Professional Engineering
Review Session
Materials Properties (5.D.)
Steve Hall, Ph.D., P.E.
shall5@lsu.edu
Louisiana State University AgCenter
Current NCEES Topics
Primary coverage:
V. D. Materials Properties; Bulk Solids
Exam %
4%
Overlaps with:
I. D. 1.
I. D. 2.
V. C.
Mass and energy balances
~2%
Applied psychrometric processes ~2%
Mass transfer between phases
4%
References
PE Review Manual; FE Review Manual
Ma, Davis, Obaldo, Barbosa, 1998. Engineering
Properties of Foods and Other Biological
Materials, ASAE.
Mohsenin,1986. Physical Properties of Materials
Rao, Rizvi, Datta, 2005. Engineering Properties
of Foods.
Merva, 1995. Physical Principles of the Plant
Biosystem.
Reynolds and Richards, 1996. Unit Operations
and Processes in Environmental Engineering.
Standards
D241.4: Density, specific gravity and massmoisture relationships of grain for storage
D243.e: Thermal properties of grain and
grain products
D245.5: Moisture relationships of plantbased ag products
EP545: Loads exerted by free-flowing grain
on shallow storage structures (S&E)
Hellevang, AE-84, Temporary grain storage,
http://www.ag.ndsu.edu/publications/landingpages/crops/temporary-grain-storage-ae-84
Specific Topics
Rheology
Density, specific gravity
Moisture content in ag and food products
Thermal properties of grain and grain products
Loads on structures from grain/flowing products
Bonus: Psychrometrics (moisture 5D; ID
Psychrometrics)
Rheology:
The study of deformation and flow of
matter (especially interesting in
agricultural and biological materials)
Stress/Strain at the atomic level
Stress/Strain
• Stress s = Fnormal to area/A
• Shear Stress t = Fparallel to area/A
• Strain e=dL/Lo [m/m; or %]
• Young’s modulus E: s = Ee or E = s/e
• For bar, d = PL/AE or FL/AE
Tension
compre
Stress-strain
Stress/strain for steel and rubber
a) linearity (E constant?)
b) average E typically lower in biomaterials
Hair
Hysteresis cycles of a rubber
Stress vs. Conventional Strain
Conventional: F/Aoriginal
True Stress: F/Aactual
Reminder: Stress/Strain
• Stress s = Fnormal to area/A
• Shear Stress t = Fparallel to area/A
• Strain e=dL/Lo [m/m; or %]
• Young’s modulus E: s = Ee or E = s/e
• For bar, d = PL/AE or FL/AE
Tension
compre
Sample problem
• A steel bar with known dimensions is
subjected to an axial compressive load. The
modulus of elasticity and Poisson’s ration
are known. What is the final thickness of
the bar?
• A) 19.004mm
• B) 19.996mm
• C) 20.00mm
• D) 20.004mm
Sample problem, food materials
emphasis
• A block of cheese with known dimensions
is stacked and thus subjected to an axial
compressive load. The modulus of
elasticity and Poisson’s ration are known.
What is the final thickness of the sample?
Stress-Strain Models
Creep behavior of cheddar cheese
Sample problem, materials
emphasis
• A block of cheese with known dimensions
is stacked and thus subjected to an axial
compressive load. After being stacked for 2
hours, what is the final thickness of the
sample?
Solution
• From the graph, strain after 2 hours (120 min) is
approx 0.09. (be careful with extrapolation, but
could use eqn for longer times).
•
•
•
•
Original dimensions: 100 x 100 x 100mm
Strain .09mm/mm so 100-100(.09) = 91mm tall
Poisson’s ratio 0.3 so expansion (in width) .03mm
103x103x91mm tall
Stress relaxation of potato tissue
Stress/Strain (estimate E)
A (chord/secant); B secant; C tangent apparent modulus
Rheological Behavior of Fluids
• A: Shearing of a
Newtonian Fluid
• B: Shear Stress Versus
Shear Rate for
Newtonian,
Pseudoplastic (Shear
Thinning), and
Dilantant (Shear
Thickening), Plastic,
and Casson-Type
Plastic Fluids
Shear modulus and viscosity
Newtonian type Fluids
•
•
•

Viscosity: m is resistance to flow
F/A = t = m du/dy
Kinematic viscosity is viscosity over density:
u = m/r
Values of Viscosity for Food Products
and Agricultural Materials Which are
Newtonian
Arrhenius Relationship:
Definition: Viscosity of
Fluid Decreases with
Temperature (Change
is typically 2% per
Degree Celsius)
• µ =Viscosity (Pa s)
• µф=A Constant (Pa s)
• Ea=Activation Energy
(Kcal g-Mole)
• R=Gas Constant (kcal/gmole ºK)
• T=Absolute Temperature
(ºK)
Behavior of Time-Dependent Fluids
• A: Apparent Viscosity
as a function of time
• B: Shear Stress as a
function of shear rate
Moisture impacts rheology
Break
stretch (but don’t strain too much!)
Bulk Density
• Bulk density is a property of particulate
materials like sand or grain. It is defined the
mass of many particles of the material
divided by the volume they occupy.
• Bulk Density = M/V [kg/m3]
• The volume includes the space between
particles as well as the space inside the
pores of individual particles.
D241.4: food properties:
bulk density, moisture
D241.4: grain properties
D243.3: thermal properties of
grain
EP545: Loads exerted by freeflowing grain on shallow storage
structures
EP545
• Total equivalent grain height: taken as the “average” grain height if the
top grain surface is not horizontal (may not be, angle of repose)
• Design approach, shallow grain holding structures:
– Determine material properties (bulk density, angle of repose, coefficient
of friction)
– Use properties to calculate total equivalent grain height
– Calculate static pressures (static vertical pressure at any point, static
lateral pressure, and vertical pressure on floor)
– Calculate resultant wall forces (resultant lateral force, resultant shear
force)
• Ex., Lateral force per unit length PH = LH2/2 where
– L is the lateral pressure (function of depth z) and H is the equivalent grain height
• Lateral pressure L(z) = kV(z)
– Where L(z) = lateral pressure at grain depth z, psf (pounds per square foot)
– k = ratio of lateral to vertical pressure, dimensionless and assumed to be 0.5
– V(z) = vertical pressure at equivalent grain depth z, psf
» V(z) = Wg where W is the bulk density (lb/ft3), g is acceleration to due
gravity
Hellevang
•
Overview of temporary grain storage (free reference
http://www.ag.ndsu.edu/publications/landing-pages/crops/temporary-grain-storage-ae84)
– The pressure grain exerts per foot of depth is called the equivalent fluid density
– Table 1. Approximate equivalent fluid density of some peaked grains.
Crop
Barley
Corn (shelled)
Oats
Grain Sorghum
Soybeans
Sunflower (non-oil)
Sunflower (oil)
Durum wheat
HRS wheat
Equivalent Fluid Density lb/cu. ft
20
23
14
22
21
9
12
26
24
Particle size distribution
• Different for different materials!
– Good reference: Chapter 35, CE manual, soil properties and testing
• Sieve sizes and corresponding opening sizes (ASTM)
• Typical particle size distribution (for soil):
• Remember statistics for particle size distribution
– Research on particle size distributions of nanoparticles
• Normal distribution
• Mean (“average”) particle size
• Measure of dispersion of particle size (standard deviation, for
example)
Particle size distribution
Sample questions
• A building with an 8-foot high wall is
storing grain. Grain was placed into the
storage building and leveled until it is
within 6 inches of the top of the wall. The
grain density is 60 pounds per bushel. The
lateral force per unit length at the base of
the wall is most nearly
• (a) 638, (b) 672, (c) 717, (d) 1360
Solution: use Hellevang
Answer is B
Sample questions
• If corn is treated as a non-cohesive granular
material (shelled), the equivalent fluid
density (pounds per cubic foot) is most
nearly:
• (a) 22
• (b) 28
• (c) 35
• (d) 56
Solution
• Look up in Hellevang table!
– Hellevang’s table for shelled corn: 23 #/sqft
– Answer is A
• Do not be deterred by the fact that the
values are not exactly the same! PE
questions are constructed to accommodate
minor differences in tabulated values!
Break!
• Stretch, drink of water, short break…
Water in Biological Materials
Steve Hall, Ph.D., P.E.
Louisiana State University AgCenter
Moisture impacts rheology
Definitions
• Mwb (wet basis) = water mass/total wet
mass
• Mdb (dry basis) = water mass/dry mass
• aw = pw/pwpure
• RH = water in a gas/maximum possible
water at T
• Equilibrium MC = MC at RH, T, t=infinity
• Hysteresis: nonlinearities in MC curves
m =
Wm
Wm Wd
D245.5: moisture relationships
• Moisture content wet basis
– Where m or mwb = wet basis moisture content (decimal)
– Wm = mass of moisture
W
m =
W W
– Wd = mass of dry matter
m
m
d
• Moisture content dry basis
– Where M or Mdb = dry basis moisture content (decimal)
– Dry basis moisture content can exceed 1 (or 100%)
M =
Wm
Wd
D245.5
• To convert from dry basis to wet basis:
m =
M
1 M
• To convert from wet basis to dry basis:
M =
m
1 m
Example: MC
• Wheat: Pan mass: 10 g; wheat + pan = 110 g
• Dried weight = 100 g
• Mwb (wet basis) = water mass/total wet mass
= 10g/100g = 10%
• Mdb (dry basis) = water mass/dry mass
= 10g/90g = 11% or (11-10)/10 = 0.1 or 10% error
• Apple: 10 g wet; 3 g dry
• Mwb (wet basis) = water mass/total wet mass
= 7/10= 70%
Mdb (dry basis) = water mass/dry mass = 7/3 = 233%
Or (233-70)/70 or 200+% error! BE CAREFUL!!
D245.5
• Isotherm data (used in
drying calculations)
– In table format or
graphical format
aw = pw/pwpure
Availability of water for microbial activity
(van den Berg and Bruin)
Equilibrium Moisture Content
Equilibrium Moisture Content:
Wheat
Corn: Hysteresis of EMC
EMC Curves
Estimating MC: Biol. Matls
•
•
•
•
•
n
-KTM
1-rh=e
.
where rh relative humidity, decimal
T = absolute temperature,°R
M = equilibrium moisture content, % d.b.
k and n are are constants as specified in the
following table.
Example Problem
• A sealed container is filled with soybeans at
20% moisture (w.b.) Estimate the relative
humidity of the interseed air. The
temperature is 60 degrees F.
• A) 15%
• B) 20%
• C) 55%
• D) 85%
•
Use equation, careful of units
Expansion due to moisture
Psychrometrics
• Moisture, RH, Temp, Enthalpy (energy) as
related to moisture in the atmosphere or in
enclosed spaces (e.g. buildings)
Psychrometric Chart
Psychrometrics
Steps to solve Psychrometrics
•
•
•
•
•
•
Read carefully
What stays constant
Follow lines
Read carefully/interpolate
Make calculations
One step at a time, then repeat
Psychrometrics (constants)
Volume
(density)
Humidity ratio
(water/air mass)
Saturation
(dewpoint)
Enthalpy
(wet bulb)
(Dry bulb) Temperature
Psychrometrics
What stays constant?
(what line do I follow?)
Temp (dry bulb)
Saturation (below dewpoint)
humidity ratio (kg/kg dry air)
Other options as stated
Example
Day ends with 70% RH at 80F
Temp drops to 70F
(what stays constant?) (rh, sat?)
Is there dew?
What is the dewpoint?
If not, what is the new RH?
Psychrometrics
Dewpt
(66)
88%RH
70
80
Example
100m3 Greenhouse: T = 70F, RH is 40%.
How much water (mist) to add to reach
50%RH?
Assume: density of dry air is 1/800th of water
or about 1.29kg/m3
Assume: temperature remains constant
(State your assumptions!)
Psychrometrics
{
.0094 lbwater/lbdry air
Diff = .002 lbwater/lb dry air
.0074 lbwater/lbdry air
How much water to mist in?
•
•
•
•
•
•
•
•
Difference = 0.002 lb water/lb dry air
So what is the amount of water to add?
Based on volume
Assume a 100 m3 greenhouse.
Still need an estimate of mass of dry air…
Assume 1.29kg/m3 *100m3 = 129 kg
129kg air*(0.002kg water/kg dry air) (why?)
Or 0.258 kg water or .258liters (~1 cup of water!)
What other questions can you ask as
biological engineers?
• Air conditioning (removes water, change
temperature) humans
• Dehumidifier (removes water) humans
• Rain adds water
• Plant transpiration adds water plants
• Sun adds energy/temp plants/animals
• Radiation at night removes energy/temp
• Drying processes or adding moisture
(bacterial, biomed, bioprocess)
Reminder:
Steps to solve Psychrometrics
•
•
•
•
•
•
Read carefully
What stays constant?
Follow lines
Read carefully/interpolate
Make calculations
One step at a time, then repeat
Conclusions
-
Remember basic definitions
Careful with Units
Use what you are given
Practice with your references
Keep a sense of time
Keep learning
Get a good night’s sleep
Eat breakfast
Any questions on V-D?
• Tips:
– Have a table or set of tables with material properties
handy
– Additional material property references:
• Johnson, Biological Process Engineering, has many material
property charts (density, specific heat, thermal conductivity,
thermal diffusivity, etc.)
• Geankoplis, Transport Processes and Separation Process
Principles (Includes Unit Operations), 4/e
– This area overlaps with many others
– Know how to convert between wet and dry basis
moisture contents!
– Remember common sense and statistics
Thank You!