EXAM 3 Flashcards
describe sphericity
most useful single measure for characterizing shape of irregular and non spherical particles
eqn for sphericity
(surface of sphere/surface of particle) at same volume
what inequality with sphericity will always be true
sphericity ≤ 1
how do we measure size of an irregularly shaped particle?
effective diameter (dp)
what is the eqn that is always true for dp?
(sphericity)*(dsph)
what is dsph?
diameter of sphere with same volume
what is the equation for dsph?
(6V/pi)^(1/3)
what is bed voidage?
space not taken up in packed bed
what is the eqn for bed voidage?
(Vb-Vp)/Vb
what is relationship of dense packing to normal packing on bed voidage v. sphericity graph?
shifted down
what is relationship of loose packing to normal packing on bed voidage v. sphericity graph?
shifted up
Reynolds eqn for packed bed?
Rep = (dpuorho)/(viscosity)
what is uo? what does it represent?
superficial velocity … the velocity if there is no packed bed present
how many terms are in the ergun eqn for incompressible fluids? what do the terms represent?
2 …. viscous losses & turbulent/inertial losses
eqn for uo?
(bed voidage)*u
eqn for u with respect to uo?
u = uo/(bed voidage)
when can you disregard the turbulent term of the ergun eqn?
Rep < 20
when can you disregard the viscous term of the ergun eqn?
Rep > 1000
how many terms in the ergun eqn used for compressible fluids?
3 (Go eqn)
what happens if you continue to increase the velocity of a fluid flowing upward through solids?
frictional resistance will increase until resistance = weight of solids and solids become suspended (fluidized)
what is the uo needed to just fluidize solids called
minimum fluidization velocity (umf)
what happens as the flow rate continues to increase beyond umf for liquid?
fluidized bed keeps expanding
what happens as the flow rate continues to increase beyond umf for gas?
fluidized bed expands only slightly
what does Lm represent?
length of packed bed before fluidization
what does εm represent?
bed voidage before fluidization
what is the relationship of superficial velocity and umf before fluidization?
uo < umf
what does Lmf represent?
length of bed at point of minimum fluidization
what does εmf represent?
bed voidage at point of minimum fluidization
what is the relationship of superficial velocity and umf at point of minimum fluidization?
uo = umf
what does Lf represent?
length of bed while fluidized
what does εf represent?
bed voidage while fluidized
what is the relationship of superficial velocity and umf during fluidization?
uo > umf
what is the difference between liquid and gas fluidization?
liquid bed continues to expand while gas does not, and bubbles seen in gas fluidiz.
what does delta Pfr equal? (two things)
rho(g)*frictional loss and the ergun eqn w two terms
for low uo, what is true about delta Pfr?
it is proportionate to uo
for high uo, what is true about delta Pfr?
it is proportionate to uo^2
describe the difference in the uo v delta Pfr graph for packed beds versus fluidization?
fluidization curve follows packed bed curve until reaching mf, where it flattens to horizontal line
when does curve of fluidization flatten?
at mf, or when (calculated friction)packed > bed weight
when will solids fluidize?
when total drag force by fluid on particles = weight of solids in bed
(delta Pfr)*At = ? where At = cross sectional area of tube
AtLmf(1-ε)*(|rho(s)-rho(g)|(g)
what is the pump requirement eqn?
-Ws = frictional loss of bed = (delta Pfr/rhog)
at u>umf, what is true of frictional loss per unit of fluid through bed?
practically unchanged
what is true of pump power at u>umf?
will change in proportion to uo
the intersection of delta Pfr eqns represents
minimum fluidization condition
if bed voidage and sphericity unknown, what eqn do you use?
one including “- 28.7”
forces causing particle to accelerate =
net weight of particle - drag force
Cd represents
drag coefficient
what is true of du/dt at terminal velocity
=0
ut represents
terminal velocity
how to differentiate ut at low Re
eqn without square root
Reynolds eqn at terminal velocity
Resph,t = (dsphutrhog)/viscosity
how to differentiate Cd at low Re
eqn containing 24
Reynolds eqn for non spherical particle
Re = (dsphurhog)/viscosity
when Ret>1, describe how to differentiate eqns used
to -3 or 1/3 power
describe relationship between mesh size and diameter?
higher mesh, smaller particle
describe relationship between diameter, terminal velocity, and mesh?
larger terminal velocity, larger diameter, smaller mesh
what happens to bed voidage as bed fluidizes?
it increases
example of packed bed?
cigarette, soil in pot
what two terms are equivalent in a force balance at minimum velocity for individual particle?
drag force and gravity
steps to calculate sphericity?
- calculate volume 2. set = vol(sphere) 3. calculate radius of sphere 4. calculate surface area of particle 5. calc surface area of sphere 6. divide surface area of sphere by surface area of particle
