Questions
7–9 questions per paper
Difficulty
Medium-Hard
Importance
High yield for HPCL/NTPC/ONGC
Overview
Fluid Mechanics and Mechanical Operations form the backbone of chemical process engineering, focusing on the behavior of fluids at rest and in motion along with solid-particle processing. Mastery of these topics is critical for PSUs as they test your ability to calculate energy losses, pump power requirements, and particle size distribution. Success requires a solid grasp of energy balance equations and empirical laws governing solid-fluid interactions.
Fluid Statics and Bernoulli's Equation
Bernoulli's equation is the energy conservation principle for incompressible, frictionless flow along a streamline. For real-world applications, it must be modified to account for friction losses using the mechanical energy balance.
- Bernoulli's Equation: P/ρ + v^2/2 + gz = constant
- Mechanical Energy Balance: Δ(v^2/2) + gΔz + ΔP/ρ + ΣF = 0
- Piezometric Head: P/ρg + z
- Total Head: P/ρg + v^2/2g + z
Pipe Flow and Losses
This section deals with calculating pressure drops in conduits under laminar and turbulent regimes. The transition between these regimes is dictated by the Reynolds number, which defines the friction factor.
- Reynolds Number (Re): Dvp/μ
- Darcy-Weisbach Equation: hf = 4fLV^2 / 2gD
- Fanning Friction Factor: f = 16/Re (laminar)
- Major Losses: Skin friction due to viscosity
- Minor Losses: Due to fittings, valves, and expansions
Flow Measurement and Pumping
Flow meters convert kinetic energy or pressure changes into measurable signals. Pumping systems are assessed by their ability to provide the necessary head required to overcome system losses.
- Venturi Meter: Q = Cd * A2 * sqrt(2gΔh) / sqrt(1 - (A2/A1)^2)
- Orifice Meter: Lower Cd compared to Venturi due to vena contracta
- Rotameter: Constant pressure drop, variable area flow meter
- Pump Power: P = QρgH / η
- NPSH: Net Positive Suction Head to prevent cavitation
Fluidization and Size Reduction
Fluidization occurs when solid particles are suspended by an upward flowing fluid, behaving like a liquid. Size reduction focuses on energy-based laws to determine work required for crushing and grinding.
- Minimum Fluidization Velocity: Ergun Equation
- Kick's Law: dE/dL = K/L
- Rittinger's Law: dE/dL = K/L^2
- Bond's Law: dE/dL = K/L^1.5
- Sphericity: Surface area ratio of sphere to particle
Formula Sheet
Re = Dvp/μ
hf = 4fLV^2 / 2gD
P = QρgH / η
Q = Cd * A2 * sqrt(2gΔh) / sqrt(1 - (A2/A1)^2)
Kick's: E = Kp * ln(L1/L2)
Rittinger's: E = Kr * (1/L2 - 1/L1)
Bond's: E = 10 * Wi * (1/sqrt(L2) - 1/sqrt(L1))
Ergun Equation for pressure drop in packed beds
Exam Tip
Always verify the Reynolds number first before choosing a friction factor correlation, as using the wrong regime formula is the most common cause of calculation errors in PSU exams.
Common Mistakes
- Confusing Fanning friction factor with Darcy friction factor (they differ by a factor of 4).
- Neglecting the kinetic energy correction factor in energy balances for non-uniform flow profiles.
- Forgetting to convert units, especially when calculating pump power in kW using mixed SI/FPS units.
More Revision Notes
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