Fluid Mechanics and Hydraulics
Fluid Mechanics and Hydraulics covers fluid properties, hydrostatic pressure, buoyancy, Bernoulli and momentum principles, pipe friction and minor losses, open-channel flow, hydraulic jumps, and dimensional analysis. Numerical questions usually hinge on correct units and choosing the right head-loss equation.
Core rules
- Hydrostatic pressure p=ρgh; the centre of pressure is below the centroid for a submerged vertical plane.
- Continuity Q=A₁V₁=A₂V₂; Bernoulli p/γ+z+V²/2g=constant for ideal steady flow.
- Darcy-Weisbach h_f=fLV²/(2gD); Chezy V=C√(RS); Manning V=(1/n)R^(2/3)S^(1/2).
- Momentum equation ΣF=ρQ(V₂−V₁) gives forces on bends and jumps.
- Specific energy E=y+V²/2g; critical flow occurs at Froude number Fr=1.
Worked example
A 200 mm diameter pipe, 100 m long, carries water at 2 m/s with f=0.02. Head loss h_f=fLV²/(2gD)=0.02×100×2²/(2×9.81×0.2)=2.04 m. If the inlet pressure head is 30 m, the outlet pressure head is about 30−2.04=27.96 m, neglecting elevation and minor losses. Here f is the Darcy friction factor, not the Fanning factor.
Traps
- Using diameter in mm in Darcy-Weisbach.
- Confusing Darcy f with Fanning f, which is four times smaller.
- Applying Bernoulli across a pump without adding pump head.
- Using diameter instead of hydraulic radius for a pipe.
- Forgetting that specific energy is measured above the channel bed.