(a) A 6-hour unit hydrograph has the following ordinates : If φ index is 0·3 cm/hr and base flow is 25 m³/s, determine the ordinates of resulting hydrograph of flow in the catchment due to the storm given below : (10 marks)

(b) The annual precipitat

Question

(a) A 6-hour unit hydrograph has the following ordinates : If φ index is 0·3 cm/hr and base flow is 25 m³/s, determine the ordinates of resulting hydrograph of flow in the catchment due to the storm given below : (10 marks)

(b) The annual precipitation and evaporation from each of the sub-areas P, Q, R and S are given below for a catchment. Calculate the following for catchment : (i) Annual average precipitation (ii) Annual average evaporation (iii) Annual runoff coefficients for the sub-areas and for the total catchment taken as a whole assuming no change in the ground water storage on an annual basis. (10 marks)

(c) Route the above flood hydrograph through a river reach : The value of x and K in the Muskingham equation have been identified as 0·25 and 8 hr. The initial outflow discharge from the reach is 10 m³/s. (10 marks)

(d) Explain the significance of the following from the point of view of water quality criteria : (i) Nitrites (ii) Nitrates (iii) E-coli (iv) B.O.D. (v) Dissolved oxygen (10 marks)

(e) In a continuous flow settling tank 4 m deep and 80 m long, calculate the flow velocity for effective removal of 0.03 mm particles at 25°C. The specific gravity of the particles is 2.65 and kinematic viscosity (v) for water may be taken as 0.01 cm²/sec. (10 marks)

UPSC Answer Check · Accepted Answer

This is a multi-part numerical question requiring precise calculations across hydrology and water quality. Begin with part (a) by constructing the storm hydrograph using φ-index and base flow separation, allocating approximately 25% time. For part (b), compute weighted averages for precipitation and evaporation using area-weighting, then derive runoff coefficients—allocate 20% time. Part (c) demands Muskingham routing with given x and K values; set up the routing equation systematically—20% time. Part (d) requires concise but comprehensive explanations of five water quality parameters with their health/ecological significance—20% time. Conclude with part (e) applying Stokes' law for settling velocity and checking against scour velocity—15% time. Present all calculations in tabular format where possible.
- Part (a): Correct application of φ-index (0.3 cm/hr) to determine effective rainfall, convolution with 6-hour UH ordinates, and addition of base flow (25 m³/s) to obtain total storm hydrograph ordinates
- Part (b): Area-weighted calculation of annual average precipitation and evaporation for the catchment; computation of runoff coefficients for sub-areas P, Q, R, S using water balance equation (P - E = R), and overall catchment runoff coefficient
- Part (c): Application of Muskingham routing equation with x = 0.25, K = 8 hr, initial outflow = 10 m³/s; correct determination of routing coefficients C₀, C₁, C₂ and computation of outflow hydrograph ordinates
- Part (d): Explanation of nitrites (toxicity, methemoglobinemia), nitrates (eutrophication, drinking water limit 45 mg/L), E-coli (fecal contamination indicator), BOD (organic pollution load, deoxygenation), and dissolved oxygen (aquatic life support, minimum 4-5 mg/L for warm-water fish)
- Part (e): Calculation of settling velocity using Stokes' law for 0.03 mm particles at 25°C (v = 0.01 cm²/s, G = 2.65), verification of Reynolds number < 1 for Stokes' validity, and determination of flow velocity ensuring detention time allows particle removal (L/v_flow = H/v_settling)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding of UH theory, φ-index concept, water balance, Muskingham routing assumptions, water quality standards (IS 10500, CPCB), and settling tank design principles; correctly identifies that Stokes' law applies only for Re < 1	Shows basic understanding of most concepts but confuses φ-index with W-index, or misapplies Muskingham routing coefficients, or provides generic water quality descriptions without specific standard values	Fundamental conceptual errors such as treating UH as direct runoff hydrograph without base flow, or applying Muskingham equation without understanding storage-discharge relationship, or confusing nitrites with nitrates
Numerical accuracy	25%	12.5	All calculations precise to 2-3 significant figures; correct unit conversions (cm/hr to m/s, mm to m); accurate interpolation of UH ordinates; routing coefficients sum to unity; settling velocity calculation uses correct particle diameter (0.03 mm = 3×10⁻⁵ m)	Minor arithmetic errors in 1-2 parts; correct method but wrong final values; inconsistent units (mixing cm and m); rounding errors affecting subsequent calculations	Major calculation errors in multiple parts; order-of-magnitude mistakes; incorrect formula application; no unit consistency; impossible results (negative flows, velocities exceeding celerity) not flagged
Diagram quality	15%	7.5	Clear labeled sketches for part (a) showing hyetograph, UH, and resulting hydrograph; schematic of catchment with sub-areas for part (b); Muskingum storage prism-wedge diagram for part (c); settling tank with zones for part (e); all axes labeled with units	Basic diagrams present but poorly labeled or missing units; hand-drawn sketches acceptable but lacking clarity; diagrams mentioned but not actually drawn	No diagrams despite clear need for visualization; or diagrams completely unrelated to question; illegible sketches without labels
Step-by-step derivation	25%	12.5	Systematic presentation: explicit formula statements, substitution of values with units, intermediate results shown, clear logical flow from given data to final answer; Muskingham coefficients derived before application; Stokes' law assumptions stated	Some steps shown but jumps in logic; final answers without intermediate working; formulas implied but not stated; messy presentation making verification difficult	Only final answers with no working; or working so disorganized that error tracing is impossible; incorrect formulas used without justification; no logical sequence
Practical interpretation	15%	7.5	Interprets results contextually: peak flow timing for flood forecasting in part (a); compares runoff coefficients with typical values for Indian catchments (0.2-0.6); discusses attenuation and lag in routing; relates water quality parameters to Ganga Action Plan or CPCB standards; checks if settling tank dimensions are practical (L/H ratio = 20)	Minimal interpretation; results stated without context; generic statements about importance; no comparison with field data or standards	No interpretation whatsoever; or absurd interpretations showing no physical understanding (e.g., negative flows accepted, or DO > saturation concentration)

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