Fluid Mechanics and Hydraulics
Fluid mechanics and hydraulics tests properties of fluids, hydrostatics, buoyancy, Bernoulli’s theorem, flow measurement, pipe losses and open-channel flow. Expect numerical questions using Manning, Darcy–Weisbach and continuity.
Core rules
- Density of water 1000 kg/m³; specific weight 9.81 kN/m³; kinematic viscosity about 1 × 10⁻⁶ m²/s at 20°C.
- Hydrostatic pressure p = ρgh, acting normal to the surface; centre of pressure is below the centroid for a vertical submerged plane.
- Continuity Q = AV; Bernoulli p/γ + V²/2g + z = constant along a streamline for ideal flow.
- Darcy–Weisbach hf = fLV²/(2gD); Chezy V = C√(RS); Manning V = (1/n)R^(2/3)S^(1/2).
- Hydraulic jump converts supercritical to subcritical flow; sequent-depth calculations use the Froude number.
Worked example
A rectangular channel is 5 m wide, carries 2 m depth, has bed slope 1 in 1000 and Manning n = 0.015. Area A = 5 × 2 = 10 m²; wetted perimeter P = 5 + 2 × 2 = 9 m; hydraulic radius R = 10/9 = 1.111 m. V = (1/0.015) × 1.111^(2/3) × (0.001)^(1/2) = 66.67 × 1.0727 × 0.03162 = 2.26 m/s. Discharge Q = AV = 10 × 2.26 = 22.6 m³/s.
Traps
Using flow depth as hydraulic radius; mixing Manning and Chezy; forgetting slope must be dimensionless; applying Bernoulli across large energy losses without a head-loss term.