4.1 Fluid Properties & Fluid Statics

Fluid Properties You Must Know

The Fundamentals of Engineering (FE) Civil exam is open only to the searchable NCEES FE Reference Handbook, so the goal is to recognize and apply fluid relations quickly, not memorize them. Start with the properties that feed every later formula.

Density (ρ) is mass per unit volume. For water, ρ = 1.94 slug/ft³ (US Customary, USC) = 1000 kg/m³ (SI). Specific weight (γ) is weight per unit volume, γ = ρg, giving water γ ≈ 62.4 lb/ft³ = 9.81 kN/m³. Specific gravity (SG) is the dimensionless ratio SG = ρ_fluid/ρ_water = γ_fluid/γ_water, referenced to water at 4°C.

Viscosity measures a fluid's resistance to shear. Dynamic (absolute) viscosity μ appears in Newton's law of viscosity, τ = μ(dv/dy), where τ is the shear stress and dv/dy is the velocity gradient (rate of shear strain). Fluids that obey this linear relation are Newtonian (water, air, oil); fluids whose apparent viscosity changes with shear rate are non-Newtonian. Kinematic viscosity ν = μ/ρ (units ft²/s or m²/s) is what enters the Reynolds number you will use for pipe flow. 0×10⁻⁶ m²/s. Remember that viscosity of a liquid decreases as temperature rises, but for a gas it increases — a frequent conceptual trap.

Surface tension (σ) is the energy per unit area at a liquid interface; it drives capillary rise h = 2σ·cos(θ)/(γ·r) in a tube of radius r, where θ is the contact angle. Water wets glass (θ ≈ 0°, water rises), while mercury does not (θ > 90°, mercury depresses). Vapor pressure is the pressure at which a liquid boils at a given temperature; when local pressure drops to the vapor pressure (e.g., on a pump suction line or impeller), the liquid flashes to vapor and cavitation occurs — a recurring exam theme tied to pumps and Net Positive Suction Head (NPSH).

The handbook tabulates these properties versus temperature; on the exam you read the value at the stated temperature rather than recalling it. Keep unit systems consistent — a slug is the USC mass unit (1 slug = 1 lb·s²/ft), and mixing pound-mass with pound-force is a classic error.

Hydrostatic Pressure & Manometry

In a static fluid, gauge pressure increases linearly with depth: p = γh, where h is the depth below the free surface. This follows from dp/dz = −γ integrated over a constant-density fluid. Pressure at a point acts equally in all directions (Pascal's principle) and is independent of the shape or total volume of the container — only depth matters. Absolute pressure adds atmospheric pressure: p_abs = p_atm + p_gauge, with standard p_atm ≈ 14.7 psi = 101.3 kPa = 33.9 ft of water = 760 mm Hg. A negative gauge pressure (below atmospheric) is a partial vacuum.

Manometers convert a pressure into a measurable column height and are solved segment-by-segment: starting from one open end, add γh going down and subtract γh going up, then set the expression equal to the pressure at the other end. For a differential manometer with a heavy gauge fluid of specific weight γ_m reading a deflection R between two points carrying a lighter fluid γ_f, the pressure difference is Δp = (γ_m − γ_f)·R. A common trap is forgetting the difference term when both legs contain the working fluid, or mixing up the direction (down adds, up subtracts).

Always track elevation changes carefully and keep specific weights in consistent units.

Forces on Surfaces & Buoyancy

For a submerged plane surface, the resultant hydrostatic force is F = γ·h_c·A, where h_c is the vertical depth to the centroid and A is the area. The force acts at the center of pressure (CP), located below the centroid by y_cp − y_c = I_xc/(y_c·A), where I_xc is the area moment of inertia about the centroidal axis. The CP is always at or below the centroid — never above.

For curved surfaces, resolve into horizontal and vertical components: the horizontal component equals the force on the vertical projection; the vertical component equals the weight of fluid (real or imaginary) above the surface.

Buoyancy (Archimedes): the upward force on a submerged or floating body equals the weight of displaced fluid, F_B = γ·V_displaced. A body floats when its weight equals F_B, so it displaces a volume V = W/γ.

Worked Example — Force on a Submerged Gate

A vertical rectangular gate 2 m wide and 3 m tall has its top edge 1 m below a water surface. Find the resultant force.

• Centroid depth h_c = 1 + 3/2 = 2.5 m; A = 2×3 = 6 m².
• F = γ·h_c·A = 9.81 kN/m³ × 2.5 m × 6 m² = 147.2 kN.
• I_xc = bh³/12 = 2(3)³/12 = 4.5 m⁴; CP offset = I_xc/(h_c·A) = 4.5/(2.5×6) = 0.30 m below centroid, so the force acts 2.8 m below the surface.