(a) What is a flood hydrograph ? The monthly discharge (Q) data of a river at a gauging station are given below : - January: 30…

(a) A flood hydrograph is a plot of discharge (Q) against time at a gauging site for a flood caused by a storm. It has a rising limb (runoff building up), a crest (peak discharge) and a recession or falling limb (depletion of storage). The flow below a base-flow separation line is base flow (groundwater), and the area above it is direct runoff. The time from the start of rise to the crest is the time to peak, and the duration of direct runoff is the time base.

The given data are mean monthly discharges, so their plot is an annual (flow) hydrograph, not the hydrograph of a single storm. The method of plotting and reading it is the same.

Plot month on the x-axis (each value at mid-month) and Q in m³/s on the y-axis, then join the points:

• January 30, February 40, March 50, April 60
• May 80, June 90, July 100, August 120
• September 110, October 90, November 80, December 70

Reading from the graph:

• Peak flow = 120 m³/s, in August (highest ordinate, after the monsoon build-up from May to July).
• Minimum flow = 30 m³/s, in January (lean season, sustained only by base flow).

(b)

(i) Evaporation is the change of water from liquid to vapour at a free water surface or a wet soil surface. Its rate follows Dalton's law, E = C(e_w − e_a), where e_w is the saturation vapour pressure at the water temperature and e_a the actual vapour pressure of the air. It increases with temperature, solar radiation, wind speed and vapour-pressure deficit, and decreases with humidity and with salinity of water. It is measured with a Class A pan, and lake evaporation ≈ 0.7 × pan evaporation.

(ii) Transpiration is the loss of water as vapour from living plants, mainly through the stomata of leaves. Water taken up by the roots moves up the plant and escapes to the air. It depends on the plant type and stage of growth, soil moisture, sunlight (stomata open by day), temperature, wind and humidity. It is measured with a phytometer.

(iii) Evapotranspiration (ET) is the total water lost from a vegetated area by evaporation from soil and water surfaces plus transpiration by plants; in practice the two cannot be separated. Potential ET (PET) is the rate when water supply to the soil and plants is unlimited; actual ET (AET) is the rate under the actual soil moisture, so AET ≤ PET. ET is the consumptive use of crops and is measured with lysimeters or estimated by the Penman or Blaney–Criddle methods.

(iv) Infiltration is the entry of water into the soil through the ground surface. The maximum rate at which a soil can absorb water at a given time is its infiltration capacity f_p; the actual rate equals rainfall intensity when intensity is below f_p, and equals f_p otherwise, the excess becoming surface runoff. Capacity falls with time as the soil wets, as in Horton's equation f = f_c + (f_0 − f_c)e^(−kt). It depends on soil texture, initial moisture, vegetation cover, compaction and rainfall intensity, and is measured with a ring infiltrometer. Downward movement of water already in the soil is percolation, not infiltration.

(c) Given P = 72.3, 86.4, 94.2, 103.8 and 71.4 cm, n = 5 and ε = 5%.

Mean: P̄ = 428.1/5 = 85.62 cm

Deviations (P − P̄) and their squares:

• 72.3: −13.32, 177.42
• 86.4: +0.78, 0.61
• 94.2: +8.58, 73.62
• 103.8: +18.18, 330.51
• 71.4: −14.22, 202.21

Σ(P − P̄)² = 784.37

Standard deviation (n − 1 in the denominator): σ = √(784.37/4) = √196.09 = 14.00 cm

Coefficient of variation: Cv = 100σ/P̄ = 100 × 14.00/85.62 = 16.36%

Optimum number of gauges: N = (Cv/ε)² = (16.36/5)² = 10.7, so N = 11

Additional raingauges needed = 11 − 5 = 6

(d) Given Q_w = 2 m³/s, L_w = 1000 mg/L; Q_r = 8 m³/s, L_r = 10 mg/L; k = 0.1/day (base e); u = 10 km/day.

At 0 km (just after mixing), by mass balance: L₀ = (Q_r L_r + Q_w L_w)/(Q_r + Q_w) = (8 × 10 + 2 × 1000)/10 = 2080/10 = 208 mg/L (ultimate CBOD)

BOD₅ = L₀(1 − e^(−5k)) = 208(1 − e^(−0.5)) = 208 × 0.3935 = 81.8 mg/L

At 20 km downstream, travel time t = 20/10 = 2 days: L₂₀ = L₀e^(−kt) = 208e^(−0.2) = 208 × 0.8187 = 170.3 mg/L (ultimate CBOD)

BOD₅ = 170.3 × 0.3935 = 67.0 mg/L

So in 2 days of travel about 38 mg/L of CBOD has been exerted (208 − 170.3), and this oxygen demand is what creates the dissolved-oxygen sag downstream. The results assume complete mixing at the outfall, plug flow, no other inflows, and k to base e. If k were to base 10, BOD₅ at 0 km would be 142.2 mg/L, and at 20 km L = 131.2 mg/L and BOD₅ = 89.7 mg/L.

(e) Per capita demand is the annual average quantity of water needed per person per day, in litres per capita per day (Lpcd). It includes domestic, commercial and institutional, industrial and public uses, fire demand, and losses in the system.

It is determined as: q = total yearly quantity of water required by the town (litres) ÷ (365 × design population)

In practice the total is built up from the separate demands, or taken from records of metered supply, and checked against CPHEEO norms. The CPHEEO norms are 135 Lpcd for towns with sewerage, 150 Lpcd for metropolitan cities and 70 Lpcd for towns without sewerage. It varies with climate, size of the city, standard of living, industries, metering and pricing, supply pressure and system losses.

Consumption is not uniform, so peak factors are applied to the average q = 135 Lpcd. Goodrich's formula p = 180 t^(−0.10) (p in % of average, t in days) gives the factors for daily, weekly and monthly peaks.

(i) Maximum daily demand (t = 1 day, p = 180%): = 1.8 × 135 = 243 Lpcd

(ii) Maximum weekly demand (t = 7 days, p = 180 × 7^(−0.1) = 148%): = 1.48 × 135 = 200 Lpcd

(iii) Maximum monthly demand (t = 30 days, p = 180 × 30^(−0.1) = 128%): = 1.28 × 135 = 173 Lpcd

(iv) Maximum hourly demand = 1.5 × average hourly demand of the maximum day = 1.5 × 1.8 × average = 2.7 × average: = 2.7 × 135 = 364.5 Lpcd (as a rate), i.e. 364.5/24 ≈ 15.2 litres per person per hour

Maximum daily demand is used to size the source, intake and treatment plant. Maximum hourly demand (or maximum daily plus fire demand, whichever is larger) is used to size the distribution pipes.