(a) (i) What is Lacey's Silt Factor? What is its value for standard silt? Design an earthen canal using Lacey's silt theory with the following data: Full supply discharge, Q = 15 m³/s, Lacey's silt factor, f = 1·0, Canal side-slope = 1/2 H : 1 V (ii)

Question

(a) (i) What is Lacey's Silt Factor? What is its value for standard silt? Design an earthen canal using Lacey's silt theory with the following data: Full supply discharge, Q = 15 m³/s, Lacey's silt factor, f = 1·0, Canal side-slope = 1/2 H : 1 V (ii) What are spillways? Which type of spillways are provided in the following dams? (i) Bhakra-Nangal Dam (ii) Ramganga (Kalagarh) Dam (iii) Hirakud Dam (iv) Rihand Dam. What forces act on a mass-concrete dam? Explain any two of these forces in detail. (10 marks)

(b) Determine the dimensions of a rectangular septic tank serving 100 persons in a hostel. The dimensions of the septic tank must be able to accommodate sedimentation, sludge digestion and sludge storage functionalities. The peak discharge of sewage can be considered as 240 litres per minute. Use the following data: - Surface area required for every 10 litres per minute of peak flow = 0·92 m² - Water depth required in the sedimentation tank = 0·3 m - Freeboard required = 0·3 m - Capacity required for sludge digestion process = 0·032 m³/capita - Capacity required for digested sludge = 0·0002 m³/capita/day - Sludge withdrawal (cleaning) frequency = once in a year - Length to width of tank ratio (L/B) = 2·5 (15 marks)

(c) Uniform sand is used as a filter medium to treat the water. The sand grains are 0·6 mm in diameter with a shape factor (φ) of 0·85 and specific gravity (G) of 2·67. The bed is 0·65 m deep with a porosity (η) of 0·45. The filter medium is to be expanded to a porosity (ηₑ) of 0·75 by hydraulic backwash. Determine the required backwash velocity, resulting expanded depth and loss through the expanded medium. Assume the following data for use: g = 9·81 m/s², Density of water (ρ) = 998·2 kg/m³, Viscosity of water (μ) = 1·002 × 10⁻³ N.s/m² (15 marks)

UPSC Answer Check · Accepted Answer

This question demands a design-oriented response with substantial numerical work across three distinct engineering domains. Allocate approximately 25% time to part (a) covering Lacey's canal design and spillway identification, 37.5% to part (b) for septic tank dimensional design, and 37.5% to part (c) for filter backwash calculations. Structure each part with clear problem statement, formula application with units, systematic calculation steps, and final dimensioned results with practical verification.
- Part (a)(i): Definition of Lacey's silt factor (f) as f = 1.76√m where m is mean particle size in mm; standard silt f = 1.0; application of Lacey's regime equations: V = (Qf²/140)^(1/6), R = 5V²/2f, S = f^(5/3)/(3340Q^(1/6)) for trapezoidal canal with ½H:1V side slope
- Part (a)(ii): Definition of spillways as overflow structures for flood discharge; identification of specific types: Bhakra-Nangal (shaft/ogee), Ramganga (chute), Hirakud (ogee with sluice), Rihand (ogee); forces on gravity dams: water pressure, uplift, earthquake, silt, ice, wave, self-weight with detailed explanation of any two
- Part (b): Septic tank design integrating three zones: sedimentation (surface area from peak flow), sludge digestion (volume from population), sludge storage (volume from cleaning frequency); calculation of L=2.5B relationship; total depth = water depth + freeboard; verification of detention time and sludge volume adequacy
- Part (c): Application of expanded bed hydraulics using Richardson-Zaki equation for backwash velocity: v_b = [4g(ρ_s-ρ)d/(3C_Dρ)]^0.5 × η_e^n where n≈4.5 for Re<0.3; expanded depth H_e = H(1-η)/(1-η_e); head loss through expanded bed using Kozeny-Carman or empirical approach
- Cross-cutting: Unit consistency throughout (m, s, kg), appropriate significant figures, physical reasonableness checks on all numerical outputs, and recognition of Indian Standard/CPHEEO guidelines where applicable

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	8	Precisely defines Lacey's silt factor with correct formula and physical meaning; accurately classifies all four dam spillway types with correct structural identification; correctly identifies all six forces on gravity dams with proper vector directions; demonstrates correct understanding of septic tank three-zone functionality and filter backwash expansion mechanics including particle Reynolds number regime	Basic definition of silt factor given but formula may be incomplete; spillway types partially correct with 2-3 dams identified; forces listed but explanations lack depth or contain minor errors; septic tank zones mentioned but integration logic unclear; backwash concept understood but regime equations confused	Incorrect or missing definition of silt factor; fundamental misunderstanding of spillway purpose; forces confused with those on other structures; septic tank treated as simple sedimentation tank; backwash velocity confused with filtration velocity or clean bed head loss
Numerical accuracy	20%	8	All calculations yield correct numerical results: canal dimensions (V≈0.76 m/s, R≈1.45 m, S≈1/5800, B≈3.8m, D≈1.75m), septic tank (surface area≈22.08 m², L≈7.4m, B≈3m, total depth≈2.9m, digestion+storage≈3.2+7.3 m³), backwash (v_b≈0.011-0.015 m/s, H_e≈1.43m, head loss≈0.6-0.8m); unit conversions flawless; final answers properly rounded	Most calculations correct but minor arithmetic errors in 1-2 parts; correct formulas applied but substitution errors; unit inconsistencies in 1 part; final dimensions reasonable but not precise; expanded depth or backwash velocity order of magnitude correct	Major calculation errors in 2+ parts; incorrect formulas applied (e.g., Manning instead of Lacey); unit confusion (cm vs m, minutes vs seconds); unrealistic results not flagged; missing critical steps leading to incorrect final dimensions
Diagram quality	20%	8	Clear labeled diagram of trapezoidal canal section showing bed width, depth, side slopes, freeboard; spillway type sketches or clear tabular comparison with force diagrams showing water pressure distribution (triangular) and uplift (parabolic/trapezoidal) on dam; septic tank sectional elevation showing sedimentation, digestion, scum storage zones with inlet/outlet arrangements; filter bed expansion diagram with before/after states	Basic canal cross-section drawn but dimensions not labeled; spillway types described without illustration; dam force diagram shows water pressure but uplift representation incorrect; septic tank shown as simple rectangle without zone differentiation; filter expansion concept described without diagram	No diagrams despite clear need; sketches irrelevant to question; diagrams copied but not understood; missing critical elements like flow direction, pressure distributions, or zone boundaries; poor proportion making dimensions misleading
Step-by-step derivation	20%	8	Systematic presentation: for (a) states all three Lacey equations before substitution, shows geometric relationships for trapezoidal section; for (b) clearly separates sedimentation, digestion, storage calculations with explicit volume summation; for (c) applies appropriate drag coefficient correlation (C_D=24/Re for Stokes regime), shows Richardson-Zaki exponent calculation, derives expanded porosity relationship; all algebraic steps visible	Most steps shown but some shortcuts taken; final formulas stated without intermediate derivation; geometric relationships assumed rather than derived; septic tank volume components calculated but summation implicit; backwash velocity stated without Reynolds number check or regime justification	Only final answers given without working; calculations跳跃 with missing links; incorrect formula manipulation; no geometric justification for canal or tank dimensions; backwash calculations completely omitted or replaced with arbitrary values
Practical interpretation	20%	8	Validates canal design against typical regime velocities (0.3-1.0 m/s) and side slopes for cohesive soils; discusses why specific spillway types suit each dam's topography (steep abutments for Bhakra shaft, wide valley for Hirakud ogee); confirms septic tank cleaning frequency aligns with CPHEEO manual; verifies backwash velocity against typical filter rates (10-15 m/hr) and expanded bed stability; notes construction implications of designed dimensions	Brief mention of design adequacy without specific standard reference; recognizes spillway choice relates to site conditions but not elaborated; septic tank dimensions stated practical without justification; backwash results accepted without comparison to operational ranges; limited connection to field reality	No validation of results against engineering standards; unrealistic dimensions accepted without comment; fails to recognize implications of design choices (e.g., excessive canal velocity causing erosion); no consideration of construction, maintenance, or operational feasibility; purely academic treatment divorced from practice

Q8

Directive word: Design

How this answer will be evaluated

Approach

Key points expected

Evaluation rubric

Practice this exact question

More from Civil Engineering 2024 Paper II