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Agitator and Reactor Mechanical Design
Agitator power scales as N_p·ρ·N³·D⁵, so power is extremely sensitive to impeller speed and diameter; the power number itself depends on the impeller type and on whether the flow is laminar or turbulent (via the impeller Reynolds number).
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.
Key formulas & points
Skim these first — then read the full notes below.
- Baffles prevent vortexing — four baffles are standard for turbulent mixing
- Gas–liquid k_L a rises with power per volume and gas superficial velocity
- Mechanical seal versus packing for the shaft penetration
Topic details
Introduction
This topic sizes stirred vessels and their drives. You compute the impeller Reynolds number to fix the flow regime, read the power number from the impeller-type chart, calculate power draw, and select impeller type, baffling and shaft/seal arrangement for the mixing duty — blending, suspension, or gas dispersion.
Key relations & formulas
(impeller Reynolds number)
(power draw, power number N_p)
(blend time in turbulent mixing)
Notation and sign conventions
Relation 1 —
(impeller Reynolds number)
Write this relation with symbols exactly as in Bhattacharya Chemical Equipment Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
(power draw, power number N_p)
Write this relation with symbols exactly as in Bhattacharya Chemical Equipment Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
(blend time in turbulent mixing)
Write this relation with symbols exactly as in Bhattacharya Chemical Equipment Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Concept in depth
The power law P = N_p ρ N³ D⁵ shows why mixing scale-up is tricky: power rises with the cube of speed and the fifth power of diameter, so a modest size increase demands a large motor. The power number N_p is roughly constant in fully turbulent flow but rises steeply in the laminar regime, so the impeller Reynolds number must be checked first. Baffles convert wasteful swirling into effective top-to-bottom turnover and prevent the central vortex that would otherwise pull in air. For gas–liquid contacting the mass-transfer coefficient k_L a is driven by power per unit volume, which is why scale-up often holds P/V constant.
Assumptions and validity limits
State assumptions explicitly before using any relation for agitator and reactor mechanical design — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Process Equipment Design viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Process Equipment Design papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to agitator and reactor mechanical design.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to agitator and reactor mechanical design.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
Agitator and Reactor Mechanical Design appears in EPCM and fabrication. In Indian chemical curricula this topic is tested because it connects theory to mechanical design of vessels and columns.
GATE and semester exams often combine agitator and reactor mechanical design with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use agitator and reactor mechanical design?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
Students treat the power number as constant even in laminar flow, forget the fifth-power diameter dependence during scale-up, and omit baffles (grossly under-predicting power). Using vessel diameter instead of impeller diameter in the power equation is a frequent slip.
Quick revision checklist
Before attempting agitator and reactor mechanical design problems, confirm you can:
1. Baffles prevent vortexing — four baffles are standard for turbulent mixing
2. Gas–liquid k_L a rises with power per volume and gas superficial velocity
3. Mechanical seal versus packing for the shaft penetration
2. Gas–liquid k_L a rises with power per volume and gas superficial velocity
3. Mechanical seal versus packing for the shaft penetration
Revise the solved examples in Bhattacharya Chemical Equipment Design — Standard reference and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Agitator power draw
Problem
A turbine (N_p = 5) of D = 0.5 m runs at N = 2 rev/s in a liquid of ρ = 1000 kg/m³ (turbulent). Find the power.
Solution
P = N_p ρ N³ D⁵ = 5×1000×2³×0.5⁵ = 5×1000×8×0.03125 = 1250 W = 1.25 kW.
Conceptual check — Agitator and Reactor Mechanical Design
Problem
In a Process Equipment Design semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of agitator and reactor mechanical design." What should a complete answer include?
Exams & GATE
Pick the power number for a turbine, propeller, or anchor impeller.
📖 Standard books (India)
Bhattacharya Chemical Equipment Design — Standard reference
Read: Syllabus unit
Referenced in Indian B.Tech syllabus
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