GATE CE flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

BOD5 formula

BOD5 (mg/L) = (D1 − D2)(1 − f)/P, where D1 and D2 are initial and final dissolved oxygen, f is seed correction fraction, and P is sample volume fraction in the 300 mL bottle.

Reynolds number pipe flow

Re = ρVD/μ = VD/ν. Laminar flow occurs below Re = 2000, transitional between 2000 and 4000, and turbulent above 4000 in circular pipes.

Darcy–Weisbach head loss

hf = f·L·V²/(2gD), where f is the Darcy friction factor, L is pipe length, V is mean velocity, g is gravitational acceleration, and D is pipe diameter.

Moment–area theorem 1

The change in slope between two points on an elastic beam equals the area of the M/EI diagram between those points: θ_B − θ_A = ∫(M/EI)dx.

Moment–area theorem 2

The tangential deviation of point B from the tangent at A equals the moment of the M/EI diagram area between A and B about B: t_B/A = ∫x·(M/EI)dx.

Slope deflection equation

M_AB = (2EI/L)(2θ_A + θ_B − 3ψ) + FEM_AB, where θ are end rotations, ψ is chord rotation, and FEM_AB is the fixed-end moment for the applied load.

Fixed-end moment UDL

For a fixed-end beam of span L carrying uniformly distributed load w, the fixed-end moment at each end is wL²/12; the midspan moment is wL²/24.

Minimum clear cover IS 456

IS 456:2000 minimum clear cover: slab 15 mm, beam 25 mm, column 40 mm, and footing 50 mm, measured to the outermost reinforcement.

Development length formula

Ld = φ·σs/(4·τbd), where φ is bar diameter, σs is stress in bar at section, and τbd is design bond stress; IS 456 increases τbd by 60% for deformed bars.

Effective stress principle

Effective stress σ' = σ − u, where σ is total stress and u is pore water pressure. Soil strength and compressibility depend on effective stress, not total stress.

Capillary rise height

hc = 2T·cosα/(d·γw), where T is surface tension (~0.073 N/m for water), α is contact angle, d is pore diameter, and γw is unit weight of water.

Terzaghi bearing capacity

For a strip footing: qu = cNc + qNq + 0.5γBNγ, where Nq = e^(π tanφ)·tan²(45° + φ/2), and Nc and Nγ depend on φ.

Degree of curve arc definition

D = 5730/R, where D is the degree of curve in degrees and R is the radius in metres; based on a 30 m arc for the GATE metric convention.

Superelevation equation

e + f = V²/(127R), where e is superelevation rate, f is lateral friction coefficient, V is design speed in km/h, and R is curve radius in metres.

Greenshields traffic model

v = vf(1 − k/kj) and q = vf·k − (vf/kj)k²; maximum flow qmax = vf·kj/4 occurs at k = kj/2 and v = vf/2.

Rational method runoff

Q = (1/3.6)·C·i·A, where Q is peak discharge in m³/s, C is runoff coefficient, i is rainfall intensity in mm/h, and A is catchment area in km².

SCS curve number method

Q = (P − 0.2S)²/(P + 0.8S) for P > 0.2S, where S = (25400/CN) − 254 in mm; CN ranges from 30 (low runoff) to 100 (impervious).

Parshall flume equation

For a Parshall flume, free flow discharge Q = K·H^n, where H is upstream head, and K and n are flume-size-specific coefficients; throat width determines K.

Trapezoidal channel Manning

Q = (1/n)·A·R^(2/3)·S^(1/2), where A is flow area, R = A/P is hydraulic radius, P is wetted perimeter, and S is bed slope.

Critical depth rectangular channel

yc = (q²/g)^(1/3), where q = Q/B is discharge per unit width and g is gravitational acceleration; critical flow occurs at minimum specific energy.

Hydraulic jump sequent depth

y2/y1 = 0.5[√(1 + 8Fr1²) − 1], where Fr1 = V1/√(g·y1) is the upstream Froude number; energy loss hL = (y2 − y1)³/(4y1y2).

Consolidation time factor

Tv = cv·t/H², where Tv is time factor, cv is coefficient of consolidation, t is time, and H is drainage path length (H = half thickness for double drainage).

Compression index from e–log p

Cc = Δe / log10(p2/p1), the slope of the virgin compression curve; used to compute primary consolidation settlement in normally consolidated clays.

Mohr–Coulomb failure criterion

τf = c + σ'·tanφ, where τf is shear strength, c is cohesion, σ' is effective normal stress, and φ is angle of internal friction.

Liquidity index formula

LI = (w − PL)/(LL − PL), where w is natural water content, PL is plastic limit, and LL is liquid limit; LI > 1 indicates soil in a viscous liquid state.

Standard Proctor compaction

Compaction energy ≈ 592.7 kJ/m³ (12,375 ft-lb/ft³); hammer 2.5 kg falling 305 mm in 3 layers of 25 blows; gives maximum dry unit weight and optimum moisture content.

CBR penetration standard

CBR = (test load / standard load) × 100, with standard loads 1370 kg at 2.5 mm penetration and 2055 kg at 5.0 mm penetration for a standard crushed stone.

Los Angeles abrasion test

Aggregate abrasion loss (%) = (initial mass − final mass)/initial mass × 100, using a rotating drum with steel balls; lower loss indicates better wear resistance.

Flexural strength of concrete

Modulus of rupture fr = 0.7√fck (IS 456), where fck is characteristic compressive cylinder strength in MPa; used for crack control in RC design.

Workability slump test

Slump is the vertical settlement of a concrete cone under its own weight; IS 456 recommends 25–75 mm for normal RC work, with higher values for heavily reinforced sections.

Sieve analysis Cu and Cc

Cu = D60/D10 (uniformity coefficient) and Cc = D30²/(D10·D60) (coefficient of curvature); well-graded soil has Cu > 6 (sands) and 1 < Cc < 3.

Permeability Hazen formula

k = C·D10², where k is hydraulic conductivity in cm/s, C is a constant (~100 for clean sands), and D10 is the effective grain size in cm.