(a) An open drain is to be designed to prevent waterlogging for an area of 576 ha. Given that the drainage coefficient is 0·06 m/day, determine the capacity of the drain required and the dimensions of the trapezoidal section with side slopes 1 : 1 an

Question

(a) An open drain is to be designed to prevent waterlogging for an area of 576 ha. Given that the drainage coefficient is 0·06 m/day, determine the capacity of the drain required and the dimensions of the trapezoidal section with side slopes 1 : 1 and Lacey's f=1·0. Also, compute the slope. (20 marks)
(b) A 0·5 m diameter well fully penetrates an unconfined aquifer whose bottom is 150 m below the undisturbed ground water table. When pumped at a steady rate of 6·0 m³/min, the drawdowns observed in two observation wells at radial distances of 10 m and 50 m are respectively 10 m and 5 m. Determine the drawdown in the well. (15 marks)
(c) What is grit ? Why is it essential to remove the grit ? Why velocity control devices are essential with unaerated horizontal flow grit chambers ? Why are the velocity control devices not required with the aerated grit chambers ? Name any two velocity control devices used with grit chambers. (15 marks)

UPSC Answer Check · Accepted Answer

This is a multi-part numerical and descriptive problem requiring systematic solving. Allocate approximately 40% time to part (a) as it carries the highest marks (20) and involves comprehensive drain design using Lacey's regime theory; 30% each to parts (b) and (c). Begin with clear problem statements for each part, show all formulae with their sources, present step-by-step calculations with proper units, and conclude with practical significance of results.
- Part (a): Correct application of drainage coefficient to compute discharge Q = C×A = 0.06×(576×10⁴)/(24×3600) m³/s; application of Lacey's regime equations (P = 4.75√Q, R = 5V²/2f, S = f^(5/3)/(3340×Q^(1/6))) to determine trapezoidal section dimensions with 1:1 side slopes
- Part (b): Application of Thiem's equation for unconfined aquifer: Q = πK(h₂²-h₁²)/ln(r₂/r₁) to determine hydraulic conductivity K, then using same equation with r = well radius (0.25 m) to find drawdown in pumping well; or alternatively using Dupuit equation
- Part (c): Definition of grit as heavy inorganic solids (sand, gravel, silt, egg shells, coffee grounds) with particle size > 0.15 mm and specific gravity 2.4-2.65; explanation of grit removal necessity to prevent abrasion of pumps/mechanical equipment, pipe clogging, and reduction of digester volume
- Part (c): Explanation that velocity control devices (proportional flow weirs, Parshall flumes, venturi flumes, or sutro weirs) are essential in unaerated chambers to maintain 0.15-0.3 m/s velocity for grit settling while keeping organic matter in suspension; contrast with aerated chambers where air diffusion creates controlled rolling action making velocity devices redundant
- Integration: Recognition that Lacey's silt factor f=1.0 indicates medium silt typical of Indian alluvial plains, and that drainage design must account for monsoon intensity patterns in waterlogged areas like the Indo-Gangetic basin

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies and applies Lacey's regime theory for part (a), Thiem/Dupuit equation for unconfined aquifer in part (b), and accurately distinguishes between aerated and unaerated grit chamber hydraulics in part (c); cites appropriate Indian standards (IS 4745 for drainage, IS 4111 for grit chambers)	Uses correct basic formulae but makes minor errors in identifying applicable conditions (e.g., uses confined aquifer equation for unconfined in part b, or confuses velocity control purposes); partial understanding of aeration effects	Fundamental conceptual errors such as using Manning's equation instead of Lacey's for regime channel design, applying steady-state radial flow equations to wrong aquifer type, or misunderstanding grit chamber functioning
Numerical accuracy	25%	12.5	All three parts show precise calculations with correct unit conversions throughout: part (a) yields Q ≈ 0.4 m³/s, bed width ≈ 1.8-2.0 m, depth ≈ 0.9-1.0 m, slope ≈ 1/5000; part (b) correctly computes K ≈ 4.5×10⁻⁴ m/s and well drawdown ≈ 12-13 m; no arithmetic errors	Correct methodology but contains 1-2 calculation errors (e.g., wrong area conversion from hectares, incorrect logarithmic evaluation in Thiem's equation, or arithmetic slips in Lacey's equations); final answers within 10-15% of correct values	Multiple calculation errors, wrong unit conversions (e.g., missing 10⁴ for hectares, minutes vs seconds confusion), or order-of-magnitude mistakes; final answers unrealistic or not physically meaningful
Diagram quality	15%	7.5	Clear labeled diagrams for part (a) showing trapezoidal drain cross-section with 1:1 side slopes, wetted perimeter, and hydraulic radius; part (b) shows well-aquifer geometry with observation wells, drawdown curve, and flow lines; part (c) illustrates grit chamber with velocity control device	Diagrams present but inadequately labeled or missing key dimensions; rough freehand sketches without proper proportions; or diagrams provided only for 1-2 parts despite all benefiting from visualization	No diagrams despite their necessity for communicating geometric relationships; or diagrams completely wrong (e.g., rectangular section for trapezoidal drain, confined aquifer sketch for unconfined problem)
Step-by-step derivation	25%	12.5	Each part shows complete logical progression: part (a) states given data → computes discharge → applies Lacey's P, R, S equations → solves simultaneous equations for B and y; part (b) derives K from observation wells then substitutes back for well drawdown; all assumptions explicitly stated	Steps shown but with gaps or jumps in logic; some intermediate results not shown; assumes certain values without justification; or combines steps excessively making verification difficult	Final answers stated without derivation; or completely illogical sequence; missing essential steps like establishing governing equations before substitution; no indication of how simultaneous equations were solved
Practical interpretation	15%	7.5	Interprets results contextually: part (a) comments on regime channel stability in alluvial soils typical of Indian irrigation commands, checks against permissible velocities; part (b) assesses whether drawdown is feasible given 150 m aquifer thickness and well efficiency; part (c) relates grit removal to protection of STP infrastructure in Indian conditions	Brief concluding statements without substantive analysis; generic comments about 'design is safe' without specific reference to calculated values; or interpretation limited to one part only	No interpretation of numerical results; fails to check reasonableness of answers against physical reality; or draws incorrect conclusions from correct calculations (e.g., claiming unstable design is stable)

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