Fluid mechanics fundamentals on the PE Mechanical exam

Bernoulli and continuity underpin a big share of the Thermal & Fluid Systems "principles" bucket and feed pump, nozzle, and pipe-flow problems. Get the energy bookkeeping right and the rest follows.

What you actually need to own

• The energy (extended Bernoulli) equation between two points: p1/γ + V1^2/2g + z1 + h_pump = p2/γ + V2^2/2g + z2 + h_turbine + h_loss. Each term is a head (length): pressure head, velocity head, elevation head. Most fluid problems are just this equation with the right terms kept or dropped.
• Continuity: A1·V1 = A2·V2 (incompressible) — the link between pipe size and velocity.
• Hydrostatics: p = γ·h (gauge pressure with depth); manometer and force-on-submerged-surface problems.
• When to add losses and machine head: include h_loss for real piping (pressure drop), h_pump where a pump adds energy, h_turbine where it's extracted. Ideal Bernoulli (no losses) is only for short, frictionless idealizations.
• Gauge vs absolute pressure, and consistent use of γ (specific weight) vs ρ (density).

Where people lose points

• Forgetting head loss (or the pump/turbine term) and applying ideal Bernoulli to a real system.
• Mixing gauge and absolute pressure within one equation.
• Velocity-head slips — wrong area in continuity, or dropping V^2/2g when velocities differ.
• Unit inconsistency between γ, ρ, and g (USCS vs SI).

How to study it

Practice writing the full energy equation first, then crossing out the terms that are zero or negligible for the problem at hand — that habit prevents both forgotten losses and over-complication. Drill continuity + Bernoulli together on nozzle, siphon, and pipe problems until the term bookkeeping is automatic.

Part of the Thermal & Fluid Systems exam. → Start your 7-day free trial — no card.