Fluid Mechanics on the FE Exam
Fluid mechanics is a core topic on several FE exam disciplines, typically accounting for 5 to 11% of the exam depending on your chosen discipline. The FE Civil, FE Mechanical, and FE Chemical exams all include significant fluid mechanics content. Mastering the fundamental concepts and key equations is essential for maximizing your score in this area.
Fluid Properties
Start by understanding basic fluid properties. Density is mass per unit volume, while specific weight is weight per unit volume (density times gravitational acceleration). Specific gravity is the ratio of a fluid's density to the density of water. Viscosity describes a fluid's resistance to shear deformation and comes in two forms: dynamic (absolute) viscosity and kinematic viscosity (dynamic viscosity divided by density).
Surface tension and capillarity are less frequently tested but may appear. Surface tension is the force per unit length at a fluid surface, and capillary rise or depression depends on surface tension, contact angle, tube diameter, and fluid properties.
Fluid Statics
Hydrostatic pressure increases linearly with depth: pressure equals the specific weight times depth plus the surface pressure. This relationship governs the design of dams, tanks, and submerged structures. Know how to calculate hydrostatic forces on flat and curved surfaces, including the location of the center of pressure.
Buoyancy follows Archimedes' principle: the buoyant force on a submerged or floating object equals the weight of the fluid displaced. Practice problems involving floating objects and submerged bodies, including stability of floating objects.
Manometry problems require applying the hydrostatic pressure equation across each fluid column. Work from a point of known pressure through the manometer, adding pressure when going down in a fluid and subtracting when going up.
Bernoulli's Equation
Bernoulli's equation is perhaps the most important equation in introductory fluid mechanics. It relates pressure, velocity, and elevation along a streamline for steady, incompressible, inviscid flow. The equation states that the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline.
Know the assumptions and limitations of Bernoulli's equation: steady flow, incompressible fluid, no friction (inviscid), flow along a streamline, and no energy addition or removal (no pumps or turbines). When these assumptions are violated, use the extended energy equation instead.
Pipe Flow
Pipe flow problems are among the most common fluid mechanics questions on the FE exam. The Reynolds number determines whether flow is laminar (Re less than 2300) or turbulent (Re greater than 4000). For laminar flow, the Darcy friction factor equals 64 divided by the Reynolds number. For turbulent flow, use the Moody diagram or the Colebrook equation.
Head loss in pipes includes major losses (friction along the pipe length, calculated using the Darcy-Weisbach equation) and minor losses (at fittings, valves, entrances, and exits, calculated using loss coefficients). The total head loss determines the pump power required to move fluid through a piping system.
Dimensional Analysis
The Buckingham Pi theorem provides a systematic method for creating dimensionless groups from a set of variables. While you may not need to derive dimensionless groups from scratch on the exam, understanding common dimensionless numbers is important: Reynolds number (inertia to viscous forces), Froude number (inertia to gravity), Mach number (flow velocity to speed of sound), and Weber number (inertia to surface tension).
Open Channel Flow
Open channel flow appears primarily on the FE Civil exam. Manning's equation relates flow velocity to channel slope, hydraulic radius, and Manning's roughness coefficient. The Froude number determines whether open channel flow is subcritical (Fr less than 1), critical (Fr equals 1), or supercritical (Fr greater than 1). Know how to calculate normal depth and critical depth for rectangular and trapezoidal channels.
Exam Tips
Draw diagrams for every fluid mechanics problem. Label all known quantities, identify the unknowns, and select the appropriate equation before calculating. Pay close attention to units, especially when converting between pressure units (Pa, psi, atm, ft of water). The FE Reference Handbook provides most fluid mechanics formulas, but practice using them efficiently during your study sessions.