Unit Operations-I: Fluid Flow and Mechanical Operations Study Guide

INTRODUCTION TO CHEMICAL ENGINEERING AND UNIT OPERATIONS

• Chemical Engineering Definitions:

  • It is the branch of engineering concerned with the design and operation of industrial chemical plants to carry out transformations of raw materials into desired products efficiently, economically, and safely.

  • Deals with the production of bulk materials from basic raw materials in the most economical way by chemical means.

  • A Chemical Engineer develops, designs, constructs, operates, and controls physical and/or chemical or biochemical changing processes.

• Scope of Professional Practice:

  • Engaged in food processing, fertilizers, insecticides, herbicides, pesticides, plastics, synthetic fibers, elastomers, drugs, pharmaceuticals, pulp, and paper.

  • Processing of petroleum crude, production of synthetic fuels, biomass, and wind energy utilization.

  • Devising methods and equipment for environmental protection.

  • Employment segments: Research and Development (R&D), Design, Production, and Sales.

• Unit Operations:

  • Operations involving physical changes in the materials handled in a system.

  • Features:         (i) Physical in nature (results in property changes requiring a driving force).         (ii) Common to diverse industries (change in conditions, not concept).         (iii) Based on same scientific principles regardless of materials.         (iv) Practical methods may vary between industries.         (v) Independent of the industry in which they are carried out.

  • Example: Distillation is used for alcohol in beverage industries and hydrocarbons in petroleum; the concept is identical.

• Broad Classification of Unit Operations:     (i) Mechanical Operations: Size reduction, conveying, filtration.     (ii) Fluid Flow Operations: Pressure difference acts as a driving force.     (iii) Heat Transfer Operations: Temperature difference acts as a driving force (e.g., evaporation).     (iv) Mass Transfer Operations: Concentration difference acts as a driving force (e.g., distillation).

• Mechanical Operations involving Particulate Solids:

  1. Size reduction (crushing/grinding).

  2. Mixing (solid-solid, liquid-liquid).

  3. Classification (screening, froth flotation, magnetic separation, jigging, tabling, electrostatic separation).

  4. Solid-fluid separations (filtration, sedimentation, centrifugal separation).

  5. Gas-solid separations (dust collection, bag filtration, electrostatic precipitation).

  6. Solid handling (storage, feeding, conveying).

  7. Size enlargement (pelletization, agglomeration, granulation, extrusion).

UNITS, DIMENSIONS, AND GAS LAWS

• Definitions:

  • Unit: An arbitrarily selected standard of measure for a physical quantity.

  • Basic Quantities: Length ($L$), Mass ($M$), Temperature ($T$), Time ($\theta$).

  • Derived Quantities: Formed from base units (e.g., area, velocity, acceleration).

• Systems of Units:

  • CGS: Centimetre (cm), Gram (gm), Celsius ($^\circ C$), Second (s).

  • MKS: Metre (m), Kilogram (kg), Celsius ($^\circ C$), Second (s).

  • FPS: Foot (ft), Pound (lb), Fahrenheit ($^\circ F$), Second (s).

  • SI: Metre (m), Kilogram (kg), Kelvin (K), Second (s).

• Specific SI Units:

  • Force: Newton ($N$) where $1\,N = 1\,(kg \cdot m)/s^2$.

  • Pressure: Pascal ($Pa$) where $1\,Pa = 1\,N/m^2$.

  • Energy/Work/Heat: Joule ($J$) where $1\,J = 1\,N \cdot m$.

  • Power: Watt ($W$) where $1\,W = 1\,J/s$.

  • Viscosity: $(N \cdot s)/m^2$ or $Pa \cdot s$.

• Pressure Relationships:

  • $Absolute\,pressure = Gauge\,pressure + Atmospheric\,pressure$

  • $Absolute\,pressure = Atmospheric\,pressure - Vacuum$

  • Standard Atmosphere ($1\,atm$):

    • $760\,mm\,Hg = 760\,torr$

    • $101325\,Pa = 101.325\,kPa$

    • $1.01325\,bar = 1.033\,kgf/cm^2$

    • $14.7\,psi = 10.33\,m\,H_2O$

• Conservation Laws:

  • Mass: Matter is neither created nor destroyed. $Input = Output + Accumulation$. Under steady-state: $Input = Output$.

  • Energy: Energy is neither created nor destroyed (First Law of Thermodynamics).

• Molecular and Compositional Units:

  • Mole: Amount of substance numerically equal to its molecular weight ($M_A$).

  • $N_A = W_A / M_A$

  • Weight Fraction of A: $\frac{W_A}{W_A + W_B + W_C + \dots}$

  • Mole Fraction of A: $\frac{N_A}{N_A + N_B + N_C + \dots}$

• Gas Laws:

  • Ideal Gas Law: $PV = nRT$

    • $R = 8.31451\,m^3 \cdot kPa/(kmol \cdot K) = 0.08206\,l \cdot atm/(mol \cdot K)$.

    • At $273\,K$ ($0^\circ C$) and $101.325\,kPa$, $1\,kmol$ occupies $22.41\,m^3$.

  • Dalton's Law: Total pressure equals sum of partial pressures ($P = p_A + p_B + p_C \dots$).

  • Amagat's Law: Total volume equals sum of pure component volumes ($V = V_A + V_B + V_C \dots$).

DIMENSIONAL ANALYSIS

• Dimensional Formulae: Expresses derived units via basic units in the form $M^\alpha L^\beta \theta^\gamma$.

  • Acceleration ($[a]$): $L\theta^{-2}$.

• Dimensionless Equations: Consistent units used throughout such that dimensions of each term cancel when divided by any one term.

• Dimensional Equations: Empirically derived; dimensions do not match on both sides (e.g., $Q/A = 0.055(\Delta T)^{1.25}(D_o)^{0.25}$).

• Methods:

  • Rayleigh Method: Expresses dependent variable as product of independent variables raised to unknown powers: $Q_1 = k Q_2^a Q_3^b \dots$

  • Buckingham's $\pi$ Theorem: The number of dimensionless groups equals total variables minus number of fundamental dimensions ($n - m$).

SIZE REDUCTION OF SOLIDS

• Concept: Comminution — cutting or breaking solids without altering the state of aggregation.

• Mechanisms: Compression, Impact, Attrition, and Cutting.

• Importance:     (i) Increase surface area to increase rate of processes (e.g., leaching, combustion).     (ii) Effect separation of constituents in isolated pockets.     (iii) Meet product size specifications.     (iv) Intimate mixing of solids.     (v) Improve dissolution, solubility, and binding strength.

• Energy and Power Requirement Laws:

  1. Rittinger's Law: Work is proportional to new surface created.         $P / \dot{m} = K_r \left[ \frac{1}{\bar{D}_{sb}} - \frac{1}{\bar{D}_{sa}} \right]$

  2. Kick's Law: Work is proportional to the log of the reduction ratio ($D/d$).         $P / \dot{m} = K_K \ln(D/d)$

  3. Bond's Law and Work Index ($W_i$): Work is proportional to $\sqrt{S_p/v_p}$.         $P / \dot{m} = 0.3162 W_i \left[ \frac{1}{\sqrt{D_{pb}}} - \frac{1}{\sqrt{D_{pa}}} \right]$

     • Work Index Definition: Energy in kWh per ton to reduce very large feed to size where 80% passes $100\,\mu m$.

• Efficiencies:

  • Crushing Efficiency ($\eta_c$): Ratio of surface energy created to energy absorbed by the solid.

  • Mechanical Efficiency ($\eta_m$): Ratio of energy absorbed by solid to total energy input to machine.

• Types of Size Reduction Equipment:

  • Crushers (Heavy Duty/Slow Speed):

    • Blake Jaw Crusher: Movable jaw pivoted at the top; maximum movement at the bottom (discharge). Continuous/Intermittent compression.

    • Dodge Jaw Crusher: Pivoted at bottom; maximum movement at top. Uniform product but prone to choking.

    • Gyratory Crusher: Conical head gyrates in a housing. Continuous action; higher throughput than jaw crushers.

    • Crushing Rolls: Two heavy cylinders rotating towards each other. Angle of Nip ($2\alpha$): Angle formed by tangents at contact; calculated by $\cos(\alpha) = \frac{r + d}{r + R}$.

  • Grinders (Intermediate/Fine - High Speed):

    • Hammer Mill: High-speed rotor with swing hammers; size reduction by impact and attrition.

    • Ball Mill: Rotating cylindrical shell charged with steel balls. Critical Speed ($N_c$): The speed where centrifuging occurs and no grinding happens.             $N_c = \frac{1}{2\pi} \sqrt{\frac{g}{R - r}}$

      • Optimum Operating Speed: 50% to 75% of $N_c$.

  • Ultrafine Grinders:

    • Fluid-Energy Mill: Particles impact each other in a high-velocity gas stream (attrition).

  • Cutting Machines: Knife cutters, dicers, slitters.

• Circuits:

  • Open Circuit: Material passes once; no attempts to return oversize.

  • Closed Circuit: Material goes to size separator; oversize is returned for regrinding.

SIZE SEPARATION OF SOLIDS (SCREENING)

• Screening: Separation of particles according to size alone.

  • Undersize/Minus (-): Material passing through openings.

  • Oversize/Plus (+): Material remaining on the screen.

• Screen Series:

  • Tyler Standard Sieve Series: Based on a 200-mesh screen ($0.074\,mm$ opening). Ratio of openings between screens is $\sqrt{2} = 1.411$.

  • Mesh: Number of openings per linear inch.

• Analysis Types:

  • Differential Analysis: Weight fraction retained on each screen.

  • Cumulative Analysis: Sum of weight fractions larger or smaller than a given size.

• Screen Effectiveness ($E$): A measure of success in separating materials. Based on mass fractions of oversize ($x_A$) and undersize ($x_B$) in Feed ($F$), Overflow ($D$), and Underflow ($B$).     $E = \frac{(x_F - x_B)(x_D - x_F) x_D (1 - x_B)}{(x_D - x_B)^2 (1 - x_F) x_F}$

• Equipment:

  • Grizzly: Parallel metal bars; used for coarse separation (>50\,mm).

  • Trommel: Revolving perforated cylinder; often arranged in series or nested.

  • Vibrating Screens: High capacity and accuracy; prevents blinding (plugging of openings).

CLASSIFICATION AND SPECIFIC PROPERTY SEPARATION

• Classification: Separation based on terminal settling velocities ($u_t$).

  • Free Settling: Particle fall is unaffected by other particles (low concentration).

  • Hindered Settling: Motion hindered by proximity of other particles (high concentration).

  • Equipment: Gravity settling tanks, Cone classifiers, Mechanical classifiers (Rake/Spiral).

• Cyclones: Uses centrifugal force to separate solids from fluids. Liquid Cyclones are called Hydroclones.

• Jigging: Separation by pulsation of liquid through a bed of solids on a screen based on specific gravity difference.

• Froth Flotation: Separation based on surface properties (affinity for air vs. water).

  • Promoters: Make particles air-avid (e.g., Sodium ethyl xanthate).

  • Collectors: Form surface films (e.g., Pine oil).

  • Frothers: Stabilize froth (e.g., Cresylic acid).

• Magnetic Separation: Separation based on magnetic attractability (Paramagnetic vs. Diamagnetic).

  • Equipment: Magnetic pulleys, Drum separators, Ball-Norton type.

• Electrostatic Separation: Based on conductivity. Conductors acquire same charge as electrode and are repelled; non-conductors are unaffected.

FILTRATION AND SEDIMENTATION

• Filtration: Separation of solids from liquid using a porous medium.

  • Cake Filtration: Particles form a layer (cake); for high solid concentrations.

  • Deep Bed Filtration: Particles trapped inside medium; for low solid concentrations.

  • Constant Pressure ($\Delta P = constant$): Rate starts high and decreases.         $t / V = (K_c / 2) V + 1/q_0$

  • Constant Rate ($dV/dt = constant$): $\Delta P$ increases from minimum to maximum.

  • Filter Aids: Diatomaceous earth or expanded perlite; increased porosity to handle slimy/difficult slurries.

  • Equipment: Plate and Frame filter press (batch), Vacuum Nutsch, Rotary Drum Filter (continuous vacuum), Centrifugal filters (suspended basket).

• Sedimentation: Separation by gravity settling.

  • Thickener: Shallow tank producing clear liquid overflow and sludge underflow.

  • Coagulants: Alum ($Aluminium\,sulphate$) or Ferrous sulphate to form large flocs for faster settling.

MIXING AND AGITATION

• Agitation: Induced motion of material in a circulatory pattern.

• Mixing: Random distribution of phases through one another.

• Impeller Types:

  1. Propellers: Axial-flow; high speed for low viscosity.

  2. Turbines: Radial-flow; effective over wide viscosities (up to $10^4\,cP$).

  3. Paddles: Laminar swirling motion; (e.g., Anchor agitator for heat transfer).

• Flow Issues:

  • Vortexing: Draw-in of air at the surface; prevented by off-center mounting or Baffles.

  • Baffles: Flat vertical strips ($width = 1/12th\,tank\,diameter$) to turn swirling into circulation.

• Power Number ($N_p$):     $N_p = \frac{P}{\rho N^3 D_a^5}$

  • Laminar flow (N_{Re} < 10): $N_p = C_o / N_{Re}$.

  • Turbulent flow (N_{Re} > 10,000): $N_p = C'$.

• Viscous Mixers: Sigma mixers (double-arm kneaders), ribbon blenders (shuffling), Banbury mixers (internal), and Muller mixers (mulling/smearing).

FLOW OF FLUIDS

• Properties:

  • Viscosity ($\mu$): Resistance to deformation. Newton's Law: $\tau = \mu (du/dy)$.

  • Kinematic Viscosity ($\nu$): $\mu / \rho$.

• Fluid Types:

  • Newtonian: Viscosity independent of shear rate.

  • Bingham Plastics: Resist flow until yield stress ($\tau_0$) is exceeded.

  • Pseudoplastic: Shear-thinning.

  • Dilatant: Shear-thickening.

• Statics:

  • Hydrostatic Balance: $P_1 - P_2 = h \rho g$.

  • Manometers: U-tube ($\Delta P = h (\rho_M - \rho)g$), Inclined, and Differential.

• Dynamics:

  • Equation of Continuity: $\dot{m} = \rho u A = constant$.

  • Bernoulli Equation: $\frac{P_1}{\rho} + g Z_1 + \frac{\alpha_1 u_1^2}{2} + \eta W_p = \frac{P_2}{\rho} + g Z_2 + \frac{\alpha_2 u_2^2}{2} + h_f$.

  • Reynolds Number ($N_{Re}$): $\frac{D u \rho}{\mu}$.

    • Laminar: N_{Re} < 2100; Turbulent: N_{Re} > 4000.

• Friction Losses:

  • Fanning Friction Factor ($f$): for laminar flow, $f = 16 / N_{Re}$.

  • Skin Friction: $h_{fs} = \frac{4 f L u^2}{2 D}$.

  • Expansion/Contraction Losses: $h_{fe} = K_e \frac{u_1^2}{2g}$; $h_{fc} = K_c \frac{u_2^2}{2g}$.

• Porous Media: Ergun Equation relates pressure drop to superficial velocity ($u_0$) and porosity ($e$).

• Measurement:

  • Venturi Meter: High pressure recovery; low coefficient of discharge ($C_v \approx 0.98$).

  • Orifice Meter: Cheap, but high power loss ($C_o \approx 0.61$).

  • Rotameter: Variable area meter where $W_{float} = Buoyancy + Drag$.

  • Pitot Tube: Measures point velocity ($u = C \sqrt{2g\Delta H}$).

  • Notches: Rectangular ($Q = \frac{2}{3} C_d B\sqrt{2g} H^{1.5}$) and V-notch ($Q = \frac{8}{15} C_d \sqrt{2g} \tan(\theta/2) H^{2.5}$).

TRANSPORTATION OF FLUIDS

• Pipe vs. Tubing: Pipe is heavy-walled and rough; tubing is thin-walled and smooth.

• Fittings: Elbows ($90^\circ = 32D$ equiv. length), Tees, Reducers, Back-pressure valves.

• Centrifugal Pumps:

  • Impellers: Open (for slurries), Semi-open, Closed (for clear liquids).

  • Casing: Volute or Diffuser (more efficient).

  • Priming: Removal of air to avoid Air Binding.

  • NPSH (Net Positive Suction Head): $\text{Absolute Pressure Head at Suction} - \text{Vapour Pressure Head}$.

  • Cavitation: Flashing of liquid into vapour when suction pressure < vapour pressure; causes noise and damage.

• Positive Displacement Pumps:

  • Reciprocating: Piston, Plunger, Diaphragm (for corrosive/viscous fluids).

  • Rotary: Gear pumps (two meshes, fixed volume/rev), Mono pumps (helical rotor).

• Gas Moving Devices:

  • Fans: Pressure < $30\,kPa$.

  • Blowers: Pressure up to $250\,kPa$ (e.g., Rootes/Lobe blower).

  • Compressors: Interstage cooling is necessary due to high heat of compression.

• Vacuum Devices: Steam-jet ejectors, Liquid ring vacuum pumps.

• Theories of Compression:

  • Isothermal Work: $W = \frac{P_1}{\rho_1} \ln\left(\frac{P_2}{P_1}\right)$.

  • Adiabatic Work: $W = \frac{P_1 \gamma}{\rho_1 (\gamma - 1)} \left[ \left(\frac{P_2}{P_1}\right)^{1 - 1/\gamma} - 1 \right]$.