GATE ES flashcards

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

BOD exertion equation

First-order model L_t = L_0(1 - e^(-kt)); at 20 °C domestic sewage k ≈ 0.23 per day (base e), so BOD_5 ≈ 68% of ultimate BOD.

Henry's law constant

Relates dissolved gas concentration to partial pressure: C = K_H·p. Low K_H means the gas is volatile and easily stripped by aeration.

Langelier Saturation Index

LSI = pH - pH_s. Positive LSI indicates CaCO3 scaling tendency, negative indicates corrosive water, and zero means near equilibrium.

Monod growth kinetics

Specific growth rate μ = μ_max·S/(K_s + S), where K_s is the half-saturation constant. Used to model substrate-limited bacterial growth in biological treatment.

Nitrification stoichiometry

Ammonia is oxidized to nitrite by Nitrosomonas then to nitrate by Nitrobacter, consuming about 4.57 mg O2 per mg NH4-N and lowering alkalinity.

Anaerobic digestion stages

Sequential hydrolysis, acidogenesis, acetogenesis, and methanogenesis. Methanogens are sensitive to pH (6.8-7.4) and temperature, optimum mesophilic around 35 °C.

Stokes law settling velocity

v_s = g(ρ_p - ρ_w)d²/(18μ). It gives terminal velocity of a spherical particle in laminar flow, used to size sedimentation basins.

Sludge volume index

SVI = (SV30 × 1000)/MLSS, in mL/g. Values near 100 indicate good settling; above 150 suggests filamentous bulking.

CT disinfection concept

Product of disinfectant residual concentration and contact time. Required CT increases with higher pH, lower temperature, and target pathogen resistance.

Gaussian plume equation

Predicts downwind concentration from a continuous point source using wind speed, effective stack height, and dispersion coefficients σ_y and σ_z.

ESP Deutsch equation

Collection efficiency η = 1 - e^(-wA/Q), where w is drift velocity, A is plate area, and Q is gas flow. Higher area-to-flow ratio improves capture.

Sound level addition

For incoherent sources, L_total = 10 log(Σ 10^(Li/10)). Doubling identical sources adds about 3 dB, not 6 dB.

Dulong calorific formula

HCV = 33,800C + 144,200(H - O/8) + 9,400S kJ/kg using mass fractions. Estimates energy content of solid waste or biomass.

Moisture content conversion

Wet basis M = W_w/W_total × 100; dry basis M_d = W_w/W_dry × 100. Convert with M_d = M/(100 - M).

Incineration three T's

Temperature, time, and turbulence. MSW incinerators typically operate above 850 °C with residence time exceeding 2 seconds for complete combustion.

Rational method

Peak flow Q = C·i·A/3.6 for Q in m³/s, i in mm/h, and A in km². C is runoff coefficient depending on land use.

Manning equation

Q = (1/n)·A·R^(2/3)·S^(1/2), with R = A/P. Roughness n is about 0.013 for concrete and 0.025 for earth channels.

SCS curve number method

Runoff Q = (P - 0.2S)²/(P + 0.8S), with S = (25400/CN) - 254 mm. Higher CN means more runoff.

Hydraulic jump sequent depth

y2/y1 = 0.5(√(1 + 8F1²) - 1). Energy loss is ΔE = (y2 - y1)³/(4y1y2), used to design stilling basins.

EIA Notification 2006

Indian framework categorizing projects as A or B. Category A is appraised by EAC at MoEFCC; Category B by SEAC, with B1 requiring EIA.

Shannon diversity index

H' = -Σ p_i ln p_i, where p_i is the proportion of species i. Higher H' indicates greater diversity; it accounts for richness and evenness.

Leopold interaction matrix

EIA tool listing project actions against environmental components. Each cell is scored for magnitude and importance from 1 to 10.

Detection limit

LOD = 3s, where s is the standard deviation of blank measurements. LOQ is usually 10s, the lowest reliably quantifiable concentration.

Beer-Lambert law

Absorbance A = εbc, where ε is molar absorptivity, b is path length, and c is concentration. Basis of spectrophotometric water analysis.

Confidence interval of mean

x̄ ± t·s/√n, where t is from Student's t table with n - 1 degrees of freedom. It estimates the population mean range.

Betz limit

Maximum theoretical wind turbine efficiency is 16/27, about 59.3%. Wind power available is P = 0.5ρAv³.

Global warming potential

Relative radiative forcing over 100 years, with CO2 = 1. AR6 values: CH4 about 27-30, N2O about 273, SF6 about 25,200.

Hydropower output

P = ρgQHη, where Q is discharge, H is head, and η is overall efficiency (typically 0.85-0.90). Gives electrical power in watts.

Average speed equal distances

For two equal-distance legs at speeds v1 and v2, average speed = 2v1v2/(v1 + v2), the harmonic mean, not the arithmetic mean.

Permutation and combination

nPr = n!/(n - r)! counts ordered arrangements; nCr = n!/(r!(n - r)!) counts unordered selections. Use combinations when order does not matter.

Compound interest formula

A = P(1 + r/n)^(nt), where n is compounding frequency per year and t is years. Simple interest uses A = P(1 + rt).

Pie chart angle

Each sector angle = (value/total) × 360°. Central angle is proportional to the share of the category in the whole dataset.