Kuichling’s formula: Fire flow (L/min) = 3182 × √P (P in thousands) P = 75 Fire flow = 3182 × √75 = 3182 × 8.66 = 27,556 L/min Convert to m³/day = 27,556 × 1.44 = 39,680 m³/day (459 L/s) 3. Problem Set 3: Pipe Flow – Darcy-Weisbach & Hazen-Williams Problem 3.1 A 400 mm diameter steel pipe (ε = 0.045 mm) carries water at 20°C (ν = 1×10⁻⁶ m²/s) over a length of 800 m. Flow rate = 0.25 m³/s. Calculate head loss using: (a) Darcy-Weisbach equation (b) Hazen-Williams (C=120)
Using h_f = K × Q^1.852 with K = 10.67×L / (C^1.852×D^4.87) D=0.25m → D^4.87 = 0.25^4.87 = 0.25^4 × 0.25^0.87 = 0.003906 × 0.305 = 0.001191 C^1.852 = 100^1.852 = 5120 (approx)
Static head = 95 – 50 = 45 m Velocity V = Q/A = 0.05 / (π×0.1²) = 0.05 / 0.0314 = 1.59 m/s Friction loss h_f = f × (L/D) × (V²/2g) = 0.02 × (1200/0.2) × (1.59²/19.62) = 0.02 × 6000 × (2.528/19.62) = 0.02 × 6000 × 0.1288 = 15.46 m Total head H = 45 + 15.46 = 60.46 m water supply engineering solved problems pdf
Reynolds Re = V×D/ν = 1.99×0.4 / 1e-6 = 796,000 (turbulent) Relative roughness = ε/D = 0.045/400 = 0.0001125 From Moody chart: f ≈ 0.014 Head loss h_f = f × (L/D) × (V²/(2g)) = 0.014 × (800/0.4) × (1.99²/(2×9.81)) = 0.014 × 2000 × (3.96/19.62) = 0.014 × 2000 × 0.202 = 5.66 m
Average increase per decade = [(55-45)+(68-55)+(84-68)] / 3 = (10+13+16)/3 = 13,000 per decade P2030 = P2010 + 2 × 13,000 = 84,000 + 26,000 = 110,000 Kuichling’s formula: Fire flow (L/min) = 3182 ×
Hydraulic power P_h = ρ × g × Q × H = 1000 × 9.81 × 0.05 × 60.46 = 1000 × 9.81 × 3.023 = 29,660 W = 29.66 kW
Q_max daily = 1.8 × 15,000 = 27,000 m³/day (312.5 L/s) Calculate head loss using: (a) Darcy-Weisbach equation (b)
Alternatively, use the Rippl method: storage = 360 m³ (rounded to 400 m³ design). These solved problems illustrate the core computational skills required for water supply engineering: population forecasting, demand estimation, friction loss calculation, pump selection, network balancing, and storage sizing. Mastery of these methods ensures reliable and cost-effective water distribution system design.