Glossary
Glossary — Terms & Symbols
Symbols are chapter-scoped: the same letter can mean different things in different chapters (standard exam notation). Every entry below names its chapter.
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Glossary — Chapter 1: Quantitative Aptitude
- Base (of a percentage): the quantity that counts as 100% for that step; every percentage change acts on the current base, not the original value.
- HCF (highest common factor): the largest integer dividing each member of a set.
- LCM (lowest common multiple): the smallest positive integer that is a multiple of each member of a set.
- Alligation: the cross method giving the ratio (q - m):(m - p) for mixing values p and q to hit mean m.
- Marked price (MP): the tagged price on which discounts are computed.
- CI-SI gap (2-year): the quantity P(R/100)^2, equal to one year's interest on one year's interest.
- Rule of 72: doubling time in years is approximately 72/R at R% per annum.
- LCM-units method: fixing total work as the LCM of individual times so all rates become integers.
- Harmonic average: 2xy/(x + y), the correct average of two speeds over equal distances.
- Relative speed: sum of speeds for approaching objects, difference for chase; upstream = boat - stream, downstream = boat + stream.
- Scale laws: under length scale factor k, area scales as k^2 and volume as k^3.
- At-least-one (complement rule): P(at least one) = 1 - P(none).
- Expected value (guessing): 0.5 x 1 - 0.5 x 0.25 = +0.375 when guessing between two options under +1/-0.25 marking.
- Symbols: % (percent, per hundred), Rs (rupees), C(n, r) (combinations of n taken r), pi (circle constant), sqrt (square root).
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Glossary — Chapter 2 (Logical Reasoning)
New terms introduced in this chapter. Chapter 1 introduced no overlapping terms, so all entries below are new.
| Term | Definition |
|---|---|
| Elimination discipline | The exam procedure of reading options first and striking out choices after every deduction, instead of solving fully and then matching. |
| Expected-value guessing | The U5 rule: attempt if known, guess at 50-50 or better, skip if clueless, given the −0.25 penalty. |
| 5-check drill | The fixed order for number series: differences, multiply chains, square/cube offsets, interleaving, primes. |
| Opposite-sum-27 | The letter-numbering fact that opposite letters (A/Z, B/Y, C/X, …) sum to 27; the opposite of position n is position 27 − n. |
| Sum code | A coding family where the code is the sum of letter positions (CAT → 24). |
| Shift code | A coding family where each letter moves a fixed number of steps (CAT → DBU for +1). |
| Opposite code | A coding family replacing each letter by its opposite-sum-27 partner (CAT → XZG). |
| Family tree method | Drawing generations top-down with squares (male), circles (female), double lines (marriage), vertical lines (parent–child) before answering. |
| Shadow rule | Morning shadows point west, evening shadows east; used with the hand rule to fix facing direction. |
| Pythagoras return | The shortest path back after perpendicular legs: the hypotenuse of the walked right triangle. |
| Venn validity test | A conclusion follows only if it is true in every Venn drawing the premises allow; one falsifying drawing rejects it. |
| Only-reversal | The translation "Only A are B" = "All B are A"; reading it as "All A are B" is the trap. |
| Converse error | The fallacy of concluding "S is A" from "All A are B" plus "S is B". |
| Conversion | Valid swaps: "Some A are B" ↔ "Some B are A"; "All A are B" → "Some B are A" only. |
| Negation test | The assumption check: negate the option — if the statement collapses, the option is a genuine assumption. |
| Fix-and-fill | The seating method: anchor the most constrained person, then place neighbour by neighbour, killing branches at the first contradiction. |
| Left–right circle rule | Facing the centre, left is the clockwise-next seat and right is the counter-clockwise-next seat (reversed when facing out). |
| Mirror image | Vertical-mirror flip: left and right swap, top stays top, character order reverses. |
| Water image | Horizontal-mirror flip: top and bottom swap, left stays left, character order is kept. |
| Dice opposite rule | Faces sharing any view are neighbours, never opposites; the face that never appears beside a given face is its opposite. |
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Glossary — Chapter 3: English (Verbal Ability)
| Term | Meaning |
|---|---|
| minimal pair | A wrong-versus-right sentence pair showing one rule. |
| hook | A one-line memory aid attached to a rule or word. |
| nearer-subject rule | Verb agrees with the closer subject in either-or / neither-nor pairs. |
| parallelism | Joined list items sharing the same grammatical form. |
| redundancy | Extra word repeating a meaning already present. |
| SCORE protocol | Skim, Capture, Options-last, Return, Expected-value: the timed RC method. |
| independent sentence | The jumble sentence that introduces a name or idea with a full noun. |
| pronoun link | A pronoun pointing back to its nearest stated antecedent. |
| active voice | Subject acts: the operator closed the valve. |
| passive voice | Object becomes subject: the valve was closed by the operator. |
| narration shift | Past reporting verb moves reported tense one step back. |
| expected-value discipline | Attempt if known, guess if 50-50, skip if clueless under minus 0.25. |
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Glossary — Chapter 4 (sidecar)
Terms
| Term | English | Definition / convention | First appearance |
|---|---|---|---|
| Eigenvalue | eigenvalue | Scalar $\lambda$ with $Av = \lambda v$ for nonzero $v$; $2 \times 2$ via trace-determinant quadratic | Ch4 |
| Trace | trace | Sum of diagonal entries, $\mathrm{tr}(A)$; equals sum of eigenvalues | Ch4 |
| Determinant | determinant | Scalar $\det A$; nonzero iff $A$ invertible; equals product of eigenvalues | Ch4 |
| Rank | rank | Number of independent rows/columns; decides linear-system cases | Ch4 |
| Characteristic equation | characteristic equation | $\det(A - \lambda I) = 0$; roots are the eigenvalues | Ch4 |
| Integrating factor | integrating factor | $\mu(x) = e^{\int P\,dx}$; collapses $y' + Py = Q$ into $d(\mu y)/dx = \mu Q$ | Ch4 |
| Auxiliary equation | auxiliary equation | $ar^2 + br + c = 0$ for $ay'' + by' + cy = 0$; 3 discriminant cases | Ch4 |
| Laplace transform | Laplace transform | $F(s) = \int_0^\infty e^{-st}f(t)\,dt$; s-shift and t-shift theorems | Ch4 |
| Unit step | unit step function | $u(t - c)$: 0 before $c$, 1 after; transforms to $e^{-cs}/s$ | Ch4 |
| Dirac impulse | Dirac delta | $\delta(t)$: unit area at 0; transforms to 1 | Ch4 |
| Conditional probability | conditional probability | $P(E \mid F) = P(E \cap F)/P(F)$ | Ch4 |
| Standard error | standard error | $\sigma/\sqrt{n}$; uncertainty of the sample mean | Ch4 |
| Simpson rule | Simpson's 1/3 rule | $(h/3)$ weighting 1-4-2-...-4-1; needs even $n$ | Ch4 |
| Newton-Raphson | Newton-Raphson method | $x_{k+1} = x_k - f/f'$; needs nonzero derivative, near start | Ch4 |
| Euler method | Euler method | $y_{n+1} = y_n + hf(x_n, y_n)$; first-order stepping | Ch4 |
Symbol conventions
| Symbol | Reading | Meaning and convention | First appearance |
|---|---|---|---|
| $A$, $B$ | "matrix A" | Matrices, uppercase throughout | Ch4 |
| $a, b, c, d$ | lowercase | Scalars and matrix entries | Ch4 |
| $x, y, z$ | "x", "y", "z" | Scalar variables; $y$ also the ODE unknown | Ch4 |
| $\lambda$ | "lambda" | Eigenvalue | Ch4 |
| $I$ | "identity" | Identity matrix | Ch4 |
| $\det A$ | "det A" | Determinant of $A$ | Ch4 |
| $\mathrm{tr}(A)$ | "trace A" | Trace of $A$ | Ch4 |
| $P(x)$, $Q(x)$ | "P of x" | Known coefficient functions in first-order linear ODE | Ch4 |
| $\mu(x)$ | "mu of x" | Integrating factor | Ch4 |
| $C, C_1, C_2$ | "C" | Arbitrary constants of integration | Ch4 |
| $r, r_1, r_2$ | "r" | Auxiliary-equation roots | Ch4 |
| $D$ | "D" | Discriminant $b^2 - 4ac$ | Ch4 |
| $\alpha$, $\beta$ | "alpha", "beta" | Real/imaginary parts of complex root pair | Ch4 |
| $t$ | "t" | Time variable (ODEs, Laplace) | Ch4 |
| $s$ | "s" | Laplace frequency-domain variable | Ch4 |
| $F(s)$, $G(s)$ | "F of s" | Laplace transforms of $f(t)$, $g(t)$ | Ch4 |
| $u(t-c)$ | "u of t minus c" | Delayed unit step | Ch4 |
| $\delta(t)$ | "delta" | Dirac impulse at 0 | Ch4 |
| $n$ | "n" | Trial count (binomial) / strip count (numerics) / sample size (statistics) | Ch4 |
| $p$ | "p" | Binomial success probability | Ch4 |
| $\mu$ (probability) | "mu" | Distribution mean (context: no $x$-dependence) | Ch4 |
| $\sigma$, $\sigma^2$ | "sigma" | Standard deviation, variance | Ch4 |
| $m$ | "m" | Poisson rate parameter | Ch4 |
| $h$ | "h" | Step width (numerics) | Ch4 |
| $y_k$, $x_k$ | "y sub k" | Ordinates / iterates at step $k$ | Ch4 |
| $f_x$, $f_y$ | "f sub x" | Partial derivatives of $f$ | Ch4 |
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Glossary — Chapter 5 (sidecar)
Terms
| Term | English | Definition / convention | First appearance |
|---|---|---|---|
| Free-body diagram | free-body diagram | Isolated body with all external forces and couples at true lines of action | Ch5 |
| Equilibrium equations | equilibrium equations | Plane: sum Fx = 0, sum Fy = 0, sum of moments = 0 | Ch5 |
| Friction angle | angle of friction | phi = arctan(mu_s); tilt of resultant at impending slip; equals angle of repose | Ch5 |
| Cone of friction | cone of friction | Cone of half-angle phi about the contact normal; sticking holds inside | Ch5 |
| Helix angle | helix angle | tan alpha = lead/(pi d_m); unwrapped thread slope | Ch5 |
| Self-locking | self-locking | Screw: alpha < phi; wedge: alpha < phi1 + phi2; load cannot drive the mechanism back | Ch5 |
| Belt friction | belt friction (capstan equation) | T_tight/T_slack = e^(mu_s beta); beta in radians only | Ch5 |
| Wedge | wedge | Angle-alpha simple machine; frictionless driving P = W tan alpha | Ch5 |
| Simple truss | simple truss | m = 2j - 3; joint loads only; two-force axial members | Ch5 |
| Zero-force member | zero-force member | Unloaded joint: two non-collinear both zero; three with two collinear, third zero | Ch5 |
| Method of joints | method of joints | Joint-by-joint equilibrium; best for full-truss solves | Ch5 |
| Method of sections | method of sections | Cut at most three members; moment about two-force intersection isolates the third | Ch5 |
| Instant centre | instantaneous centre of zero velocity | Zero-velocity point; v_P = omega r_{P/IC} | Ch5 |
| Coriolis acceleration | Coriolis acceleration | a_c = 2 omega v_rel, 90 deg from sliding, sense of omega | Ch5 |
| Coefficient of restitution | coefficient of restitution | e = separation speed / approach speed along line of impact | Ch5 |
| Virtual work | principle of virtual work | delta U = 0 for any constraint-consistent virtual displacement in equilibrium | Ch5 |
Symbol conventions
| Symbol | Reading | Meaning and convention | First appearance |
|---|---|---|---|
| $F_x, F_y$ | "F x", "F y" | Force components along x, y | Ch5 |
| $M_O$ | "M O" | Moment about point O | Ch5 |
| $N$ | "N" | Contact normal force | Ch5 |
| $F$ | "F" | Friction force (also member force $F_{AB}$ with subscripts) | Ch5 |
| $\mu_s$ | "mu s" | Coefficient of limiting (static) friction | Ch5 |
| $\phi$ | "phi" | Friction angle, arctan(mu_s) | Ch5 |
| $\alpha$ | "alpha" | Helix angle (screw) / wedge angle / incline angle by context | Ch5 |
| $d_m$ | "d m" | Mean thread diameter | Ch5 |
| $L$, $p$ | "lead", "pitch" | Thread lead; pitch (L = p single start) | Ch5 |
| $T_1, T_2$ | "T one", "T two" | Tight-side / slack-side belt tensions | Ch5 |
| $\beta$ | "beta" | Belt contact angle, always radians in exponents | Ch5 |
| $m$, $j$ | "m", "j" | Truss member count / joint count | Ch5 |
| $u$, $\theta$ | "u", "theta" | Projectile launch speed / launch angle | Ch5 |
| $R, T, H$ | "range", "time", "height" | Projectile range / flight time / max height | Ch5 |
| $g$ | "g" | Gravitational acceleration, 9.81 m/s^2 | Ch5 |
| $\omega$ | "omega" | Angular velocity (rad/s) | Ch5 |
| $v_{rel}$ | "v rel" | Velocity relative to rotating body | Ch5 |
| $a_c$ | "a c" | Coriolis acceleration | Ch5 |
| $a_t, a_n$ | "a t", "a n" | Tangential / normal acceleration components | Ch5 |
| $\rho$ | "rho" | Radius of curvature | Ch5 |
| $T$ (energy) | "T" | Kinetic energy (context: no belt/period meaning) | Ch5 |
| $U$ | "U" | Mechanical work | Ch5 |
| $e$ | "e" | Coefficient of restitution (also Euler number in belt exponent by context) | Ch5 |
| $\delta U$, $\delta r$ | "delta U", "delta r" | Virtual work / virtual displacement | Ch5 |
| $W$ | "W" | Weight / load | Ch5 |
| $k$ | "k" | Spring stiffness | Ch5 |
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Glossary sidecar — Chapter 6
Terms
| Term | English | Definition / convention | First appearance |
|---|---|---|---|
| Yield strength | yield strength | Axial stress at which a ductile material begins plastic flow; denoted sigma-y | 6.1.1 |
| Factor of safety | factor of safety | Allowable stress equals strength divided by this factor; design keeps equivalent stress inside it | 6.1.6 |
| Principal stress | principal stress | Normal stress on a zero-shear plane; ordered sigma-1, sigma-2, sigma-3 | 6.1.5 |
| Neutral axis | neutral axis | Beam fibre with zero bending stress; bending stress varies linearly with distance from it | 6.1.8 |
| Section modulus | section modulus | Z = I / y-max; maximum bending stress equals M / Z | 6.1.8 |
| Effective length | effective length | L-e = K x L per end conditions; the Euler load uses L-e squared | 6.1.13 |
| Slenderness ratio | slenderness ratio | lambda = L-e / k with k = sqrt(I/A); decides Euler vs Rankine | 6.1.13 |
| Proof resilience | proof resilience | Strain energy stored at yield, sigma-y squared x V / 2E | 6.1.4 |
| Wahl factor | Wahl factor | Curvature plus direct-shear correction K for spring stress | 6.1.11 |
Symbol conventions
| Symbol | Reading | Meaning and convention | First appearance |
|---|---|---|---|
| sigma | sigma | Normal stress in MPa; positive tensile; sigma-x, sigma-y are plane-stress components, sigma-1/sigma-2 principals, sigma-y yield, sigma-h hoop, sigma-l longitudinal | 6.1.1 |
| tau | tau | Shear stress in MPa; tau-xy on x-face in positive y-direction (math convention); tau-max is maximum shear | 6.1.1 |
| theta | theta | Angle in radians or degrees; theta-p principal-plane orientation, theta shaft twist | 6.1.5 |
| epsilon | epsilon | Normal strain, dimensionless (mm/mm) | 6.1.1 |
| nu | nu | Poisson ratio, dimensionless; lateral over axial strain with minus sign | 6.1.1 |
| E, G, K | E, G, K | Young, shear, bulk moduli in MPa (GPa in text, converted to MPa for numerics) | 6.1.1 |
| delta | delta | Elongation or deflection in mm; delta-st is static deflection in impact formulas | 6.1.2 |
| M, V | M, V | Bending moment in N-mm and shear force in N on beam sections | 6.1.7 |
| I, Z, J | I, Z, J | Second moment of area, section modulus (mm3), polar moment (mm4); I about neutral axis, J about shaft axis | 6.1.8 |
| T | T | Torque in N-mm (converted from kN-m or N-m before substitution) | 6.1.10 |
| p, d, t | p, d, t | Internal pressure (MPa), vessel diameter, wall thickness (mm); hoop = p-d/2t | 6.1.12 |
| P-cr, L-e, k | P-cr, L-e, k | Euler critical load (N), effective column length (mm), radius of gyration (mm) | 6.1.13 |
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Glossary sidecar — Chapter 7 (Theory of Machines, Vibrations & Machine Design)
Terms
| Term | English | Definition / convention | First appearance |
|---|---|---|---|
| Degree of freedom (mobility) | Mobility M | Number of independent inputs fixing a mechanism's position; planar Kutzbach form M = 3(n−1) − 2·j1 − j2 | 7.1.1 |
| Grashof chain | Grashof chain | Four-bar with s + l ≤ p + q, so at least one link fully rotates | 7.1.2 |
| Inversion | Kinematic inversion | Same chain, different link fixed, giving a different mechanism | 7.1.2 |
| Instant centre | Instantaneous centre (IC) | Point of a body with zero velocity at an instant; v = ω × r about it | 7.1.3 |
| Kennedy's theorem | Three-centre theorem | Three pairwise ICs of three bodies in plane motion are collinear | 7.1.3 |
| Coriolis acceleration | Coriolis component | 2·ω·v on a slider moving along a rotating link, normal to sliding | 7.1.3 |
| Module | Module m = D/T | Tooth size measure shared by meshing gears | 7.1.4 |
| Contact ratio | Contact ratio | Arc of contact over circular pitch; must exceed 1 | 7.1.4 |
| Interference / undercut | Interference / undercutting | Tip-flank fouling and root weakening below the minimum tooth count | 7.1.4 |
| Epicyclic train | Planetary train | Gear train with gears orbiting on a moving arm; solved by tabular method | 7.1.5 |
| Coefficient of fluctuation | Cs = (ωmax − ωmin)/ω | Speed swing specification sizing the flywheel via ΔE = I·ω²·Cs | 7.1.6 |
| Sensitiveness (governor) | Sensitiveness | (N2 − N1)/N over sleeve travel; eagerness of response | 7.1.7 |
| Hunting / isochronism | Hunting / isochronism | Overcorrecting oscillation / equal speed at all radii (one setting only) | 7.1.7 |
| Static vs dynamic balance | Static / dynamic balancing | Mass centre on axis (force) vs additionally zero couple (two planes) | 7.1.8 |
| Whirling | Shaft whirling | Lateral shaft resonance at ωc = √(g/δ) | 7.1.8 |
| Log decrement | Logarithmic decrement δ | (1/n)·ln(x0/xn) = 2πζ/√(1−ζ²) per-cycle decay measure | 7.1.10 |
| Transmissibility | Transmissibility TR | Transmitted over exciting force; TR < 1 only for r > √2 | 7.1.11 |
| Torsional node | Node | Stationary cross-section in torsional vibration | 7.1.12 |
| Critical speed | Critical speed | Running speed matching a transverse natural frequency | 7.1.12 |
| Joint efficiency | Riveted-joint efficiency η | Weakest failure mode per pitch over solid-plate strength | 7.1.13 |
| Throat thickness | Weld throat 0.707·s | Shear-carrying thickness of a fillet of leg s | 7.1.14 |
| Preload | Bolt preload | Clamping tension keeping a joint closed under external load | 7.1.15 |
| L10 life | Rating life L10 | Life in million revolutions survived by 90% of a bearing population | 7.1.17 |
| Sommerfeld number | Sommerfeld number S | (μ·Ns/P)·(R/c)²; equal S means equal journal operating point | 7.1.18 |
| Lewis form factor | Lewis factor Y | Tooth-count geometry factor in σb = Wt/(b·m·Y) | 7.1.19 |
| Self-locking | Self-locking screw | tan α ≤ μ (efficiency below 50%); load held without a brake | 7.1.21 |
Symbol conventions
| Symbol | Reading | Meaning and convention | First appearance |
|---|---|---|---|
| ωn | omega-n | Undamped natural frequency, rad/s; √(k/m), √(Kt/I), or √(g/δ) by context | 7.1.9 |
| ζ | zeta | Damping ratio c/cc, dimensionless; ζ = c/(2√(k·m)) | 7.1.10 |
| r | frequency ratio r | Excitation over natural frequency, r = ω/ωn; isolation needs r > √2 | 7.1.11 |
| Cs | C-s (fluctuation) | Coefficient of speed fluctuation, dimensionless | 7.1.6 |
| C / P | C over P | Bearing dynamic capacity over equivalent load, same force units | 7.1.17 |
| Y | Lewis Y | Bending form factor, dimensionless, rising with tooth count | 7.1.19 |
| M | mobility | Planar degrees of freedom from Kutzbach count | 7.1.1 |
| m | module | Gear module D/T, length units (mm in this book) | 7.1.4 |
| δ | delta | Static deflection (7.1.9) or log decrement (7.1.10) per context, with units stated | 7.1.9 |
| cc | c-critical | Critical viscous damping coefficient, N·s/m | 7.1.10 |
| TR | transmissibility | Force transmissibility ratio, dimensionless | 7.1.11 |
| S | Sommerfeld S | Sommerfeld number, dimensionless | 7.1.18 |
| α, φ | alpha, phi | Screw helix angle and friction angle; self-lock iff α ≤ φ | 7.1.21 |
| η | eta | Efficiency (joint, weld, or screw) with subscript or context stated | 7.1.13 |
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Glossary — Chapter 8 (sidecar)
Terms
| Term | English | Definition / convention | First appearance |
|---|---|---|---|
| Newtonian fluid | Newtonian fluid | Shear stress proportional to velocity gradient, $\tau = \mu\,du/dy$ | Ch8 |
| Capillarity | capillarity | Tube rise/fall $h = 4\sigma\cos\theta/(\rho g d)$; rise for wetting, fall for non-wetting | Ch8 |
| Centre of pressure | centre of pressure | Line of action of hydrostatic force; lies below the centroid | Ch8 |
| Metacentric height | metacentric height | $GM = I/V - BG$; positive means stable floating body | Ch8 |
| Streamline | streamline | Tangent to velocity at one instant; equals pathline only in steady flow | Ch8 |
| Irrotational flow | irrotational flow | Zero vorticity; velocity potential exists | Ch8 |
| Bernoulli equation | Bernoulli equation | $p/\rho g + V^2/2g + z$ constant under the four conditions | Ch8 |
| Energy equation | energy equation with pump and loss terms | Bernoulli plus $h_{pump}$, $h_{turbine}$, $h_L$ | Ch8 |
| Venturi meter | Venturi meter | Streamlined constriction meter, $C_d \approx 0.97$–$0.99$ | Ch8 |
| Orifice meter | orifice meter | Sharp-plate meter, $C_d \approx 0.60$–$0.65$ | Ch8 |
| Pitot tube | Pitot tube | Stagnation-pressure velocity probe | Ch8 |
| Darcy-Weisbach loss | Darcy-Weisbach head loss | $h_f = f(L/D)(V^2/2g)$; scales as $1/D^5$ at fixed $Q$ | Ch8 |
| Friction factor | friction factor | $f = 64/Re$ laminar; Blasius/Moody turbulent | Ch8 |
| Water hammer | water hammer | Pressure surge $\rho c \Delta V$ on sudden closure | Ch8 |
| Siphon | siphon | Summit runs sub-atmospheric; limited by vapour pressure | Ch8 |
| Hagen-Poiseuille flow | Hagen-Poiseuille flow | Laminar pipe: parabolic profile, centreline $2\times$ average, $\Delta p = 32\mu L V/D^2$ | Ch8 |
| Boundary-layer separation | boundary-layer separation | Detachment under adverse pressure gradient; cured by streamlining | Ch8 |
| Specific speed | specific speed | Turbines $N\sqrt{P}/H^{5/4}$; pumps $N\sqrt{Q}/H^{3/4}$ (not interchangeable) | Ch8 |
| Unit quantities | unit speed, discharge, power | $N_u = N/\sqrt{H}$, $Q_u = Q/\sqrt{H}$, $P_u = P/H^{3/2}$ | Ch8 |
| Draft tube | draft tube | Exit passage recovering kinetic head after a reaction runner | Ch8 |
| Thoma number | Thoma cavitation number | $\sigma = (H_{atm} - H_v - H_s)/H$; need $\sigma > \sigma_c$ | Ch8 |
| Affinity laws | pump affinity laws | $Q \propto N$, $H \propto N^2$, $P \propto N^3$ | Ch8 |
| NPSH | net positive suction head | $\mathrm{NPSH}_a > \mathrm{NPSH}_r$ required; suction throttling forbidden | Ch8 |
| Priming | pump priming | Filling casing and suction line with liquid before start | Ch8 |
| Air vessel | air vessel | Cushion chamber smoothing reciprocating-pump pulsations | Ch8 |
Symbol conventions
| Symbol | Reading | Meaning and convention | First appearance |
|---|---|---|---|
| $\tau$ | "tau" | Shear stress | Ch8 |
| $\mu$ | "mu" | Dynamic viscosity | Ch8 |
| $\nu$ | "nu" | Kinematic viscosity, $\mu/\rho$ | Ch8 |
| $\sigma$ (surface) | "sigma" | Surface tension (context: capillarity/Weber) | Ch8 |
| $\theta$ | "theta" | Contact angle (capillarity); V-notch angle (weirs) | Ch8 |
| $h_c$, $h_f$, $h_L$, $h_m$ | "h sub" | Centroid depth; Darcy friction loss; total loss; minor loss | Ch8 |
| $F_b$ | "F sub b" | Buoyant force | Ch8 |
| $G$, $B$, $M$ | "G", "B", "M" | Centre of gravity, buoyancy, metacentre | Ch8 |
| $GM$ | "G M" | Metacentric height | Ch8 |
| $Q$ | "Q" | Discharge (volume flow rate) | Ch8 |
| $H$ | "H" | Total head; turbine head under root in unit quantities | Ch8 |
| $h_{pump}$, $h_{turbine}$ | "h pump" | Pump head added; turbine head extracted | Ch8 |
| $C_d$ | "C sub d" | Coefficient of discharge (meters) | Ch8 |
| $Re$ | "Reynolds number" | $\rho V D/\mu$ | Ch8 |
| $f$ | "friction factor" | Darcy friction factor (not frequency in this chapter) | Ch8 |
| $K$ | "K" | Minor-loss coefficient | Ch8 |
| $c$ (hammer) | "c" | Pressure-wave speed in water hammer | Ch8 |
| $\delta$ | "delta" | Boundary-layer thickness | Ch8 |
| $Re_x$ | "R sub x" | Local Reynolds number $\rho V x/\mu$ | Ch8 |
| $Fr$, $Ma$, $Eu$, $We$ | "Froude" etc. | Froude, Mach, Euler, Weber numbers | Ch8 |
| $N_s$ | "N sub s" | Specific speed (turbine vs pump formulas differ) | Ch8 |
| $N_u$, $Q_u$, $P_u$ | "unit speed" etc. | Turbine unit quantities | Ch8 |
| $N$ | "N" | Rotational speed in rpm (machines) | Ch8 |
| $H_m$ | "H sub m" | Manometric head of a pump | Ch8 |
| $\mathrm{NPSH}_a$, $\mathrm{NPSH}_r$ | "N P S H available/required" | Available vs required suction head | Ch8 |
| $p_v$, $H_v$, $H_s$ | "vapour pressure" etc. | Vapour pressure head terms in NPSH/Thoma checks | Ch8 |
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Glossary — Chapter 9: Heat Transfer, Thermodynamics and Power Engineering
- Fourier law: q = -k A dT/dx; heat flux proportional to the temperature gradient.
- Thermal resistance: slab L/(k A); cylinder ln(r2/r1)/(2 pi k L); sphere (1/r1 - 1/r2)/(4 pi k).
- Critical radius: r_c = k/h (cylinder), 2k/h (sphere); insulation inside r_c increases loss.
- Fin effectiveness: q_fin / q_without_fin (worth adding only if well above 1).
- Fin efficiency: q_fin / q_ideal_isothermal_fin (how close to perfect, not worth).
- Dittus-Boelter: Nu = 0.023 Re^0.8 Pr^n; n = 0.4 heating, 0.3 cooling.
- LMTD: (delta-T1 - delta-T2)/ln(delta-T1/delta-T2); counter-flow exceeds parallel-flow.
- NTU: U A / C_min; fouling adds a series resistance that eats U.
- Critical heat flux (CHF): nucleate-boiling peak; crossing it risks burnout.
- SFEE: m_dot(h + V^2/2 + g z) in plus Q_dot equals out plus shaft work.
- Throttling: isenthalpic (h1 = h2), entropy rises.
- Dryness fraction: x = vapour mass / total mass; h = h_f + x h_fg inside the dome.
- Cut-off ratio: r_c = V3/V2 in Diesel heat addition; larger r_c lowers efficiency.
- Back work ratio: compressor work / turbine work; characteristically large in Brayton.
- Octane: SI knock resistance (branched/aromatic good); cetane: CI ignition quality (straight-chain good).
- Morse test: cylinder-by-cylinder cut-out at constant speed to recover indicated power.
- Volumetric efficiency: 1 + C - C r_p^(1/n); clearance C taxes breathing.
- Carnot COP pair: COP_R = T_L/(T_H - T_L); COP_HP = COP_R + 1.
- Subcooling: extra condenser cooling of liquid; raises refrigerating effect at same work.
- Psychrometry: DBT thermometer reading; WBT evaporation-cooled reading; DPT condensation onset; RH partial/saturation pressure.
- Cooling-tower range: hot-in minus cold-out (load); approach: cold-out minus wet-bulb (limit).
- Choked flow: Mach 1 at the throat; mass flow capped at the critical pressure ratio.
- Symbols: q (heat rate, W), k (conductivity, W/m K), h (convection coefficient, W/m2 K), R (thermal resistance, K/W), U (overall coefficient, W/m2 K), sigma (Stefan-Boltzmann constant, 5.67e-8 W/m2 K4), epsilon (emissivity), alpha (absorptivity), Re/Pr/Nu/Gr/Ra (Reynolds/Prandtl/Nusselt/Grashof/Rayleigh numbers), r (compression ratio), r_c (cut-off ratio or critical radius per context), r_p (pressure ratio), k (specific-heat ratio c_p/c_v), R (gas constant), x (dryness fraction), COP (coefficient of performance), C (clearance ratio), eta_vol (volumetric efficiency), m_dot (mass flow rate), s (specific entropy), n (polytropic index).
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Glossary — Chapter 10 (sidecar)
Terms
| Term | English | Definition | First appearance |
|---|---|---|---|
| BCC/FCC/HCP/BCT | body-centred cubic / face-centred cubic / hexagonal close-packed / body-centred tetragonal | Crystal lattices; BCT is distorted BCC of martensite | 10.1.1 |
| Vacancy / dislocation | vacancy / dislocation | Missing atom / extra half-plane enabling slip | 10.1.1 |
| Hall-Petch relation | Hall-Petch relation | Yield rises as grains refine | 10.1.1 |
| Ferrite / austenite / cementite | ferrite / austenite / cementite | BCC low-C phase / FCC high-C phase / Fe3C compound | 10.1.2 |
| Pearlite / ledeburite / martensite / bainite | pearlite / ledeburite / martensite / bainite | Layered mix / eutectic mix / BCT quench product / austemper product | 10.1.2 |
| Eutectoid / eutectic | eutectoid / eutectic | Solid-state / liquid-state invariant reactions (0.77%/727 C, 4.3%/1147 C) | 10.1.2 |
| Hypo/hyper-eutectoid | hypo/hyper-eutectoid | Below/above 0.77% C steels | 10.1.2 |
| Gray/white/nodular/malleable iron | gray/white/nodular (SG)/malleable cast iron | Cast irons by graphite form | 10.1.3 |
| Annealing / normalising / quenching / tempering / austempering | annealing / normalising / quenching / tempering / austempering | Bulk heat-treatment routes | 10.1.5 |
| Carburising / nitriding | carburising / nitriding | Surface-hardening by C/N diffusion | 10.1.5 |
| TTT nose | TTT (time-temperature-transformation) nose | Minimum-stability point of supercooled austenite | 10.1.5 |
| VT/DPT/MPT/UT/RT/ECT | visual / dye-penetrant / magnetic-particle / ultrasonic / radiographic / eddy-current testing | NDT methods | 10.1.6 |
| Chvorinov rule / modulus | Chvorinov rule / casting modulus | ts = Cm*M^2, M = V/A | 10.1.8 |
| Riser / chill | riser (feeder) / chill | Feed reservoir / fast-cooling insert | 10.1.8 |
| TIG/MIG/SAW | GTAW / GMAW / submerged-arc welding | Arc welding processes | 10.1.9 |
| Soldering / brazing | soldering / brazing | Joining with filler below/above 450 C | 10.1.9 |
| Springback / BHF | springback / blank-holder force | Elastic recovery / wrinkling-control force in sheet forming | 10.1.10 |
| Merchant circle / shear angle | Merchant circle / shear angle | Orthogonal-cutting force model; tan(phi) relation | 10.1.11 |
| Taylor equation | Taylor tool-life equation | V*T^n = C | 10.1.11 |
| EDM/ECM/USM/AJM/LBM | EDM / ECM / USM / AJM / LBM | Non-traditional machining processes | 10.1.11 |
| Least count / sine bar | least count / sine bar | MSR/VSR resolution / angle gauge (sin = h/L) | 10.1.12 |
| GO/NO-GO gauge | GO / NO-GO gauge | Maximum/minimum-material limit gauges | 10.1.12 |
| X-bar-R / p/np/c charts | X-bar-R / p, np, c control charts | Variables/attributes SPC charts | 10.1.12 |
| OC curve | operating-characteristic curve | Acceptance probability vs lot quality | 10.1.12 |
| EOQ / ROP | economic order quantity / reorder point | sqrt(2DS/H) / demand-in-lead-time + safety | 10.1.13 |
| ABC/VED/FSN | ABC / VED / FSN classification | Value / criticality / movement-speed inventory classes | 10.1.13 |
| M/M/1 | M/M/1 queue | Single-server Poisson/exponential queue; rho = lambda/mu | 10.1.13 |
| PERT/CPM | PERT / CPM | Probabilistic / deterministic project networks | 10.1.14 |
| Crash slope | crash slope | (Crash cost − Normal cost)/(Normal time − Crash time) | 10.1.14 |
Symbols
| Symbol | Reading | Meaning | First appearance |
|---|---|---|---|
| ts, Cm, M | t-s, C-m, modulus | Solidification time, mould constant, V/A modulus | 10.1.8 |
| H = VI/v | heat input | Arc energy per unit length | 10.1.9 |
| phi, alpha, r | phi, alpha, r | Shear angle, rake angle, chip-thickness ratio | 10.1.11 |
| V, T, n, C | V, T, n, C | Cutting speed, tool life, Taylor exponent, Taylor constant | 10.1.11 |
| Q*, D, S, H | Q-star, D, S, H | EOQ, annual demand, ordering cost, holding cost | 10.1.13 |
| lambda, mu, rho | lambda, mu, rho | Arrival rate, service rate, utilisation | 10.1.13 |
| o, m, p, te, sigma | o, m, p, t-e, sigma | PERT estimates, expected time, std. deviation | 10.1.14 |
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Glossary — Chapter 11: Full Mocks, Error Log & Cheat Sheets
- Expected value (attempt): p × 1 − (1 − p) × 0.25 under +1/−0.25 marking; attempt only when it is clearly positive after time cost.
- Guess discipline: attempt if known, guess if down to two options (EV +0.375) or one eliminated (EV +1/6), skip if clueless.
- Time-boxing: Quant 22 → Reasoning 18 → English 10 minutes plus a 10-minute buffer for Section A.
- Formula sweep (pass 1): the 60-minute domain round answering every direct-substitution question first.
- Star-marking: tick (solve now), star (solvable but lengthy — return in round two with the method named), cross (skip for the exam, never revisit).
- Mistake diary: date/mock-Q, what went wrong plus the correct rule, cause class, fix.
- Cause class: concept (rule unknown), arithmetic (computation slip), trap (condition violated), time (method known, minutes ran out).
- Cheat sheet: the one-page hand-copied formula set with applicability conditions; copying is the memorisation.
- Self-test (O14): a 5-question set for one weak topic — recall, substitution, condition check, trap variant, cross-link — with +1/−0.25 marking, 7.5 minutes, pass 3.5/5.
- Marking scheme: the score rule of a test (+1/−0.25, time limit, pass mark).
- Applicability condition: the restriction under which a formula holds (e.g. thin shell t < d/10, Bernoulli's four checks, isolation r > √2).
- Buffer: unassigned minutes reserved for starred questions, never pre-spent.
- Symbols: ★ (return later), ✗/cross (skip for the exam), EV (expected value), te (PERT expected time), σ (PERT standard deviation), L10 (bearing life, million rev).