# Inclined settling device can give a much higher sedimentation rate ...

Mechanics

Feb 22, 2014 (4 years and 2 months ago)

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Unit Operation(II)

First Exam. 9
2
,
3/29

Prob.1 (
40
%)

(1)

(a)cake filtration, (b)deep bed filtration

(c)cross flow filtration

(10%)

(2)

(3)

free settling

hindered settling

(4)

cyclone

(5)

(6)

Q
1

cut point diameter

D
pc,1
，則當體積流率提高至
2Q
1

cut point
diameter

Prob. 2 (2
5
%)

The particle size distribution of a powder with
cubical
particles
(

) measure
d by
sieving analysis
is reported as :

f(D
p
)

mass (1/mm)

frequency

D
p
(
m
m)

(a)

Calculate the cumulative mass fraction for D
p
= 4 mm of the powder,

(b)

Calculate the cumulative number fraction fo
r D
p
= 4 mm of the powder,

(c)

Calculate the specific surface area per unit volume of the powder in m
2
/m
3
.

Prob.3 (
20
%)

A concentrated slurry consisting of particles of density 2800 kg/m
3

and size 200
μ
m in
water

=1000 kg/m
3
,

=1.0cp)

is designed to be thickened by gravity sedimentation. If the
particles are spherical and the mass fraction of particles in the slurry is 0.15, estimate the
settling velocity of the slurry by the empirical re
lation as v
t
=v
ts
ε
4.65
, where
ε
is the
volumetric fraction of liquid in the slurry.

Prob.4 (15%)

The filtration equation for a slurry

filtered under
constant pressure

drop

,
Δ
P,
is reported as

V
t
K
1
Δ
P

0.5
V+

K
2
Δ
P

1.0

where

t is in s

,

V in m
3

,
Δ
P in N/m
2
, and K
1

and K
2

are constants. If now a filter of surface
A is used for the slurry and designed to operate at a constant rate, v, where v is in m/s,
estimate the running time t for reaching the maximum pressure drop,
Δ
P
max
, permissib
le for
the filter (

).

Given Eqs.:

cake filtration:
PA
Δ
R
μ
V
pA
Δ
C
μα
dV
dt
m
2
av

Stoke’s law

(for N
Re,P
<1.0)
for a spherical sphere settling by gravity:

μ
18
gD
v
2
p
t
p

For N
Re,p

in the range from 1 to 10
4
, the drag coefficient for sphe
re is

34
.
0
3
24
Re,
Re,

p
p
D
N
N
C