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:

Exam %

V. D. Materials Properties; Bulk Solids

4%

Overlaps with:

I. D. 1.

Mass and energy balances

~2%

I. D. 2.

Applied psychrometric processes

~2%

V. C.

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 mass-moisture relationships of grain for storage

D243.e: Thermal properties of grain and grain products

D245.5: Moisture relationships of plant-based 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/landing-pages/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 = Fnormal to area/A

• Shear Stress = Fparallel to area/A

• Strain =L/Lo [m/m; or %]

• Young’s modulus E: = Eor E

• For bar, = PL/AE or FL/AE

Tensioncompression

Stress-strain

Stress/strain for steel and rubbera) 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 = Fnormal to area/A

• Shear Stress = Fparallel to area/A

• Strain =L/Lo [m/m; or %]

• Young’s modulus E: = Eor E

• For bar, = PL/AE or FL/AE

Tensioncompression

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: is resistance to flow• F/A = = u/y• Kinematic viscosity is viscosity over density:

Values of Viscosity for Food Products and Agricultural Materials Which are

Newtonian

Arrhenius Relationship:

• µ =Viscosity (Pa s)

• µф=A Constant (Pa s)

• Ea=Activation Energy (Kcal g-Mole)

• R=Gas Constant (kcal/g-mole ºK)

• T=Absolute Temperature (ºK)

Definition: Viscosity of Fluid Decreases with Temperature (Change is typically 2% per Degree Celsius)

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 free-flowing 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-ae-84)

– 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 Equivalent Fluid Density lb/cu. ft

Barley 20Corn (shelled) 23Oats 14Grain Sorghum 22Soybeans 21Sunflower (non-oil) 9Sunflower (oil) 12Durum wheat 26HRS wheat 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

D245.5: moisture relationships

• Moisture content wet basis – Where m or mwb = wet basis moisture content (decimal)

– Wm = mass of moisture

– Wd = mass of dry matter

• Moisture content dry basis– Where M or Mdb = dry basis moisture content (decimal)

– Dry basis moisture content can exceed 1 (or 100%)

dm

m

WW

Wm

dm

m

WW

Wm

d

m

W

WM

D245.5

• To convert from dry basis to wet basis:

• To convert from wet basis to dry basis:

M

Mm

1

m

mM

1

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

• 1-rh=e-KTMn .

• 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)

Enthalpy(wet bulb)

Saturation(dewpoint)

(Dry bulb) Temperature

Volume(density) Humidity ratio

(water/air mass)

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

8070

Dewpt(66)

88%RH

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

.0074 lbwater/lbdry air

.0094 lbwater/lbdry airDiff = .002 lbwater/lb dry 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!