Fluid Mechanics
Fluid mechanics is the single largest knowledge area on the FE Other Disciplines exam, so it rewards fluency with a small set of governing equations. Nearly every problem reduces to fluid statics (pressure with depth), continuity (mass conservation), or energy (the Bernoulli equation) plus friction losses.
Fluid Statics
Hydrostatic pressure increases linearly with depth: p = rho·g·h, where rho is density, g is gravity, and h is the depth below the free surface. Pressure at a point acts equally in all directions and is independent of container shape. Manometers and submerged-surface forces all follow from this relation.
Continuity and the Bernoulli Equation
Conservation of mass for incompressible flow gives A1·V1 = A2·V2, so velocity rises where area shrinks. The Bernoulli equation, p/rho + V^2/2 + g·z = constant along a streamline, trades pressure, velocity, and elevation head for one another in the absence of losses. Real systems add friction (head-loss) terms.
Flow Regime and Losses
The dimensionless Reynolds number Re = rho·V·D/mu distinguishes laminar (Re below about 2,100 in a pipe) from turbulent flow. Pipe friction losses use the Darcy-Weisbach equation; open channels use Manning's equation. Recognizing the regime tells you which loss model and friction factor apply.