Fluid Mechanics and Heat Transfer
What the exam tests
Pipe and duct hydraulics, pump and compressor selection, NPSH, packed and fluidised beds, flow metering, and heat-exchanger thermal design - LMTD, effectiveness–NTU, fouling, boiling and condensation.
Core rules
- Reynolds number uses the inside diameter and bulk velocity; use Colebrook or Swamee–Jain for friction factor; minor losses are ΣKv²/2g and equivalent length.
- Pump duty is the intersection of the pump curve and the system curve; Bernoulli with pump head added gives the required head.
- NPSHa = (p_s − p_v)/ρg + z − h_f. Require NPSHa above NPSHr by at least 1 m or 1.1×NPSHr.
- LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂); apply correction factor F for multipass shell-and-tube.
- 1/U_o = 1/h_o + R_f,o + (D_o/D_i)R_f,i + (D_o/D_i)(1/h_i) + wall resistance.
- Effectiveness ε = Q/Q_max, with NTU = UA/C_min for the chosen flow arrangement.
Worked example
A counter-current exchanger runs hot side 150 → 90 °C and cold side 30 → 70 °C. ΔT₁ = 150 − 70 = 80 K, ΔT₂ = 90 − 30 = 60 K. LMTD = (80 − 60)/ln(80/60) = 20/0.2877 = 69.5 K. With U = 500 W/m²K and Q = 2.0 MW, area A = 2×10⁶/(500 × 69.5) = 57.6 m². Co-current operation would give ΔT₁ = 120, ΔT₂ = 20 and LMTD = 57.7 K, requiring more area - flow arrangement is a real design variable.
Traps
- Using arithmetic mean temperature difference when ΔT₁/ΔT₂ exceeds about 2.
- Omitting fouling, which can add 20–50% to required area.
- Computing NPSHa without suction-line friction losses.
- Selecting a tube velocity below 1 m/s (fouling) or above 3 m/s (erosion).