GATE Agricultural Engineering Agricultural Process Engineering Flashcards

24 sample cards from the Agricultural Process Engineering deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Define psychrometry and the dry-bulb temperature of air.

   Psychrometry is the study of the thermodynamic properties of moist air (air-water-vapour mixtures) and their use in processes that change air temperature and humidity. The dry-bulb temperature is the air temperature measured by an ordinary thermometer shielded from radiation and moisture.

2. Define absolute humidity (humidity ratio) of moist air and give its formula.

   Absolute humidity (humidity ratio) $W$ is the mass of water vapour per unit mass of dry air: $$W = \frac{m_{v}}{m_{a}} = 0.622\,\frac{p_{v}}{P - p_{v}}$$ where $p_{v}$ is the partial pressure of water vapour, $P$ is total pressure, and $0.622$ is the ratio of molar masses ($18/29$).

3. Define relative humidity and contrast it with absolute humidity.

   Relative humidity is the ratio of the actual vapour partial pressure to the saturation vapour pressure at the same temperature: $$\mathrm{RH} = \frac{p_{v}}{p_{vs}} \times 100\%$$ It is a dimensionless percentage that depends on temperature, whereas absolute humidity (humidity ratio) is the actual mass of vapour per kg dry air and is temperature-independent.

4. Distinguish dew-point temperature and wet-bulb temperature of moist air.

   Dew-point temperature is the temperature to which moist air must be cooled at constant pressure and humidity ratio to reach saturation (condensation begins). Wet-bulb temperature is the steady temperature reached by a wetted thermometer in moving air, reflecting simultaneous heat and mass transfer (evaporative cooling). For unsaturated air: $T_{dry} > T_{wet} > T_{dew}$.

5. Define the enthalpy of moist air per kg of dry air.

   $$h = c_{pa}\,T + W\,(\lambda_{0} + c_{pv}\,T)$$ where $c_{pa}\approx1.005\ \mathrm{kJ\,kg^{-1}\,K^{-1}}$ (dry air), $c_{pv}\approx1.88\ \mathrm{kJ\,kg^{-1}\,K^{-1}}$ (vapour), $\lambda_{0}\approx2501\ \mathrm{kJ\,kg^{-1}}$ (latent heat at $0\,^{\circ}\mathrm{C}$), $W$ = humidity ratio, $T$ = dry-bulb temperature in $^{\circ}\mathrm{C}$.

6. Define humid (specific) volume of moist air.

   Humid volume $v_{H}$ is the volume of moist air per unit mass of dry air: $$v_{H} = \left(\frac{1}{29} + \frac{W}{18}\right)\frac{R\,T}{P}$$ approximately $v_{H} = (0.00283 + 0.00456\,W)\,T\ (\mathrm{m^{3}\,kg^{-1}\ dry\ air})$, with $T$ in kelvin. It increases with temperature and humidity ratio.

7. On a psychrometric chart, what process is represented by a horizontal line, and what by a constant-enthalpy line?

   A horizontal line (constant humidity ratio $W$) represents sensible heating or cooling — only dry-bulb temperature changes. A constant wet-bulb / constant-enthalpy line (sloping down to the right) approximates an adiabatic saturation/evaporative-cooling process, where dry-bulb falls as humidity rises at nearly constant enthalpy.

8. State Rittinger's law for energy in size reduction and the property it assumes.

   Rittinger's law: energy required is proportional to the new surface area created, i.e. proportional to the increase in specific surface (inverse of particle size): $$E = K_{R}\left(\frac{1}{d_{2}} - \frac{1}{d_{1}}\right)$$ where $d_1,d_2$ are feed and product sizes. Best suited to fine grinding.

9. State Kick's law of size reduction.

   Kick's law: the energy required is proportional to the logarithm of the size-reduction ratio (energy per unit mass is constant for a given reduction ratio): $$E = K_{K}\,\ln\!\left(\frac{d_{1}}{d_{2}}\right)$$ where $d_1$ and $d_2$ are initial and final particle sizes. Best for coarse crushing.

10. State Bond's law and define the work index.

    Bond's law: $$E = K_{B}\left(\frac{1}{\sqrt{d_{2}}} - \frac{1}{\sqrt{d_{1}}}\right)$$ The work index $W_{i}$ is the energy (kWh per tonne) needed to reduce material from theoretically infinite size to 80% passing $100\ \mu\mathrm{m}$. Bond's law is intermediate between Kick's and Rittinger's, used for intermediate grinding.

11. Show that Kick's, Rittinger's and Bond's laws are special cases of the general (Walker) differential equation $dE = -C\,\frac{dx}{x^{n}}$.

    Integrating $dE=-C\,x^{-n}\,dx$: for $n=1$ gives Kick's law (energy $\propto \ln(d_1/d_2)$); for $n=2$ gives Rittinger's law (energy $\propto 1/d_2 - 1/d_1$); for $n=1.5$ gives Bond's law (energy $\propto 1/\sqrt{d_2}-1/\sqrt{d_1}$). Thus the exponent $n$ distinguishes the three laws.

12. Define the reduction ratio in a size-reduction (comminution) operation.

    Reduction ratio is the ratio of a characteristic feed size to the corresponding product size: $$R = \frac{d_{feed}}{d_{product}}$$ Often based on 80%-passing sizes ($d_{80}$). It measures how much the material has been reduced in one pass.

13. Define mean particle diameters used in particle-size analysis of comminuted solids: the surface-volume (Sauter) mean.

    The Sauter (surface-volume) mean diameter is $$D_{sv} = \frac{\sum n_{i} d_{i}^{3}}{\sum n_{i} d_{i}^{2}} = \frac{1}{\sum (x_{i}/d_{i})}$$ where $x_i$ is the mass fraction in size interval $i$ with mean diameter $d_i$. It is the diameter of a sphere having the same surface-to-volume ratio as the whole sample, important for surface-area-controlled processes.

14. Define the fineness modulus and uniformity index obtained from sieve analysis of ground feed.

    Fineness modulus (FM) is obtained by summing the cumulative percentages of material retained on a standard set of sieves and dividing by 100; higher FM means coarser product. The uniformity index expresses the proportions of coarse, medium and fine fractions (often as a three-figure ratio) describing the spread of the size distribution.

15. In screening, define screen effectiveness (efficiency).

    Screen effectiveness measures how well a screen separates oversize from undersize. A common overall form is the product of recovery of undersize in the underflow and rejection of oversize: $$E = E_{o}\,E_{u}$$ where each term compares actual mass of correctly sorted material to the amount in the feed. Higher feed rate generally lowers effectiveness.

16. Write the material balance for an ideal screen separating feed $F$ into overflow $D$ (oversize) and underflow $B$ (undersize).

    Total: $F = D + B$. Component (fraction of material finer than the cut, $x$): $$F\,x_{F} = D\,x_{D} + B\,x_{B}$$ Solving gives $\dfrac{D}{F} = \dfrac{x_{F}-x_{B}}{x_{D}-x_{B}}$ and $\dfrac{B}{F} = \dfrac{x_{D}-x_{F}}{x_{D}-x_{B}}$.

17. What is the relationship between mesh number and aperture size in standard screens?

    Mesh number is the number of openings per linear inch of screen. As mesh number increases, the aperture (opening) size decreases, so higher mesh numbers pass finer particles. Aperture also depends on wire diameter: $\text{aperture} = \frac{1\ \text{inch}}{\text{mesh}} - (\text{wire diameter})$.

18. Name and distinguish the common industrial screening equipment by motion.

    Grizzly: static inclined parallel bars for coarse scalping. Trommel: rotating cylindrical screen. Vibrating screen: high-frequency vibration for efficient sizing. Gyratory/oscillating screen: gyratory horizontal motion for fine separation. They differ in the motion imparted (none, rotation, vibration, gyration) and the size range handled.

19. What is the terminal velocity of a particle and its role in pneumatic/aspiration separation of grains?

    Terminal velocity is the constant velocity a particle attains in a fluid when gravity balances drag and buoyancy: $$v_{t} = \sqrt{\frac{4\,g\,d\,(\rho_{p}-\rho_{f})}{3\,C_{D}\,\rho_{f}}}$$ Particles with different terminal velocities are separated in an air stream (aspiration), e.g. cleaning grain from chaff and light impurities.

20. In the constant-rate drying period, why does the surface stay at the wet-bulb temperature of the drying air?

    During the constant-rate period the surface is fully wetted, so all sensible heat supplied by the air is consumed as latent heat of evaporating free water. This dynamic equilibrium between convective heat gain and evaporative cooling holds the surface at the air's wet-bulb temperature until the critical moisture content is reached.

21. What is hysteresis in moisture sorption isotherms of grains?

    Sorption hysteresis is the phenomenon where the equilibrium moisture content at a given relative humidity is higher along the desorption (drying) isotherm than along the adsorption (wetting) isotherm. The two curves form a loop, attributed to capillary condensation, pore-shape ('ink-bottle') effects and structural changes.

22. Give the Brunauer (BET) interpretation relevant to sorption isotherms of foods.

    The BET equation describes multilayer moisture sorption and is used to estimate the monolayer moisture value $M_{0}$: $$\frac{a_{w}}{(1-a_{w})M} = \frac{1}{M_{0}C} + \frac{C-1}{M_{0}C}\,a_{w}$$ where $a_{w}$ is water activity, $M$ moisture content, and $C$ a constant. The monolayer value indicates the moisture for maximum storage stability.

23. Define water activity and its significance in drying and storage of foods.

    Water activity $a_{w} = \dfrac{p_{v}}{p_{vs}} = \dfrac{\mathrm{ERH}}{100}$ is the ratio of the vapour pressure of water in the food to that of pure water at the same temperature (equal to equilibrium relative humidity/100). It governs microbial growth, enzymatic and chemical reactions; lowering $a_w$ by drying improves shelf stability (most bacteria need $a_w>0.9$).

24. Differentiate the through-flow and cross-flow (parallel) air patterns in tray dryers.

    In cross-flow (parallel-flow) tray dryers heated air passes horizontally over the surface of the product on the trays. In through-flow tray dryers air is forced vertically through perforated trays and the bed of product, giving greater contact area, faster and more uniform drying, but higher fan power.

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