Water Demand, Population Forecasting and Water Quality
Per capita demand and peak factors, population forecasting methods, physical, chemical and biological water quality parameters, hardness, alkalinity, pH and drinking water standards.
A water supply scheme starts with two questions: how much water will the town need over the design period, and what must be removed to make it safe?
Water demand
- Per capita demand in India: about 135 litres per capita per day (lpcd) for cities with full sewerage (CPHEEO), with lower values for smaller towns.
- Peak factors (fire demand aside): maximum daily demand ≈ 1.8 × average; maximum hourly demand ≈ 1.5 × maximum daily = 2.7 × average.
- Fire demand: Kuichling's formula Q = 3182 √P (L/min, P in thousands), or as specified locally.
- Design periods: about 30 years for the scheme as a whole.
Population forecasting
With past census populations:
| Method | Formula | Suits |
|---|---|---|
| Arithmetic increase | P_n = P₀ + n x̄ | Old, stable cities |
| Geometric increase | P_n = P₀ (1 + r)ⁿ | Young, fast-growing cities |
| Incremental increase | P_n = P₀ + n x̄ + n(n + 1) ȳ/2 | Average cities |
| Logistic curve | S-shaped growth to a saturation value | Long-term planning |
x̄ = average increase per decade, ȳ = average increment of the increases, r = geometric mean growth rate per decade.
Water quality
Physical: turbidity (NTU), colour, taste and odour, temperature.
Chemical:
- pH = −log₁₀[H⁺]; drinking water 6.5–8.5.
- Hardness (Ca²⁺ and Mg²⁺) as mg/L CaCO₃: hardness = Σ (concentration × 50/equivalent weight). Carbonate hardness ≤ alkalinity; the rest is non-carbonate hardness.
- Alkalinity: OH⁻, CO₃²⁻ and HCO₃⁻, also expressed as CaCO₃.
- Chlorides, nitrates (blue-baby syndrome above about 45 mg/L as NO₃), fluoride (dental and skeletal fluorosis above 1.5 mg/L), iron, manganese, arsenic.
Biological: coliforms indicate faecal contamination. MPN (most probable number) test, membrane filter test. Drinking water must have no E. coli in 100 mL.
Standards: IS 10500 (Indian drinking water specification).
Worked example
Water contains 40 mg/L Ca²⁺ and 12 mg/L Mg²⁺ (equivalent weights 20 and 12).
- Hardness = 40 × 50/20 + 12 × 50/12 = 100 + 50 = 150 mg/L as CaCO₃.
Practice
A town has 50,000 people now and grows geometrically at 20% per decade. What is the population after 2 decades?
Show answer and explanation
Answer: 72000P = 50,000 × 1.2² = 72,000.
A city of 1 lakh people uses 135 lpcd. What is the maximum hourly demand in MLD, taking 2.7 × average? (Give 3 decimal places.)
Show answer and explanation
Answer: 36.45Average = 13.5 MLD; × 2.7 = 36.45 MLD (rate).
A water sample has pH 5. What is its hydrogen ion concentration in mol/L?
Show answer and explanation
Answer: ApH = −log[H⁺], so [H⁺] = 10⁻⁵ mol/L.
Water has 60 mg/L Ca²⁺ (equivalent weight 20) and no magnesium. What is its total hardness as mg/L CaCO₃?
Show answer and explanation
Answer: 150Hardness = 60 × 50/20 = 150 mg/L as CaCO₃.