Pipe flow & pressure drop on the PE Mechanical exam

Pressure drop in piping shows up constantly on the Thermal & Fluid Systems depth (and in hydronic HVAC work) — it feeds pump sizing, system curves, and energy balances. Master the Darcy-Weisbach workflow and the Moody diagram and a whole class of problems becomes fast.

What you actually need to own

• Darcy-Weisbach: h_f = f · (L/D) · (V^2 / 2g), the head loss for major (friction) losses.
• Reynolds number: Re = ρVD/μ = VD/ν, which sets the flow regime — laminar (Re < ~2300) vs turbulent (Re > ~4000).
• The friction factor f:
  • Laminar: f = 64/Re (no chart needed).
  • Turbulent: read f from the Moody diagram using Re and relative roughness ε/D (or solve Colebrook). Know how to enter the chart correctly.
• Minor (local) losses: h_minor = K · V^2 / 2g, summed over fittings, valves, entrances, and exits.
• Continuity (A1·V1 = A2·V2) and the energy equation to carry pressure drop into a full system (with pump head and elevation). For water specifically, Hazen-Williams is an alternate empirical method some problems use.

Where people lose points

• Using the laminar f = 64/Re in turbulent flow (or skipping the regime check entirely).
• Misreading the Moody diagram — wrong relative-roughness curve or wrong Re.
• Dropping minor losses, or mixing head loss (ft) with pressure drop (psi) without converting (Δp = γ·h_f).
• Velocity errors from using the wrong area (nominal vs actual inside diameter).

How to study it

Build a fixed routine: compute Re → pick the regime → get f (formula or Moody) → apply Darcy + minor losses → convert head to pressure. Drill it on series and parallel piping until the steps are reflexive, then connect the pressure drop to the pump and system curve.

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