Properties of Agricultural Materials Questions and Answers

Answer: A

Correct answer: The equal-volume sphere's surface area over the grain's own surface area

Sphericity measures how nearly a particle approaches a sphere. Formally it is the surface area of a sphere having the same volume as the grain, divided by the grain's actual surface area:

\[ \Phi = \frac{A_{\text{sphere, equal volume}}}{A_{\text{particle}}} \]

Because a sphere has the least surface area of any body enclosing a given volume, the numerator can never exceed the denominator, so \( \Phi \le 1 \) always, reaching 1 only for a true sphere. In practice it is computed from the three principal dimensions as \( \Phi = (LWT)^{1/3} / L \), the geometric mean diameter over the longest dimension. The other options describe a packing fraction, an aspect ratio and porosity respectively - none of which is bounded at one in the same way.

Answer: B

Correct answer: Mass divided by the total volume, voids included

Bulk density treats the grain lot as though it were a single continuous material:

\[ \rho_b = \frac{m}{V_{\text{bulk}}} \]

where \( V_{\text{bulk}} \) is the volume the lot occupies in the container, air spaces and all. Mass over the volume of solid material alone is true density, and the two differ by exactly the porosity. Bulk density is the working figure for storage: it converts a bin volume directly into tonnes, and it is why the same wheat gives different test weights after settling or vibration.

Answer: C

Correct answer: One minus bulk over true density

Porosity is the fraction of the bulk volume that is air:

\[ \varepsilon = \frac{V_{\text{void}}}{V_{\text{bulk}}} = 1 - \frac{\rho_b}{\rho_t} \]

The identity follows because the same mass appears in both densities, so the ratio \( \rho_b/\rho_t \) is the solid fraction and its complement is the void fraction. Expressing it this way is convenient because bulk and true density are both measurable - the first by filling a known container, the second by liquid or gas displacement - whereas void volume is not measured directly. Typical cereal grain lots sit near 40 per cent porosity, which is what makes aeration through a bin possible at all.

Answer: D

It describes how a material behaves when tipped into a pile and is the first figure used in designing bins, chutes and conveyors. It rises as moisture content increases, which is why damp lots bridge where dry ones flow.

Answer: A

Correct answer: The wall loads in a storage bin

Grain in a deep bin does not press on the floor with its full weight. Friction between the grain and the wall transfers part of the load into the wall itself, and Janssen's analysis makes the coefficient of static friction the parameter that governs how much.

The consequence is practical: a smooth steel bin and a rough concrete one of identical dimensions carry different vertical wall loads with the same grain, and the floor pressure reaches an asymptote rather than growing without limit as the bin is filled. Terminal velocity is aerodynamic, and specific heat and equilibrium moisture content are thermal and hygroscopic properties, none of which enters the wall-load calculation.

Answer: B

Correct answer: Drag exactly balances the weight

A particle released in an upward air stream accelerates until the aerodynamic drag equals its net weight, after which it moves with the air at constant relative velocity:

\[ C_d\,A\,\frac{\rho_a v_t^{2}}{2} = mg \]

That balance velocity is the terminal velocity. It depends on the particle's mass, projected area and drag coefficient, so different components of a harvested mixture have different values - which is precisely what an aspirator exploits. Setting the air velocity between the terminal velocity of the chaff and that of the sound grain lifts one and leaves the other behind.

Answer: C

Correct answer: The mass of the wet sample

On a wet basis the denominator is the whole sample as weighed:

\[ M_{wb} = \frac{m_{\text{water}}}{m_{\text{wet}}} \times 100 \]

This is the basis used in trade and in grading standards, because the wet mass is what the buyer actually receives and can weigh. Its arithmetic limit is 100 per cent. The dry basis, by contrast, divides by the dry matter alone and is preferred in drying calculations because the denominator stays constant while water is being removed. Confusing the two is a common source of error: 20 per cent wet basis is 25 per cent dry basis.

Answer: D

Correct answer: The grain neither gains nor loses moisture

Equilibrium moisture content is the value a grain settles at when held in air of a given temperature and relative humidity long enough that net moisture exchange stops. The vapour pressure of the water in the grain then equals that of the surrounding air.

It is a property of the pair, not of the grain alone: change the relative humidity and the equilibrium shifts. This is why safe storage is specified as a moisture content and a storage atmosphere, and why grain dried below the equilibrium value for its store will simply reabsorb moisture until it returns to it.

Answer: A

Correct answer: The two curves do not coincide

Sorption hysteresis means the adsorption curve, obtained by wetting dry material, lies below the desorption curve obtained by drying wet material. At the same relative humidity the material holds more water if it arrived there by drying than by wetting.

The usual explanation is capillary condensation together with structural changes in the matrix: pores that filled at one humidity do not empty until a lower one is reached. The practical consequence is that a single equilibrium moisture content figure is incomplete - the history of the sample has to be stated with it, and drying and rewetting data are not interchangeable.

Answer: B

Correct answer: Rises with moisture content

Grain is a mixture of dry matter and water, and water's specific heat, about 4.18 kJ/kg K, is far above that of the dry solids, roughly 1.0 to 1.5 kJ/kg K. The mixture's specific heat is therefore close to a mass-weighted average of the two, and adding water raises it.

The common empirical forms reflect exactly this, being linear in moisture - for instance \( c = 1.0 + 3.2M \) kJ/kg K with \( M \) the dry basis moisture as a fraction. It matters in drier design, because wet incoming grain absorbs more heat per degree of temperature rise than the same mass of dry grain.