(a) A storm over a catchment of area 5 km² had a duration of 14 hours. The mass curve of rainfall of the storm is as follows:

| Time from Start of Storm, t (h) (1) | Accumulated Rainfall (cm) (2) |
|-------------------------------------|------------

Question

(a) A storm over a catchment of area 5 km² had a duration of 14 hours. The mass curve of rainfall of the storm is as follows:

| Time from Start of Storm, t (h) (1) | Accumulated Rainfall (cm) (2) |
|-------------------------------------|-------------------------------|
| 0 | 0 |
| 2 | 0·6 |
| 4 | 2·8 |
| 6 | 5·2 |
| 8 | 6·7 |
| 10 | 7·5 |
| 12 | 9·2 |
| 14 | 9·6 |

If the φ index for the catchment is 0·4 cm/h, determine (i) the effective rainfall (ER) hyetograph and (ii) the volume of direct runoff from the catchment due to the storm. Show clearly one set of calculations and summarize your results in a tabular form. (iii) Also, plot the effective rainfall hyetograph.

20

(b) (i) Using the data pertaining to a wastewater treatment plant, determine the quantity of sludge produced per day:

Wastewater flow = 10 MLD

Suspended solids (SS) in raw wastewater = 250 mg/L

Efficiency of PST = 62%

Sludge concentration = 5%

Volatile solids (VS) = 60%

Specific gravity of VS = 0·980

Fixed solids = 40%

Specific gravity of fixed solids = 2·65

10

(ii) A 30 cm diameter circular sewer is laid in a section where invert slope is 1 in 500. Determine the velocity and sewage flow in the section and check for self-cleansing velocity. Take Manning's coefficient as 0·015. Assume that the sewer is running full.

5

(c) (i) Explain the problems encountered during the operation of filters in water treatment and suggest how these are controlled.

10

(ii) Enumerate the factors to be considered while designing an intake structure. Sketch a river intake and name its components.

5

UPSC Answer Check · Accepted Answer

This is a multi-part numerical and descriptive problem requiring systematic solving. Allocate approximately 40% time to part (a) given its 20 marks and computational intensity; 30% to part (b) covering sludge production and sewer hydraulics; and 30% to part (c) on filter operation problems and intake design. Begin with clear problem statements, show all calculations with proper units, present results in tabular form as demanded, and conclude with practical interpretations relevant to Indian water infrastructure contexts.
- For (a): Correctly derive incremental rainfall from mass curve, compute φ-index based effective rainfall hyetograph by subtracting 0.4 cm/h losses, identify periods with zero/positive ER, and calculate total direct runoff volume = Σ(ER) × catchment area
- For (a)(iii): Plot ER hyetograph with time on x-axis and intensity (cm/h) on y-axis, showing only bars where rainfall intensity exceeds φ-index
- For (b)(i): Calculate mass of SS removed = 10 MLD × 250 mg/L × 0.62, then sludge volume using specific gravity of solids mixture (weighted average of VS and FS) and 5% concentration
- For (b)(ii): Apply Manning's equation V = (1/n)R^(2/3)S^(1/2) for full circular sewer, compute discharge Q = VA, and compare velocity with self-cleansing criterion (typically 0.6-0.75 m/s for sanitary sewers)
- For (c)(i): Explain filter problems (mud balls, cracking, air binding, sand incrustation) with specific control measures (surface washing, backwashing rate adjustment, filter media replacement)
- For (c)(ii): Enumerate intake design factors (water quality, flood levels, navigation, ice, future demand) and sketch river intake showing components like screen, sump, pump house, and approach channel

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly applies φ-index concept for effective rainfall; understands mass curve to incremental rainfall conversion; grasps sludge volume calculation with composite specific gravity; knows Manning's equation for sewer flow; identifies all major filter operational problems and intake design factors	Basic understanding of φ-index but errors in identifying periods of effective rainfall; attempts sludge calculation but confuses mass-volume relationships; applies Manning's equation with minor errors; lists some filter problems and intake factors but incomplete	Fundamental misunderstanding of φ-index (e.g., subtracts total rather than hourly); confuses mass curve with hyetograph; incorrect specific gravity handling; wrong application of Manning's equation; vague or incorrect description of filter problems and intake design
Numerical accuracy	25%	12.5	All calculations accurate: incremental rainfall (0.6, 2.2, 2.4, 1.5, 0.8, 1.7, 0.4 cm), ER intensities, total ER = 6.6 cm, runoff volume = 0.33 Mm³ or 330,000 m³; sludge mass = 1550 kg/day, volume ≈ 31 m³/day; sewer V ≈ 0.84 m/s, Q ≈ 0.059 m³/s with correct self-cleansing check	Minor arithmetic errors in one or two sub-parts; correct methodology but calculation mistakes in ER tabulation or sludge specific gravity computation; Manning's calculation mostly correct but rounding errors; acceptable error range ±10%	Major computational errors across multiple sub-parts; wrong formulas (e.g., using Horton's instead of φ-index); unit conversion errors (cm to m, MLD to m³/s); incorrect sewer area or hydraulic radius; results physically unrealistic
Diagram quality	15%	7.5	Clear ER hyetograph with properly scaled axes, labeled bars showing intensity (cm/h) vs time, only positive ER periods shown; neat river intake sketch with all components labeled (screening chamber, sump well, pump house, delivery pipe, approach channel); professional presentation with title and dimensions	ER hyetograph present but poorly scaled or missing labels; intake sketch shows basic components but incomplete labeling; diagrams understandable but lack professional finish; missing titles or units	Missing ER hyetograph despite explicit demand; sketch absent or unrecognizable as river intake; diagrams too small or messy; no labels or incorrect component identification; failure to use ruling and proper engineering drawing conventions
Step-by-step derivation	25%	12.5	Complete tabular presentation for (a) showing time, accumulated rainfall, incremental rainfall, intensity, φ-index deduction, and ER; one full calculation set explicitly shown as demanded; clear derivation of composite specific gravity for sludge; Manning's equation substitution with all terms identified; logical flow with equation → substitution → result format	Most steps shown but skips some intermediate calculations; table present but incomplete columns; one calculation set shown but not the clearest example; some steps combined or implied rather than explicit; acceptable but not exemplary presentation	Missing required tabular summary; no explicit calculation set shown despite demand; jumps directly to answers without derivation; disorganized working with no clear problem-solution structure; illegible or scattered calculations without logical sequence
Practical interpretation	15%	7.5	Interprets ER hyetograph significance for flood forecasting and hydrograph modeling; comments on sludge handling challenges in Indian STPs (dewatering, disposal); discusses self-cleansing importance in Indian sewer maintenance context; relates filter problems to Indian raw water quality (high turbidity, seasonal variations); mentions specific intake examples (e.g., Hooghly, Yamuna intakes) or challenges (floods, pollution)	Brief mention of practical relevance without elaboration; generic statements about importance of calculations; some context on Indian conditions but not specific; acknowledges real-world application without detailed insight	No practical interpretation provided; purely mathematical exercise without engineering context; fails to mention why self-cleansing matters, or implications of sludge production; no connection to water supply/sewerage infrastructure in India

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