Mixing and agitation

Chemical Engineering (B.E./B.Tech) · Fluid and particle mechanics · free study notes for exams, placements and interviews

In short

Mixing and agitation is the unit operation that uses a rotating impeller (or a static device) to create bulk flow and turbulence in a vessel so that composition, temperature, suspended solids, dispersed drops or gas bubbles become uniform. It decides blend time, heat-transfer coefficient, crystal size, reaction selectivity and fermenter oxygen supply, so almost every stirred reactor, blend tank, crystalliser, neutraliser and bioreactor is designed around it. In exams it is tested through standard tank geometry, the power number versus impeller Reynolds number curve, power and scale-up calculations, and Zwietering's just-suspended-speed correlation; GATE (CH) asks numerical power, N_P, N_Re and scale-up questions. Indian employers who test it include fertiliser and petrochemical majors, paints and specialty-chemical makers (Asian Paints, Pidilite, Atul, Aarti, SRF), pharma and biotech (Sun Pharma, Cipla, Biocon, Serum Institute) and process-equipment suppliers (Chemineer-type agitator vendors, L&T, Thermax).

Explained

What mixing means and how it is classified

Mixing reduces non-uniformity (concentration, temperature, phase) in a system; agitation is the induced motion of material in a vessel in a defined pattern, usually by an impeller. Agitation need not mix (a swirling vortex rotates fluid without exchanging it).
Scales of mixing: *macromixing* - bulk convective circulation around the tank; *mesomixing* - dispersion of a feed plume; *micromixing* - molecular-scale blending inside the smallest eddies. Reaction selectivity and crystal nucleation depend on micromixing, blend time on macromixing.
Duty-based classification: liquid-liquid blending (miscible), solid-liquid suspension and dissolution, liquid-liquid dispersion (emulsification), gas-liquid dispersion (absorption, aeration), heat transfer, and multi-duty reactor mixing.
Mechanisms in powder (solids) mixing: convective (bulk transfer), diffusive (random inter-particle motion), shear (slip planes). Ribbon blenders, V-cone, double-cone and plough-share mixers are used; solids mixing can *demix* by size or density difference, which liquid blending does not.
Degree of mixedness for solids: *mixing index* based on standard deviation of composition of spot samples against the fully random value.

Impellers, vessel geometry and flow patterns

Flow pattern classes: *axial flow* (pumps fluid along the shaft axis - pitched-blade turbine, hydrofoil, marine propeller) suits blending and solid suspension at low power; *radial flow* (throws fluid out to the wall - flat-blade disc turbine/Rushton, paddle) gives high shear, suits gas and liquid dispersion; *tangential flow* (anchor, helical ribbon) suits high viscosity.
Turbine impellers: six-blade Rushton disc turbine (radial, N_P ≈ 5-6 baffled turbulent), pitched-blade turbine 45° (mixed/axial, N_P ≈ 1.3-1.5), hydrofoil (axial, N_P ≈ 0.3), marine propeller (axial, N_P ≈ 0.35 at pitch = D).
Close-clearance impellers for viscous fluids: anchor (sweeps the wall, used above roughly 20-50 Pa·s), helical ribbon (gives axial top-to-bottom motion up to very high viscosity, laminar regime), screw with draft tube.
High-shear devices: saw-tooth disperser for pigment dispersion, rotor-stator homogeniser for emulsions, colloid mill.
Standard "square" tank geometry (the configuration assumed in exam problems): flat-bottom or dished vertical cylinder, liquid depth H = T (tank diameter), impeller diameter D = T/3, impeller clearance from bottom C = T/3 (or D), four vertical baffles of width T/10 or T/12 set 90° apart, blade width W = D/5, blade length L = D/4, disc diameter = 2D/3.
Baffles convert swirl into top-to-bottom circulation, stop central vortexing and air entrainment, and make power draw reproducible. Four baffles of T/10-T/12 are near-optimum; more add little. Off-centre or angled mounting is an alternative in small or glass-lined vessels; baffles are often omitted for very viscous fluids (Re < ~20) where swirl does not develop.
Draft tube forces a defined circulation loop; used in crystallisers (DTB) and some fermenters.
Multiple impellers are used when H/T > 1.2-1.5, spaced about one D apart and sized so each handles roughly one "square" zone.

Power consumption - the central correlation

Power drawn by an impeller in a Newtonian fluid depends on N, D, ρ, μ, g and geometry. Dimensional analysis gives N_P = f(N_Re, N_Fr, geometric ratios).
Impeller Reynolds number N_Re = ρND²/μ: laminar below about 10, transitional 10-10⁴, fully turbulent above about 10⁴.
Power curve (log N_P vs log N_Re) for a fixed geometry:
1. *Laminar* (N_Re < 10): N_P = K_L/N_Re, so P ∝ μN²D³ - power is viscosity-controlled and independent of density.
2. *Transition*: slope changes gradually.
3. *Turbulent* (N_Re > 10⁴, baffled): N_P = constant, so P ∝ ρN³D⁵ - independent of viscosity.
Froude number N_Fr = N²D/g matters only in unbaffled tanks where a surface vortex forms; power is then corrected by N_Fr^m. In a fully baffled tank the Froude correction is dropped.
Gassing lowers power: P_g/P_0 falls to about 0.4-0.6 for a Rushton turbine at normal aeration rates because bubbles form low-density cavities behind the blades. Aeration number N_A = Q_g/(ND³).
Non-Newtonian fluids: use an apparent viscosity from the average shear rate near the impeller, commonly γ̇_avg = k_s N with k_s ≈ 11-13 for turbines; then μ_app = K(k_s N)ⁿ⁻¹ for a power-law fluid and read N_P off the standard curve.

Blend time, pumping capacity and mixing quality

Blend (mixing) time θ is the time to reach a stated uniformity (usually 95% or 99%). In the turbulent regime for a given geometry, Nθ = constant, so θ ∝ 1/N; blend time is independent of viscosity once turbulent.
A useful correlation form for turbulent blending to 95%: θ ≈ 5.9 (T^1.5 H^0.5)/(N_P^1/3 N D²) - treat the numerical coefficient as geometry-dependent, since different texts quote slightly different values.
Pumping (circulation) capacity Q = N_Q N D³, where N_Q (flow number) ≈ 0.72-0.79 for a pitched-blade turbine, ~0.5-0.55 for a hydrofoil, ~0.72 for a Rushton. Circulation time t_c = V/Q; blend time is typically 4-5 circulation times.
Flow versus shear trade-off: at the same power, Q ∝ N_Q N D³ and head/shear ∝ N²D², so a *large, slow* impeller gives high flow and low shear (blending, suspension) while a *small, fast* impeller gives high shear and low flow (dispersion, emulsification).
Tip speed πND (m/s) is the practical shear indicator - roughly 2.5-4 m/s for gentle blending, 5-7 m/s for dispersion, 10+ m/s for high-shear duties and a limit for shear-sensitive cells or flocs.
Specific power input P/V (W/m³ or kW/m³) is the common sizing yardstick: ~0.05-0.2 kW/m³ mild blending, 0.3-0.6 kW/m³ solids suspension, 1-2 kW/m³ gas dispersion and vigorous reaction, 2-5 kW/m³ for fermenters and emulsification.
Kolmogorov microscale η = (ν³/ε)^0.25 sets the smallest eddy size; drop and bubble break-up and micromixing scale with the local energy dissipation ε.

Solid suspension, gas dispersion and heat transfer

Degrees of solid suspension: *on-bottom motion* → *just complete (off-bottom) suspension* (no particle rests on the base longer than 1-2 s - Zwietering criterion) → *uniform suspension*. Design is usually to N_js plus a margin.
Zwietering correlation: N_js = S ν^0.1 (g Δρ/ρ_L)^0.45 X^0.13 d_p^0.2 / D^0.85; S depends on impeller type and C/T (e.g. ~6-8 for a pitched-blade turbine at C = T/4, higher for a Rushton high off the bottom). Lower clearance (C = T/4 or T/6) reduces N_js.
Gas dispersion: sparger below the impeller; below a minimum speed the gas floods the impeller (passes straight up without dispersion). Flooding-to-dispersion transition correlates with N_A and N_Fr. Rushton or concave/Scaba-type blades handle gas best.
Mass transfer: k_L a = C (P_g/V)^α (u_s)^β with α ≈ 0.4-0.7 and β ≈ 0.2-0.5 - fitted per system, so quote the form, not fixed constants.
Liquid-liquid dispersion: drop size is set by a balance of inertial break-up and interfacial tension - Weber number We = ρN²D³/σ; Sauter mean diameter d₃₂ falls as We rises.
Heat transfer in jacketed stirred tanks: Nu = a·Re^2/3·Pr^1/3·(μ/μ_w)^0.14 with Re = ρND²/μ; coils or half-pipe jackets raise U. Agitation can raise the inside film coefficient several-fold.
Static (motionless) mixers - helical or lattice elements in a pipe - mix by repeated splitting and recombination with no moving parts; sized by pressure drop and number of elements. Used for inline dosing, polymer blending and coagulant mixing in water plants. Jet mixers in large storage tanks use a pumped nozzle; air-lift / sparged mixing is used where no shaft is wanted.

Scale-up, mechanical design and Indian codes

Geometric similarity is the usual basis: keep all length ratios and scale by one variable. The scale ratio R = D₂/D₁.
You cannot keep all dimensionless groups constant at once. Common choices:
- Equal P/V (most common for turbulent blending, suspension and fermenters): N₂ = N₁(D₁/D₂)^2/3.
- Equal tip speed (shear-sensitive products, dispersion): N₂ = N₁(D₁/D₂).
- Equal blend time (Nθ constant): N₂ = N₁, which makes P/V rise as R² - usually impossible at large scale.
- Equal Reynolds number: N₂ = N₁(D₁/D₂)², giving absurdly low power at scale - rarely used.
Consequence of equal P/V scale-up: tip speed rises as R^1/3, blend time rises as R^2/3, Reynolds number rises as R^4/3. So large tanks are *more* turbulent locally but *slower* to blend - the classic exam point.
Mechanical items: shaft sized for torque (T = P/2πN) plus bending from hydraulic side loads, checked against critical (whirling) speed; stuffing box, lip seal, single or double mechanical seal for pressure vessels; steady bearing/bottom bush for long shafts; gearbox with motor; for glass-lined reactors, retreat-curve impeller.
Indian practice and codes: unfired stirred pressure vessels are designed to IS 2825 (Code for unfired pressure vessels) or ASME Section VIII Div. 1, with flanges to IS 6392 / ASME B16.5; materials to IS 2062 for carbon steel plate and ASTM A240 / IS grades for stainless; motors to IS/IEC 60034 with IE3-class efficiency mandated for most industrial induction motors under the BEE/Energy Conservation Act framework; hazardous-area agitator drives to IS/IEC 60079. Pharma mixing vessels follow Schedule M of the Drugs and Cosmetics Rules (revised GMP schedule, with the upgraded requirements phased in from 2025) plus WHO-GMP, needing sanitary finish, CIP/SIP and no dead legs. Worker safety around rotating machinery - guarding, lock-out, confined-space entry for tank cleaning - now falls under the Occupational Safety, Health and Working Conditions Code, 2020, in force from 21 November 2025, which replaced the Factories Act, 1948. ISO/IS numbers for mixer testing vary by equipment class - verify the current edition before citing one.

Key points

Agitation vs mixing - agitation is induced motion; mixing is reduction of non-uniformity. Swirl without exchange is agitation, not mixing.
Standard tank - H = T, D = T/3, C = T/3, four baffles of T/10-T/12, W = D/5.
Power number N_P = P/(ρN³D⁵) - constant (≈5-6 for Rushton, 1.3-1.5 for 45° PBT, ~0.3 for hydrofoil) in baffled turbulent flow.
Impeller Reynolds number N_Re = ρND²/μ - laminar <10, turbulent >10⁴.
Laminar regime - P ∝ μN²D³, independent of density; turbulent regime - P ∝ ρN³D⁵, independent of viscosity.
Froude number N²D/g - only relevant in unbaffled tanks where a vortex forms.
Baffles - kill swirl, prevent vortexing and air entrainment, raise power draw and make it reproducible.
Axial impellers for blending and solid suspension; radial impellers for gas and liquid-liquid dispersion.
Flow number Q = N_Q N D³ - large slow impeller means high flow, low shear; small fast impeller the reverse.
Nθ = constant in turbulent flow, so blend time is inversely proportional to speed and independent of viscosity.
Tip speed πND - the practical shear measure and the limit for cells, flocs and crystals.
P/V - the sizing yardstick: ~0.1 kW/m³ blending to ~2-5 kW/m³ fermentation and emulsification.
Zwietering N_js - the speed for just-complete solid suspension; falls with lower impeller clearance.
Gassed power P_g/P_0 ≈ 0.4-0.6 for a Rushton at normal aeration; flooding occurs if speed is too low for the gas rate.
Scale-up at equal P/V - N ∝ D^−2/3; tip speed ∝ R^1/3, blend time ∝ R^2/3, Re ∝ R^4/3.
Viscous fluids - anchor and helical ribbon in the laminar regime; mixing is by stretching and folding, not eddies.
Static mixers - no moving parts, mix by split-and-recombine, sized by number of elements and pressure drop.
Solids blending differs - convective, diffusive and shear mechanisms, with segregation possible on continued mixing.

Formulas and examples

N_P = P / (ρ N³ D⁵) - power number (dimensionless). P = power, W; ρ = density, kg/m³; N = impeller speed, rev/s; D = impeller diameter, m.
N_Re = ρ N D² / μ - impeller Reynolds number. μ = viscosity, Pa·s.
N_Fr = N² D / g - Froude number; g = 9.81 m/s².
Laminar: P = K_L μ N² D³ ; Turbulent (baffled): P = N_P ρ N³ D⁵
Q = N_Q N D³ - pumping capacity, m³/s; circulation time t_c = V/Q, s.
Tip speed = π N D, m/s ; Torque = P/(2πN), N·m.
Nθ = constant (turbulent) - θ = blend time, s.
N_js = S ν^0.1 [g(ρ_s − ρ_L)/ρ_L]^0.45 X^0.13 d_p^0.2 / D^0.85 - Zwietering; ν = kinematic viscosity m²/s, X = mass of solid per 100 mass of liquid, d_p = particle size m, S = geometry factor.
Scale-up at equal P/V: N₂ = N₁ (D₁/D₂)^2/3 ; equal tip speed: N₂ = N₁ (D₁/D₂)
ε = P/(ρV) - mean specific energy dissipation, W/kg; Kolmogorov scale η = (ν³/ε)^0.25, m.
Power-law apparent viscosity at the impeller: μ_app = K (k_s N)ⁿ⁻¹, k_s ≈ 11-13.
Gas-liquid: N_A = Q_g/(N D³) ; k_L a = C (P_g/V)^α u_s^β.

Example 1 - Turbulent power draw of a Rushton turbine. A baffled tank, T = 1.8 m, holds water (ρ = 1,000 kg/m³, μ = 1.0 × 10⁻³ Pa·s) to H = T. A six-blade Rushton turbine, D = T/3 = 0.6 m, runs at 120 rpm = 2.0 rev/s. Take N_P = 5.5.

N_Re = 1,000 × 2.0 × 0.6²/1.0 × 10⁻³ = 1,000 × 2.0 × 0.36/0.001 = 7.2 × 10⁵ → fully turbulent, so N_P is constant.
D⁵ = 0.6⁵ = 0.07776 m⁵; N³ = 8.0.
P = 5.5 × 1,000 × 8.0 × 0.07776 = 3,422 W ≈ 3.42 kW.
Liquid volume V = (π/4)(1.8²)(1.8) = 0.7854 × 3.24 × 1.8 = 4.58 m³ → P/V = 3.42/4.58 = 0.75 kW/m³ (vigorous blending duty).
Motor: shaft power 3.42 kW plus gearbox and seal losses (~15%) ≈ 3.9 kW → select a 4 kW (5.5 hp) motor as the next standard IEC frame (step up to 5.5 kW if more margin is wanted).
Tip speed = π × 2.0 × 0.6 = 3.77 m/s; torque = 3,422/(2π × 2.0) = 272 N·m.

Example 2 - Laminar power in a viscous fluid. Same impeller (D = 0.6 m) at N = 0.5 rev/s in a resin of ρ = 1,100 kg/m³ and μ = 60 Pa·s. For this geometry K_L ≈ 71 (laminar constant for a Rushton turbine).

N_Re = 1,100 × 0.5 × 0.36/60 = 198/60 = 3.3 → laminar.
P = K_L μ N² D³ = 71 × 60 × 0.25 × 0.216 = 230 W.
Check via the curve: N_P = K_L/N_Re = 71/3.3 = 21.5; P = 21.5 × 1,100 × 0.125 × 0.07776 = 230 W - consistent.
Note the power is *lower* than the water case even though viscosity is 60,000 times higher, because the speed is one-quarter: this is why viscous duties use large, slow, close-clearance impellers rather than turbines.

Example 3 - Scale-up at equal power per unit volume. A pilot tank of 0.05 m³ uses D₁ = 0.15 m at N₁ = 300 rpm (5 rev/s), N_P = 1.4 (45° PBT), ρ = 1,000 kg/m³. Scale geometrically to 5 m³ (volume ratio 100, so length ratio R = 100^1/3 = 4.642), D₂ = 0.15 × 4.642 = 0.696 m.

Pilot power P₁ = 1.4 × 1,000 × 5³ × 0.15⁵ = 1.4 × 1,000 × 125 × 7.594 × 10⁻⁵ = 13.3 W → P₁/V₁ = 13.3/0.05 = 266 W/m³.
Equal P/V: N₂ = N₁ R^−2/3 = 5 × 4.6416^−2/3 = 5/2.7826 = 1.797 rev/s ≈ 108 rpm.
P₂ = 1.4 × 1,000 × 1.797³ × 0.696⁵ = 1.4 × 1,000 × 5.803 × 0.16333 = 1,327 W ≈ 1.33 kW → P₂/V₂ = 1,327/5 = 265 W/m³, equal to P₁/V₁ as required.
Why P/V must match: P ∝ N³D⁵ ∝ R⁻²R⁵ = R³ while V ∝ R³, so equal P/V is automatic - use it as the arithmetic check. (Watch the exponent: R^2/3 for R = 4.6416 is 2.783, not 2.154.)
Consequences: tip speed rises from π × 5 × 0.15 = 2.36 m/s to π × 1.797 × 0.696 = 3.93 m/s (ratio R^1/3 = 1.666 ✓); if Nθ = 50, blend time rises from 50/5 = 10 s to 50/1.797 = 27.8 s (ratio R^2/3 = 2.78 ✓).

Example 4 - Just-suspended speed (Zwietering). Sand (ρ_s = 2,600 kg/m³, d_p = 200 μm = 2 × 10⁻⁴ m) is suspended in water (ρ_L = 1,000 kg/m³, ν = 1 × 10⁻⁶ m²/s) at 10 kg solid per 100 kg water (X = 10). Tank T = 1.2 m, pitched-blade turbine D = 0.4 m, C = T/4, S = 6.0.

ν^0.1 = (10⁻⁶)^0.1 = 10^−0.6 = 0.2512.
[g Δρ/ρ_L]^0.45 = [9.81 × 1,600/1,000]^0.45 = 15.70^0.45. ln 15.70 = 2.754 → × 0.45 = 1.2393 → e^1.2393 = 3.453.
X^0.13 = 10^0.13 = 1.349.
d_p^0.2 = (2 × 10⁻⁴)^0.2: ln(2 × 10⁻⁴) = −8.517 → × 0.2 = −1.7034 → e^−1.7034 = 0.1821.
D^−0.85 = 0.4^−0.85: ln 0.4 = −0.9163 → × (−0.85) = 0.7789 → e^0.7789 = 2.179.
N_js = 6.0 × 0.2512 × 3.453 × 1.349 × 0.1821 × 2.179 = 6.0 × 0.2512 = 1.507; × 3.453 = 5.204; × 1.349 = 7.020; × 0.1821 = 1.278; × 2.179 = 2.79 rev/s ≈ 167 rpm.
Design at ~1.1-1.2 × N_js → about 185-200 rpm. Power at 2.79 rev/s with N_P = 1.4, ρ_slurry ≈ 1,059 kg/m³ (1/ρ = 0.0909/2,600 + 0.9091/1,000): P = 1.4 × 1,059 × 21.7 × 0.4⁵ = 1.4 × 1,059 × 21.7 × 0.01024 = 329 W; V = 0.7854 × 1.44 × 1.2 = 1.357 m³ → 243 W/m³.

Example 5 - Gassed power and blend time in a fermenter. A 10 m³ fermenter (T = 2.2 m, H ≈ 2.7 m) has two Rushton turbines of D = 0.73 m at 110 rpm (1.833 rev/s) in broth of ρ = 1,020 kg/m³, μ = 2 × 10⁻³ Pa·s.

N_Re = 1,020 × 1.833 × 0.73²/2 × 10⁻³ = 1,020 × 1.833 × 0.5329/0.002 = 996.3/0.002 = 4.98 × 10⁵ → turbulent.
Ungassed power per impeller: D⁵ = 0.73⁵ = 0.2073; N³ = 6.159. P = 5.5 × 1,020 × 6.159 × 0.2073 = 7,163 W. Two impellers, second at ~80% effectiveness: P₀ ≈ 7,163 + 5,730 = 12.9 kW → 1.29 kW/m³.
Gassed at P_g/P₀ = 0.55: P_g ≈ 7.1 kW → 0.71 kW/m³ - the motor must be sized for the *ungassed* 12.9 kW case (plus losses), because gas can fail.
Blend time with Nθ ≈ 45 for a dual-turbine tall tank: θ = 45/1.833 ≈ 25 s.
Aeration: 0.5 vvm → Q_g = 5 m³/min = 0.0833 m³/s; N_A = 0.0833/(1.833 × 0.389) = 0.117 - below the flooding-to-dispersion limit for this geometry (≈ 30(D/T)^3.5·N_Fr ≈ 0.16 here), so the impeller disperses rather than floods.

Impeller	Flow	N_P (baffled, turbulent)	N_Q	Best for
Rushton disc turbine (6 blade)	Radial	5.0-6.0	~0.72	Gas dispersion, high shear
Flat-blade paddle	Radial	1.5-2.5	-	Simple blending, viscous
45° pitched-blade turbine (4 blade)	Axial/mixed	1.3-1.5	0.72-0.79	Solid suspension, blending, heat transfer
Hydrofoil (high-efficiency)	Axial	0.3-0.4	0.5-0.55	Low-shear blending, large volumes
Marine propeller (pitch = D)	Axial	~0.35	~0.5	Small tanks, portable mixers
Anchor	Tangential	0.3-0.5 (laminar, Re-dependent)	-	μ > ~20 Pa·s, wall heat transfer
Helical ribbon	Axial, laminar	K_L/N_Re (K_L ~ 150-350)	-	Very high viscosity, pastes

Scale-up basis	N₂/N₁	P/V ratio	Tip speed ratio	Blend time ratio
Equal P/V	R^−2/3	1	R^1/3	R^2/3
Equal tip speed	R⁻¹	R⁻¹	1	R
Equal blend time (Nθ)	1	R²	R	1
Equal Reynolds number	R⁻²	R⁻⁴	R⁻¹	R²

(R = D₂/D₁, geometric similarity, turbulent regime.)

Where it is used

Bulk and specialty chemicals: neutralisers, sulphonators, nitrators and batch reactors at Aarti Industries, Atul, SRF and Deepak Nitrite, where mixing sets selectivity and hot-spot control.
Paints, inks, adhesives: high-shear saw-tooth dispersers for pigment wetting followed by low-shear blending at Asian Paints, Berger, Pidilite - the classic flow-versus-shear choice.
Pharma and biotech: stirred fermenters and crystallisers at Biocon, Serum Institute, Sun Pharma and Divi's - sized on kLa, tip-speed limits for shear-sensitive cells, and Schedule M sanitary design.
Fertiliser, metallurgical and mineral processing: leach tanks, CCD thickener feed, slurry agitators at IFFCO, Coromandel, Hindalco and HZL - designed on Zwietering just-suspension plus a margin.
Water and effluent treatment: rapid-mix (flash mixers, static mixers) for coagulant dosing and slow flocculators with paddle gates, per CPHEEO manual practice in municipal plants and ETPs.
Job roles: process design engineer (agitator datasheets, power and N_js calculations), rotating-equipment and project engineers (shaft, seal, critical speed, IS 2825 nozzle loads), plant/production engineers troubleshooting batch non-uniformity, and process-equipment sales and application engineers with agitator vendors.

Interview questions

Q: Why are baffles used in a stirred tank? A: They convert solid-body swirl into top-to-bottom circulation, so they prevent surface vortexing and air entrainment, improve mixing and give a reproducible, viscosity-independent power draw.
Q: What does the power number represent and when is it constant? A: N_P = P/(ρN³D⁵) is the ratio of imposed drag force to inertial force; it is constant for a given geometry in fully turbulent, baffled flow (N_Re above about 10⁴).
Q: Why does the Froude number drop out of the power correlation in a baffled tank? A: The Froude number accounts for gravity waves at a vortexing free surface; baffles suppress the vortex, so gravity no longer influences power.
Q: In the laminar regime does power depend on density? A: No - P = K_L μ N² D³ depends on viscosity, speed and diameter; density drops out because viscous forces dominate inertia.
Q: For the same power input, which gives more flow - a large slow impeller or a small fast one? A: The large slow impeller; flow scales as ND³ while shear/head scales as N²D², so a big slow impeller is high-flow low-shear and a small fast one the opposite.
Q: Which impeller would you pick to suspend sand in water, and why? A: A pitched-blade or hydrofoil axial-flow turbine at low clearance (C = T/4), because its downward axial jet sweeps the tank bottom at far less power than a radial turbine.
Q: How does blend time change when you scale up at equal power per unit volume? A: It increases as R^2/3 (R = diameter ratio), because N falls as R^−2/3 while Nθ stays constant - so big tanks blend more slowly despite being more turbulent.
Q: Why does aeration reduce impeller power draw, and how do you size the motor? A: Gas cavities behind the blades reduce the effective fluid density, cutting power to roughly 40-60% of ungassed; the motor is sized for the ungassed condition because a sparger trip would otherwise overload it.
Q: What is impeller flooding? A: When the gas rate is too high (or speed too low), gas rises in a column through the impeller without being dispersed, so mass transfer collapses; cured by raising speed, lowering gas rate or using concave-blade impellers.
Q: How do you mix a 50 Pa·s polymer solution? A: With a close-clearance anchor or helical ribbon at low speed in the laminar regime - mixing comes from stretching and folding and wall sweep, not turbulent eddies; a turbine would only churn a local cavern.
Q: What is a "cavern" in yield-stress fluid mixing? A: A well-mixed zone around the impeller surrounded by stagnant fluid where the imposed shear stress falls below the yield stress; it is overcome with larger-diameter or wall-sweeping impellers, not more speed.
Q: When would you use a static mixer instead of a stirred tank? A: For continuous inline duties with modest viscosity ratios - coagulant dosing, pH trim, polymer additive blending - where no moving parts, no seals, small footprint and plug-flow residence time are advantages, and the pressure drop is acceptable.

Common mistakes

Using N in rpm instead of rev/s in N_P, N_Re, Q and tip-speed formulas - the single most frequent numerical error, as it changes power by 60³.
Taking N_P from the standard curve while ignoring that the curve is tied to one geometry (D/T, C/T, W/D, baffling) - changing clearance or baffles changes the number.
Applying the turbulent relation P ∝ ρN³D⁵ to a viscous fluid without checking N_Re, or applying the Froude correction in a fully baffled tank.
Forgetting that blend time *rises* on scale-up at equal P/V; students often assume a bigger, more turbulent tank mixes faster.
Sizing the agitator motor on gassed power instead of ungassed power, so the drive trips when the sparger fails.
Mixing up flow and shear requirements - choosing a Rushton turbine for gentle large-volume blending (wasted power) or a hydrofoil for emulsification (no shear).
Using slurry volume but pure-liquid density (or vice versa) in power and N_js calculations, and ignoring that N_js needs particle size in metres and X as mass per 100 mass of liquid.