Mechanical Operations Cheatsheet

Cheatsheet Content

UNIT 1: Size Reduction & Mechanical Separation (Part 1) 1.1. Size Reduction of Solids Concept: Process of reducing solid material from larger to smaller pieces. Purpose: Increase surface area, facilitate material handling, achieve desired product size. Mechanisms: Compression, impact, attrition (rubbing), cutting, shear. Crushing: Definition: Primary stage of size reduction, reducing large lumps. Dominant Force: Compression. Examples: Jaw crushers, gyratory crushers. Grinding: Definition: Secondary/tertiary stage, reducing material to fine powders. Dominant Forces: Attrition, impact, shear. Examples: Ball mills, rod mills, hammer mills. Energy Requirements for Size Reduction: Comminution is highly energy-intensive. Energy input depends on material properties (hardness, toughness), size reduction ratio, and equipment efficiency. Empirical Laws of Comminution: Relate energy ($E$) to particle size reduction ($L_1 \to L_2$). Kick's Law: $E = C_K \ln(L_1/L_2)$ (for coarse crushing). Energy proportional to reduction ratio. Rittinger's Law: $E = C_R (1/L_2 - 1/L_1)$ (for fine grinding). Energy proportional to new surface area created. Bond's Law: $E = W_i \left(\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}}\right)$ (most widely used, for intermediate sizes). Energy related to crack propagation. $W_i$: Work Index (kWh/ton), material-specific energy for 80% passing 100 microns. $P_{80}$: Product size (80% passing, in $\mu m$). $F_{80}$: Feed size (80% passing, in $\mu m$). Particle Size Distribution: Describes the range and proportion of different particle sizes in a sample. Methods: Sieve analysis, laser diffraction, sedimentation. 1.2. Mechanical Separation (Part 1: Screening) Concept: Separation of particles based on size using screens with defined openings. Types of Screens: Stationary Screens: Inclined bars/rods (Grizzlies). For coarse primary separation, low capacity. Grizzlies: Heavy-duty stationary screens for separating very large lumps. Trommels (Revolving Screens): Rotating cylindrical screens. Material tumbles, fines pass through. Good for sticky materials. Vibrating Screens: Most common. Mechanically or electrically vibrated decks. High capacity and efficiency. Circular, linear, or elliptical motion. Screen Effectiveness: Measure of separation efficiency. $$E = \frac{\text{Mass of undersize in product}}{\text{Mass of undersize in feed}}$$ Factors affecting: particle shape, moisture, screen area, vibration, feed rate. UNIT 2: Filtration, Sedimentation, Centrifugation, & Separators 2.1. Filtration Concept: Separating solids from fluids by passing the fluid through a porous filter medium. Types of Filter Equipment: Plate and Frame Filter Press: Operation: Batch. Slurry pumped into chambers formed by plates and frames. Filtrate passes through cloth, cake builds up in frames. Advantages: High filtration area, good for high solids, produces dry cake. Disadvantages: Batch, labor-intensive. Continuous Rotary Vacuum Filter (CRVF): Operation: Continuous. Drum rotates in slurry, vacuum pulls filtrate through, cake forms, is washed, dried, and discharged. Advantages: Continuous, automated, large volumes. Disadvantages: Less effective for very fine/sticky solids. Filter Aids: Porous materials (e.g., diatomaceous earth) added to slurry or pre-coated on filter. Purpose: Increase cake porosity, prevent blinding, improve filtration rate and clarity. Darcy's Law: $Q = \frac{K A \Delta P}{\mu L}$ (describes flow through filter cake). 2.2. Sedimentation Concept: Separating solids from liquids by gravity due to density differences. One-Dimensional Motion of Particles Through Fluid: Particles settle at a terminal velocity ($v_t$) when drag force balances net gravitational force. Stokes' Law (Laminar flow, $Re_p For small spherical particles. $$v_t = \frac{g d_p^2 (\rho_p - \rho_f)}{18 \mu}$$ Thickeners: Batch Thickeners: Settling in a tank over time, used for studies and small batches. Continuous Thickeners: Large tanks (often circular) with rakes. Continuous feed, clarified overflow, concentrated underflow. Used for concentrating slurries. 2.3. Centrifuge Concept: Separation using centrifugal force, often much stronger than gravity. $F_c = m \omega^2 r$. Types of Centrifuges: Tubular Bowl Centrifuge: High-speed, narrow bowl. For liquid-liquid or liquid-solid (low solids, fine particles) clarification. Disk Centrifuge (Disk-Stack Centrifuge): Stack of conical disks increases settling area. Efficient for liquid-liquid and liquid-solid, e.g., milk skimming. Batch Basket Centrifuge: Perforated basket with filter cloth. For dewatering crystalline or granular solids. Batch operation. 2.4. Separators (Gas-Solid) Cyclone Separators: Principle: Centrifugal force created by tangential gas entry separates solids from gas. Application: Primary dust collection for particles $> 5-10 \mu m$. Simple, low cost. Electrostatic Precipitators (ESPs): Principle: Electrically charges particles which are then collected on charged plates. Application: High efficiency for very fine particles ( Magnetic Precipitator: Principle: Uses magnetic fields to separate ferromagnetic particles. Application: Removal of tramp iron, mineral processing. UNIT 3: Conveying Systems & Material Handling 3.1. Concept of Conveying: Transportation of bulk materials from one point to another. 3.2. Types of Conveying Systems: Mechanical Conveying System: Uses physical components. Belt Conveyors: Continuous belt, high capacity, long distances. Screw Conveyors: Helical screw, enclosed, for powders/granules. Bucket Elevators: Vertical transport using buckets. Chain Conveyors: Robust, for heavy/abrasive materials. Pneumatic Conveying System: Uses gas (usually air) to transport solids through pipelines. Dilute Phase: High gas velocity, low solids concentration. Dense Phase: Low gas velocity, high solids concentration (slug flow). 3.3. Storage and Handling of Materials: Equipment: Silos, hoppers, bins, feeders, stackers, reclaimers. Considerations: Material properties (flowability, angle of repose), capacity, discharge control. 3.4. Design and Power Requirement: Based on material properties, throughput, distance, elevation, friction, and efficiency. UNIT 4: Agitation & Mixing, Fluidization 4.1. Application of Mechanical Operation Equipment (General) Integration of various mechanical operations in a process flow sheet (e.g., crushing-grinding-screening circuit, filtration-drying unit). 4.2. Agitation and Mixing of Liquids Agitation: Inducing motion in a fluid. Mixing: Random distribution of components to achieve uniformity. Purpose: Blending, dissolving, dispersion, heat transfer, reaction enhancement. Impeller Types: Propellers: Axial flow, high speed, for low viscosity. Turbines: Radial/axial flow, high shear, for varied viscosities (e.g., Rushton turbine). Paddles: Slow speed, gentle mixing, for high viscosity. Power Consumption: $P = N_p \rho N^3 D^5$ ($N_p$: Power Number, $N$: rotational speed, $D$: impeller diameter). Reynolds Number: $Re = \frac{\rho N D^2}{\mu}$ (determines flow regime). 4.3. Conditions of Fluidization Concept: Solid particles behave like a fluid when a gas or liquid passes upwards through them at sufficient velocity. Minimum Fluidization Velocity ($U_{mf}$): The fluid velocity at which the bed begins to fluidize. At $U_{mf}$, pressure drop equals weight of the bed per unit area: $\frac{\Delta P}{L} = (\rho_p - \rho_f) g (1-\epsilon_{mf})$. Can be estimated using modified Ergun equation. 4.4. Aggregate and Particulate Fluidization Particulate (Smooth) Fluidization: Uniform expansion of the bed, no bubbles. Occurs with liquids or very fine solids with gases. Bed behaves as a homogeneous fluid. Aggregate (Bubbling) Fluidization: Excess gas forms bubbles that rise through the bed. Common for gas-solid systems. Vigorous mixing, good for heat/mass transfer, but gas bypass can reduce contact efficiency. 4.5. Flow Through Packed and Fluidized Beds Packed Beds: Stationary bed of solids. Fluid flows through void spaces. Pressure Drop: Described by the Ergun Equation. Fluidized Beds: Particles suspended by fluid flow. High mixing, uniform temperature. Pressure Drop: Approximately constant and equal to the weight of the bed per unit area for velocities above $U_{mf}$. Applications: Catalytic reactors, dryers, combustors.