stress and shear rate not linearly related
pseudoplastic
materials that decrease in viscosity with increased shear, shear-thinning
dilatent
materials that show an increase in viscosity with increase shear, shear-thickening
bingham plastic
requires a finite yield stress before flow begins
no slip boundary condition
fluid at the boundary will move at the same velocity as the boundary
laminar flow
flow is gentil with parallel streamlines
fully developed flow
steady flow, no entry/exit effects, flow does not vary along the axis of the flow
shear stress profile in circular pipe
approximately 0 in the middle and maximum at the walls
HP equation assumptions
laminar
steady
FDF
continuous
newtonian
no slip
incompressible
Partial time derivative
local derivative, assumes fixed position observer
total time derivative
d/dt, moving observer
substantial time derivative
D/Dt, observer moving with system, time rate of change of a fluid or flow variable along the path of fluid element
Continuity equation
DP/Dt = -rho( del dot v), describes the rate of change in the density as seen by an observer moving with the fluid
Continuity eq for incompressible fluid
del dot v = 0
Vector form of NS eq
rho(Dv/Dt)=rho(g)-delP+mu(del^2 v)
Assumptions for NS eq
incompressible, constant viscosity, laminar/turbulent
Euler’s eq
for inviscid flow, rho(Dv/Dt) = rho(g)-delP
vorticity
rotation of a fluid element, a measure of the moment of momentum of a small fluid particle about its own center of mass
vorticity (mathematical)
the curl of the velocity vector
irrotational flow
regions where flow properties have no net rotation, inviscid regions of flow far away from solid walls
kinematics
a branch of dynamics dealing with motion in time and space disregarding mass and force
Velocity potential
exists in 3D, flow must be irrotational
Orthogonal
The velocity potential and stream function are this to each other
source flow
radially upward from an origin
sink flow
directed toward an origin
geometric similarity
exists between 2 systems if ratios of significant dimensions are equal
kinematic similarity
if geometric sim exists and all velocity ratios are equal
dynamic similarity
if all relevant dimensionless numbers are identical between 2 systems
foundational units
mass, length, time
Froude number
inertial force/gravity force: v^2/gL
Euler number
pressure force/inertial force: P/rho v^2
Reynold’s number
rho v L/mu
2300
Re threshold for circular pipes
drag force
caused by shear stresses at the surface of a solid object moving through a viscous fluid
BLT hypothesis
the effects of fluid motion at high Re are limited to a thin layer of fluid near the boundary
BLT assumptions
a thin boundary layer at high Re, incompressible flow, 2D flow over flat plate
3x10^6
Re threshold for turbulent flow on a flat plate
2x10^5
Re threshold for laminar flow on a flat plate
wall turbulance
contact of the flowing stream with solid walls or boundaries
free turbulance
contact of 2 layers of fluid with different velocities
eddies
groups of fluid particles of various sizes
Leq
length of pipe that produces head loss equivalent to the head loss in a particular fitting
elevation head
fluid elevation above an arbitrary level, proportional to liquid’s PE
velocity head
height of a column of liquid that can be supported when a liquid is forced to stop, proportional to KE