Chapter2Physical
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Transcript Chapter2Physical
Physical Characteristics
Dr. Muanmai Apintanapong
Physical Characteristics
Considering either bulk or individual units
of material.
– Shape, size, volume, specific gravity
surface area, bulk density and etc.
Size
Shape
Weight
Volume
Shape and size
Inseparable in a physical object
= (sh, s)
=
Index
sh
=
shape
s
=
size
Other applications
= (sh, s, o, p, f,…)
Y = b1X1+b2X2+b3X3+b4X4+b5X5
Irregular in shape
Seeds, grains, fruits and vegetables are
irregular in shape
important to know what criterion should
be used to decide when adequate number
of measurements has been made to define
the form of object.
Griffith (1964) : related volume (V) to their
axial dimension (a)
V = a1b1 a2b2 a3b3 … anbn
log V = b1 log a1 + b2 log a2 +….+ bn log an
Criteria for describing shape and size
Size : a representative dimension
In fruit and cereal: 3 main projected area
– a = length
– b = width
– c = thickness
Average dimension
Arithmatic mean size
length width thickness
3
Geometric mean size
(length width thickness)1 3
Size based on volume
V De De (6V )1 3
6
3
Average dimension
Size based on surface area
S A Ds Ds (S A )1 2
2
Size based on projected area
Ap Dp / 4 Dp (4 Ap )
2
12
Measuring Grain Dimension
Grain Type
very long
long
medium
short
Length (mm)
> 7.5
> 6.5 < 7.5
>5.5 < 6.5
< 5.5
Physical Properties>>shape
The concept of shape
factor
– Geometric
dimensions (L,W,T)
of various objects
are plotted against
their volumes,
surface areas or
projected areas
– The slope of
regression line
yields shape factor
(α)
V
αv
LWT
SA
αSA
(LWT)2/3
Ap
αAp
(LWT)2/3
Example
Axial dimension (cm)
Weight
(g)
Volume
(cm3)
a
b
c
apples
7.0
6.76
5.64
145.5
180.3
potatoes
8.2
7.2
5.3
204.0
184.0
tomatoes
6.45
5.92
4.72
127.3
126.2
Determine: v, density, equivalent diameter of
sphere, average diameter, geometric mean
diameter
Charted standards
Compare longitudinal and lateral cross section
with the shapes listed on a charted standard
Roundness
Measure of sharpness of the corners of the solid
Ap = largest projected area in natural rest position
Ac = area of smallest circumscribing circle
Roundness
r
Roundness
NR
r = radius of curvature as defined in figure
R = radius of maximum inscribed circle
N = total number of corners summed in
numerator
Roundness
r
Roundness
R
r = radius of curvature of the shapest
corner
R = mean radius of object
Sphericity
di
Sphericity
dc
di = diameter of the largest inscribed circle
dc = diameter of the smallest
circumscribed circle
Sphericity
de
Sphericity
dc
dc
de = diameter of a sphere of same volume of
object
dc = diameter of the smallest circumscribed
sphere (usually the longest diameter of
object)
Sphericity
Vol of solid
Sphericity
Vol of circum scribed sphere
Sphericity
abc
6
3
a
6
1
1
3
3
bc
2
a
1
3
abc
geom etricm eandiam eter
Sphericity
6
m ajordiam eter
a3
6
a = longest intercept
b = longest intercept normal to a
c = longest intercept normal to a and b
1
3
abc 3
1
a
Shape factor ()
SAof spherehavingsam evolum e
Shape factor( )
SAof object
Measurement of axial dimension
Use photographics enlarger to determine
a, b, c
Use shadowgraph
Resemblance to geometric bodies
Shape can be approximated by one of the
following standard geometric shapes:
– Prolate spheroid
– Oblate spheroid
– Right circular cone or cylinder
Resemblance to geometric bodies
Prolate spheroid
– Volume
V=
– Surface area
S=
A prolate spheroid is a
spheroid in which the polar
diameter is longer than the
equatorial diameter.
a, b = major & minor semi-axes of ellipse of rotation
1
e = eccentricity
2
b 2
e 1
V = volume
a
S = surface area
Resemblance to geometric bodies
Oblate spheroid
– Volume
V=
– Surface area
S=
An oblate spheroid is a
rotationally symmetric ellipsoid
having a polar axis shorter than
the diameter of the equatorial
circle whose plane bisects it.
a, b = major & minor semi-axes of ellipse of rotation
1
e = eccentricity
2
b 2
e 1
V = volume
a
S = surface area
Resemblance to geometric bodies
Frustum of right cone
– Volume
V=
– Surface area
S=
r1 & r2 = radii of base & top
h = altitude
A cone that has its apex aligned
directly above the center of its
base.
Right Circular Cylinder
A right cylinder with bases that are circles.
Resemblance to geometric bodies
Estimation of V and S in this manner
should be corrected.
Correction factor is determined by finding
actual
volume
and
surface
area
experimentally and establish correction
factor for the typical shape of each variety
of product.
Average projected area
Camera set up for recording the criterion
area (above left) of fruits and vegetables
for several orientations.
Average projected area
Based on Theory of Convex body (Bannesen
and Fenchel, 1948)
– Sphere:
V
6
D 3 , S D 2
2
3
D
V
6
1
3
3
S
36
D 2
2
– Nonsphere:
V2
1
3
S
36
Polya & Szega (1951)
Assume averaged projected area of convex
body = ¼ of surface area
For sphere:
V2
1
, S 4 Ap
3
S
36
2
V
1
3
36
4 Ap
Ap 1.21V
2
3
1
9 3
K
1.21
16
For nonsphere: K 1.21
Volume and Density
Platform balance method: for large objects
such as fruits and vegetables
wt. of displacedwater
V
wt. densityof water
wt. in air sp. gr. of water
specific gravity
wt. of displacedwater
Example
Assuming a specific gravity of 1.0 and a weight
density of 62.4 lb/ft3 for water, using a platform
scale method, the volume and specific gravity of
an apple was determined as follows:
– Weight of apple in air = 0.292 lb
– Weight of container+water = 2.24 lb
– Weight of container+water+apple submerged =
2.61 lb
– Weight of displaced water = 2.61-2.24 = 0.37
lb
Specific gravity balance
For smaller objects such as small fruits,
peas and beans, kernels of corn, etc.
Specific gravity balance
If solid is heavier than water:
V
wt. in air wt in water
wt. densityof water
wt. in air
SG of water
specific gravity
wt
.
in
air
wt
in
water
If solid is lighter than water (attach another
solid as sinker)
Wa object
SG of water
specific gravity
W
W
both
W
W
sin
ker
w
a
w
a
Wa = wt. in air
Ww = wt. in water
Specific gravity gradient tube
Fast and accurate
Ex: toluene & CCl4
(sp. gr. 0.87-1.59)
Measure the height
after object reaches
equilibrium and
calculated and
compared with
calibration curve.
Air comparison pycnometer
The density of a solid in any form can be
measured at room temperature with the gas
comparison pycnometer. The volume of a
substance is measured in air or in an inert
gas in a cylinder of variable calibrated
volume. For the calculation of density one
mass measurement is taken after
concluding the volume measurement.
Air comparison pycnometer
Pycnometer method
Specific gravity bottle and toluene
Toluene (C6H5CH3) has the advantages of:
– Little tendency to soak into the kernel
– Low surface tension, enabling it to flow smoothly
over kernel
– Little solvent action on constituents of kernel
especially fats and oils
– High boiling point
– Not changing its specific gravity and viscosity on
exposure to atmosphere
– Having low specific gravity
Pycnometer method
sg . gr. of tolueneat 20C wt. of grain
specific gravity
wt. of toluenedisplacedby grain
Example
Consider the volume measurement for a
sample of 16 corn kernels coated with
Pliabond
– Weight of sample = 4.4598 g
– Weight of pycnometer = 55.6468 g
– Weight of pycnometer+toluene = 78.2399 g
– Weight of pycnometer+toluene+sample =
79.6226 g
– Weight of pycnometer+water = 81.7709 g
Porosity
Void volume or pore volume (empty space)
relative to total volume
volum eof void
porosity
total volum e
volum eof void
void ratio
volum eof solid
void ratio porosity
porosity f (m oisturecontent, particlesize)
Porosity tank
V2
void volum e
V1
Example
To determine the porosity of dry shelled
corn, tank 2 of the apparatus is filled with a
sample of this corn to a bulk density of 47
lb/ft3. The pressure readings were P1 =
15.2 and P2 = 10.4 in Hg
Porosity
Porosity is also referred to as packing
factor (PF):
solid densityof particles densityof packing
PF
solid densityof particles
Porosity and bulk density
Weight and surface area
W
V
SA KW
23
Surface area
Leaf and stalk surface area
Light planimeter
Indirect estimation (projected area)
Surface coating method
– Estimated by the weight of coating material
– Material is coated on grains and glass beads of
known surface area (control).
Surfaceareasample
surfaceareaglass beads
Wglassbeads
Air permeability method
Wsample
Shape, Size and Area
Using image analysis
– The image analysis setup consists of a color CCD
camera and a circular lighting chamber connected to
a host Pentium II 400 MHz computer.
Top view of the Image Analysis Set up
CCD Camera
Illumination Chamber
Image Analysis Software
Two image analysis software are available for extracting the
dimensional feature of rice kernels
1. Image Tool 2: This program was developed at the
University of Texas Health Science center at San Antonio,
Texas and available from the internet
(http://ddsdx.uthscsa.edu/dig/download.html).
2. Particle Image Analysis: This program was developed
by Procure Vision AB Ltd., Stockholm, Sweden and the
evaluation version is available from the internet
(http://www.acoutronic.com).