Fluid Mechanics – Part I Basics (School of PE – FE Exam Review)

Vocabulary flashcards summarizing fundamental terms, equations, and concepts introduced in the Fluid Mechanics – Part I lecture notes for FE Exam preparation.

Fluid

A substance in the liquid or gas phase that cannot sustain shear stress and conforms to the shape of its container.

Intensive Property

A property independent of the mass of a system (e.g., temperature, pressure, density).

Extensive Property

A property that depends on the size or extent of a system (e.g., total mass, total volume).

Specific Property

An extensive property expressed per unit mass (e.g., specific volume, specific energy).

Density (ρ)

Mass per unit volume of a fluid; units kg/m³ or lbm/ft³.

Specific Volume (v)

Volume per unit mass; reciprocal of density (v = 1/ρ).

Specific Weight (γ)

Weight per unit volume; γ = ρ g; units N/m³ or lbf/ft³.

Specific Gravity (SG)

Ratio of a fluid’s density (or specific weight) to that of a standard fluid (water at 4 °C for liquids, air at STP for gases).

Stress

Force acting over an elemental area; normal or shear components; units Pa or N/m².

Shear Stress (τ)

Tangential force per unit area in a fluid; for Newtonian fluids τ = μ (dv/dy).

Newtonian Fluid

Fluid whose shear stress is linearly proportional to the rate of shear deformation (n = 1 in power-law).

Non-Newtonian Fluid

Fluid whose shear stress–strain-rate relation is nonlinear (includes pseudoplastic, dilatant, Bingham).

Pseudoplastic Fluid

Shear-thinning non-Newtonian fluid (n < 1); e.g., paints, polymer solutions.

Dilatant Fluid

Shear-thickening non-Newtonian fluid (n > 1); e.g., starch or sand suspensions.

Bingham Plastic

Material behaving as a rigid body until a yield stress is exceeded, then flows (e.g., toothpaste, drilling mud).

Dynamic (Absolute) Viscosity (μ)

Ratio of shear stress to shear rate; units N·s/m² (Pa·s) or lbf·s/ft².

Kinematic Viscosity (ν)

Dynamic viscosity divided by density (ν = μ/ρ); units m²/s or ft²/s.

Surface Tension (σ)

Force per unit length acting along a liquid surface due to molecular attraction; units N/m.

Capillary Rise (h)

Height a liquid column rises or falls in a small tube: h = 4 σ cos β / (ρ g d).

Cohesion

Attractive force between like molecules within a fluid (e.g., mercury).

Adhesion

Attractive force between unlike molecules (e.g., water and glass).

Absolute Pressure

Actual pressure relative to a perfect vacuum.

Gauge Pressure

Pressure measured relative to local atmospheric pressure (Pabs = Patm + Pgauge).

Hydrostatic Equation

Pressure change with depth in a static fluid: dP/dz = –ρ g.

Manometer

Fluid column device for measuring pressure differences based on hydrostatic balance.

Barometer

Closed-tube manometer used to measure atmospheric pressure.

Resultant Hydrostatic Force

Total force on a submerged surface; equals average pressure times area, acts at center of pressure.

Center of Pressure

Point on submerged surface where resultant hydrostatic force acts; below the centroid.

Buoyant Force

Upward force on a submerged or floating body equal to weight of displaced fluid (Archimedes’ Principle).

Center of Buoyancy

Centroid of the displaced fluid volume where buoyant force acts.

Continuity Equation

Conservation of mass for steady incompressible 1-D flow: A₁V₁ = A₂V₂.

Bernoulli Equation

Energy conservation for steady incompressible flow: P/γ + z + V²/2g = constant (plus head loss terms for real fluids).

Head Loss (h_f)

Energy loss per unit weight due to friction and fittings in a pipe system.

Hydraulic Gradient Line (HGL)

Plot of (P/γ + z) along a pipeline; indicates static head distribution.

Energy Grade Line (EGL)

Plot of total head (P/γ + z + V²/2g); lies above HGL by the velocity head amount.

Reynolds Number (Re)

Dimensionless parameter Re = ρVD/μ = VD/ν that characterizes laminar (< 2100), transitional, or turbulent (> 10 000) flow.

Critical Reynolds Number

Value (~2100 for pipes) at which laminar flow becomes turbulent.

Hydraulic Diameter (D_H)

Characteristic length for non-circular conduits: D_H = 4A/P.

Darcy-Weisbach Equation

Friction head loss in a pipe: h_f = f (L/D) (V²/2g).

Friction Factor (f)

Dimensionless coefficient in Darcy-Weisbach equation; depends on Re and relative roughness (ε/D).

Minor Loss Coefficient (K)

Dimensionless multiplier relating head loss in fittings to velocity head: h_L = K V²/2g.

Pump Head (h_p)

Energy per unit weight added to a fluid by a pump, included in Bernoulli equation as +h_p.

Impulse-Momentum Principle

Resultant external force equals rate of change of momentum across a control volume: ΣF = Σṁ Vout – Σṁ Vin.

Pitot Tube

Instrument measuring fluid velocity by converting kinetic energy into a stagnation pressure difference.

Venturi Meter

Device that measures flow rate via pressure difference created by a converging-diverging section; Q = C_v A₂ √[2g(Δh)/(1−(A₂/A₁)²)].

Orifice Meter

Plate with sharp-edged hole inserted in a pipe to measure flow rate using the pressure drop across the orifice.

Vena Contracta

Location of minimum cross-section downstream of an orifice where velocity is maximum.

Jet Propulsion Force

Thrust produced by fluid jet: F = ṁ (Vexit − Vinlet) ≈ ρA V² for jet issuing to atmosphere.

Laminar Pipe Velocity Profile

Parabolic distribution v(r)=vmax[1−(r/R)²]; vmax = 2 v_avg.

Shear Stress Ratio in Pipe

τ/τ_w = r/R for laminar flow in a circular pipe.

Hydrostatic Force on Vertical Gate

Acts 2/3 of the depth from the surface (1/3 up from bottom) on a rectangular vertical gate.

Capillary Wetting Angle (β)

Angle between liquid surface and tube wall: β < 90° (wetting) causes rise; β > 90° (non-wetting) causes depression.

Mach Number (M)

Ratio of fluid velocity to local speed of sound; Pitot formula valid for M ≤ 0.3.

Entrance & Exit Loss Coefficients

Typical head losses: K ≈ 0.5 at a sharp-edged entrance, K ≈ 1.0 at a sudden pipe exit.

Hydraulic Radius (R_H)

Cross-sectional area divided by wetted perimeter; R_H = A/P (equal to D/4 for a full circular pipe).