Fluid Mechanics
Fluid mechanics is the single largest knowledge area on the FE Other Disciplines exam, so fluency here pays off more than anywhere else. Almost every problem collapses into one of a few tools: fluid statics (pressure with depth), continuity (mass conservation), the Bernoulli energy equation, or a friction-loss model. Learn to recognize which tool a problem calls for and most of the work is done.
Fluid properties and specific weight
A fluid is described first by its density ρ (mass per volume) and its specific weight γ = ρ·g (weight per volume). For water at standard conditions ρ = 1000 kg/m³, so γ = 1000·9.81 = 9,810 N/m³ ≈ 9.81 kN/m³. Specific gravity SG is the ratio of a fluid's density to that of water: an oil with SG = 0.8 has ρ = 800 kg/m³. Viscosity μ (dynamic) and ν = μ/ρ (kinematic) measure a fluid's resistance to shear and control whether flow is smooth or turbulent. The FE almost always hands you ρ, g, and SG directly, so the skill being tested is converting cleanly between density, specific weight, and specific gravity.
Fluid statics: pressure with depth
In a static fluid, gauge pressure grows linearly with depth: p = ρ·g·h = γ·h, where h is the vertical distance below the free surface. Pressure at a point acts equally in all directions and does not depend on container shape or the total volume of fluid. A tank of oil (SG 0.8) 5 m deep gives p = 800·9.81·5 ≈ 39.2 kPa gauge. Absolute pressure adds atmospheric: p_abs = p_gauge + p_atm. Manometers apply the same rule column by column — a mercury column (SG 13.6) of 0.2 m represents p = 13,600·9.81·0.2 ≈ 26.7 kPa. The classic trap is mixing gauge and absolute pressure, or using slant length instead of true vertical height.
Buoyancy and submerged forces
Archimedes' principle: the buoyant force on a submerged or floating body equals the weight of the fluid it displaces, F_b = ρ_fluid·g·V_displaced. A body floats when its average density is less than the fluid's, sinking until displaced weight equals body weight. For a flat submerged surface, the resultant hydrostatic force is F = p_centroid·A = γ·h_c·A, acting at the center of pressure, which lies below the centroid because pressure increases with depth. Recognizing that the force uses the pressure at the centroid — not the maximum pressure — is a common point-earner.
Continuity and volumetric flow
Conservation of mass for steady incompressible flow gives the continuity equation A₁·V₁ = A₂·V₂, so velocity rises where the area shrinks. Halving the pipe area doubles the velocity. Volumetric flow rate is Q = A·V (m³/s); for a round pipe A = π·D²/4. Water at 3 m/s in a 0.1 m pipe carries Q = (π/4)(0.1)²·3 ≈ 0.0236 m³/s. Mass flow rate is ṁ = ρ·Q. The frequent mistake is forgetting that area scales with diameter squared, so a small diameter change produces a large velocity change.
The Bernoulli energy equation
Along a streamline with no losses, p/γ + V²/(2g) + z = constant, where each term is a 'head' in meters: pressure head, velocity head, and elevation head. Energy simply trades among the three. A tank draining through a small opening a depth h below the surface gives Torricelli's result V = √(2·g·h) — for h = 5 m, V ≈ 9.9 m/s — because pressure and elevation head at the surface convert entirely to velocity head at the jet. Real systems append a head-loss term h_L to the downstream side to account for friction.
Flow regime, friction, and open channels
The dimensionless Reynolds number Re = ρ·V·D/μ = V·D/ν sets the regime: below about 2,100 pipe flow is laminar (smooth, ordered), above about 4,000 it is turbulent, with a transition band between. Pipe friction loss uses Darcy-Weisbach, h_L = f·(L/D)·V²/(2g), where the friction factor f depends on Re and relative roughness (read from a Moody chart). Open-channel flow uses Manning's equation for velocity as a function of slope, roughness, and hydraulic radius. On the FE the first move is almost always to compute Re, because it tells you which loss model and friction correlation are valid.
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