Fluid Mechanics and Hydraulics
Fluid Mechanics and Hydraulics tests fluid properties, hydrostatics, continuity, Bernoulli's equation, momentum, flow measurement, pipe friction, open-channel flow, and hydraulic jumps. Problems are usually short but unit-sensitive.
Core rules
- Hydrostatic pressure is p = ρgh; the centre of pressure lies below the centroid for a vertical submerged plane.
- Continuity: Q = A₁V₁ = A₂V₂; Bernoulli: p/ρg + V²/2g + z = constant along a streamline for ideal flow.
- Darcy-Weisbach: h_f = fLV²/(2gD); Manning for open channels: V = (1/n)R^(2/3)S^(1/2).
- Hydraulic radius R = A/P, not the flow depth.
- Froude number Fr = V/√(gy); Fr = 1 is critical flow, Fr < 1 subcritical, Fr > 1 supercritical.
Worked example
A rectangular channel is 2 m wide, carries 1 m depth, has n = 0.015, and bed slope S = 0.001. A = 2 × 1 = 2 m²; P = 2 + 2(1) = 4 m; R = 0.5 m. Then V = (1/0.015) × 0.5^(2/3) × 0.001^(1/2) = 66.67 × 0.630 × 0.0316 ≈ 1.33 m/s, and Q = AV ≈ 2.66 m³/s. Keep R in metres and slope dimensionless.
Traps that cost marks
- Using diameter instead of radius in pipe area, or depth instead of hydraulic radius in Manning.
- Mixing gauge and absolute pressure.
- Applying Bernoulli across a pump or turbine without adding the head term.
- Forgetting that specific energy is minimum at critical depth.
Exam focus
Practise pipe-flow, venturi, orifice, and open-channel problems; check whether the flow is laminar or turbulent before choosing a friction formula.