Fluid Mechanics
Fluid mechanics for civil engineers: water properties, hydrostatic pressure and forces on dams and gates, buoyancy, continuity, Bernoulli's energy equation, and how they apply to dams, tanks, spillways and water supply.
Civil engineers hold back, move, store and treat enormous volumes of water. Dams resist hydrostatic thrust, pipelines and canals carry flow, and treatment plants depend on controlled flow through tanks and filters.
A small set of principles — pressure grows with depth, mass is conserved, energy is conserved (minus losses) — explains almost all of it.
An analogy
Water in a dam is like a heavy crowd leaning on a fence: the deeper you go, the harder they push, so the fence (dam) must be thickest at the bottom.
Hydrostatics
Pressure acts equally in all directions and increases 9.81 kPa per metre of water depth. The resultant thrust on a vertical wall of depth H is ½γ_wH² per metre width, acting at one third of the depth from the bottom. This drives design of dams, tanks, locks and gates.
Gravity dams
A gravity dam resists water thrust with its own weight. Checks: overturning about the toe, sliding along the base or foundation, and bearing/tension at the heel. Uplift pressure from water seeping under the dam reduces effective weight dramatically — drainage galleries and grout curtains reduce it.
Continuity and energy
Flow rate is conserved; velocity rises in narrow sections. Bernoulli's equation trades elevation, pressure and velocity heads, with head losses in real flows. The energy grade line (EGL) and hydraulic grade line (HGL) visualise these along pipelines and canals.
Hydraulic structures
Spillways discharge floods safely, stilling basins dissipate energy with hydraulic jumps, and intakes and surge tanks manage transients. Physical models (Froude similarity) and CFD are used to design complex structures.
Formulas
- Hydrostatic pressure:
p = γ_w h - Thrust on vertical face (per m):
P = ½ γ_w H² at H/3 above base - Continuity:
Q = A₁V₁ = A₂V₂ - Bernoulli / energy:
z₁ + p₁/γ + V₁²/2g = z₂ + p₂/γ + V₂²/2g + h_L - Uplift (triangular, no drains):
U = ½ γ_w H B
Worked example: Thrust on a dam
Given: Water depth 10 m against a vertical face
Find: Thrust and overturning moment per metre.
- P = ½ × 9.81 × 10² = 490.5 kN/m
- Acts 10/3 = 3.33 m above base → M = 1635 kN·m/m
Answer: 490.5 kN/m; 1635 kN·m/m
Worked example: Stability of a triangular gravity dam
Given: Height 10 m, base 8 m, vertical upstream face; Concrete 24 kN/m³, μ = 0.7
Find: FS overturning and sliding (no uplift).
- W = ½ × 8 × 10 × 24 = 960 kN/m, lever from toe = 8 − 8/3 = 5.33 m
- FS_o = 960 × 5.33/1635 = 3.13 ✓
- FS_s = 0.7 × 960/490.5 = 1.37
Answer: FS_o ≈ 3.1, FS_s ≈ 1.37 (before uplift!)
Common mistakes
- Wrong: Ignoring uplift under dams and basements. — Right: Uplift can reduce effective weight by 40 % or more — provide drains or design for it.
- Wrong: Placing hydrostatic resultant at mid-depth. — Right: It acts at H/3 above the base (centroid of the triangle).
Applications
- Dams & barrages: Hydrostatic thrust, uplift and seepage govern design.
- Water tanks & reservoirs: Wall thickness and reinforcement from hydrostatic pressure.
- Water supply: Continuity and energy equations size mains and pumping heads.
Key takeaways
- p = γ_w h; thrust ½γ_wH² at H/3.
- Continuity and energy equations govern flow.
- Check dams for overturning, sliding and uplift.
- Drainage reduces uplift and improves stability.
Going further
- Froude similarity: Hydraulic scale models match Froude number so gravity-driven flows scale correctly.
- Seepage analysis: Flow nets and FE seepage models estimate uplift and exit gradients under dams.
- Dam safety: Probable maximum flood, earthquake and instrumentation form dam safety programmes.