Free MELE Exam Flashcards

Train value = product of the driving gear teeth divided by product of the driven gear teeth. An idler placed between two gears reverses the direction of rotation but cancels out of the ratio, so adding one changes sense only, never speed.

At least one link can fully rotate when S + L is less than or equal to P + Q, where S and L are the shortest and longest links. Fail the test and every link only oscillates, so no motor-driven crank is possible.

Allowance is the intended difference between mating parts at maximum material condition, so it is the minimum clearance or the maximum interference. Tolerance is only the permitted variation on one dimension. Allowance decides the type of fit; tolerance decides how much each part may drift.

sigma_a / Se + sigma_m / Sy = 1 / N, where sigma_a is the alternating stress and sigma_m the mean stress. It anchors the design line on yield strength, making it the most conservative fatigue criterion; Goodman substitutes ultimate strength Su for Sy and permits a higher mean stress.

Pcr = pi^2 x E x I / (K x L)^2, with K = 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned and 2.0 fixed-free. Euler holds only for long columns; below the critical slenderness ratio the column yields before it buckles and an empirical formula such as J.B. Johnson applies.

Throat = 0.707 x leg size for an equal-leg fillet, and the shear area is throat x weld length. Sizing the weld on the leg dimension instead of the throat overstates its strength by about 41%.

L10 = (C / P)^k million revolutions, with k = 3 for ball bearings and 10/3 for roller bearings. L10 is the life that 90% of identical bearings reach, so doubling the load cuts ball-bearing life to about one-eighth.

F1 / F2 = e^(mu x theta) at the point of slipping, with theta the angle of contact in radians. Power transmitted = (F1 - F2) x belt speed, so increasing the wrap on the smaller pulley raises capacity without raising tight-side tension.

T = K x F x d, where K is the nut factor (about 0.20 as-received steel, 0.15 lubricated) and d is the nominal bolt diameter. K carries all the friction, so the same wrench torque on a lubricated bolt produces roughly a third more preload.

delta = 8 x F x D^3 x n / (G x d^4), with D the mean coil diameter, d the wire diameter and n the active coils. Deflection varies with the fourth power of wire diameter, so wire only 10% thicker makes the spring about 46% stiffer.

P = D^3 x N / C horsepower, with D in inches, N in rpm, and C = 80 for main power-transmitting shafts, 53.5 for line shafts carrying pulleys, and 38 for small short shafts. The larger constant is the more conservative case: a main shaft carries extra bending, so the same diameter and speed are rated for less power than a short shaft.

F = 2T / D at the shaft surface, where D is the shaft diameter. The key is then checked twice, in shear across width x length and in bearing on half the height x length, and the weaker of the two sets the required key length.

Module m = D / N in millimetres, circular pitch p = pi x m, and diametral pitch Pd = N / D in teeth per inch. Two gears mesh only if they share the same module or diametral pitch, and p x Pd always equals pi.

Tangential (hoop) stress = p x D / (2t); longitudinal stress = p x D / (4t). Hoop stress is twice the longitudinal, which is why a pressurised pipe splits along its length rather than around its circumference.

V = pi x D x N, or V = pi x D x N / 1000 in m/min with D in millimetres. Cutting speed is dictated by the tool and workpiece material pair, so the machinist looks up V and solves for spindle speed N.

HHV = 33,820C + 144,212(H - O/8) + 9,304S kJ/kg, with C, H, O and S as mass fractions. The O/8 term subtracts the hydrogen already bound as water in the fuel, so omitting it overstates the heating value.

Load factor = average load / peak load; capacity factor = average load / rated plant capacity. A plant can hold a high load factor while its capacity factor stays low, which is the signal that installed capacity exceeds the demand it serves.

Reheat returns partly expanded steam to the boiler and expands it a second time, raising turbine work while keeping exhaust moisture below roughly 12% to protect the last-stage blades. Regenerative feedwater heating is the different measure: it raises efficiency by warming feedwater with extraction steam.

Mechanical efficiency = brake power / indicated power. Indicated power comes from the cylinder pressure-volume diagram and brake power from the dynamometer; the gap is friction and auxiliary drive, so brake thermal efficiency is always the lower of the two thermal figures.

eta = 1 - (1 / rp)^((k - 1) / k), where rp is the compressor pressure ratio. Efficiency depends on pressure ratio alone, not on turbine inlet temperature, although that temperature is what sets the net work the unit actually delivers.

Water power = rho x g x Q x H, then multiplied by turbine and generator efficiencies for plant output. H is the net head, so penstock friction must be deducted from gross head before the calculation.

Conduction follows Fourier, Q = k x A x dT / L; convection follows Newton, Q = h x A x dT; radiation follows Stefan-Boltzmann, Q = e x sigma x A x T^4. Only radiation requires absolute temperature, so a Celsius value in that term is a guaranteed error.

At a fixed impeller diameter, flow varies with speed, head with speed squared and power with speed cubed. Cutting speed by 20% therefore drops flow 20% but power about 49%, which is the whole argument for variable-speed drives over throttling.

Frequency rate = disabling injuries x 1,000,000 / employee-hours worked; severity rate = days charged x 1,000,000 / employee-hours worked. Frequency measures how often injuries occur, severity how much time each one costs, so a plant can improve one while the other worsens.

NPSHa = atmospheric head - vapour pressure head, plus or minus static suction head, minus suction friction head. Cavitation starts once NPSHa drops below the manufacturer's NPSHr, which is why hot liquids and long suction lines force the pump to be set lower.

Total pressure = static pressure + velocity pressure, and air power = volume flow x total pressure. Rating a fan on static pressure alone understates the work it does whenever the discharge velocity is significant.

Px = square root of (P1 x P2), which gives both stages the same pressure ratio and the same work. It assumes perfect intercooling back to suction temperature; without that, the ideal split shifts and total work rises.

Range = hot water in minus cold water out; approach = cold water out minus entering air wet-bulb temperature. Range is set by the plant heat load, approach by tower size, and approach can never reach zero because the wet-bulb is the theoretical floor.

1 TR = 3.516 kW = 211 kJ/min = 12,000 Btu/hr. It is defined as the cooling rate that freezes one short ton of water at 0 degC into ice in 24 hours, so it names a rate of heat removal, never a quantity of heat.

Q = m x cp_water x (T - 0) + m x Lf + m x cp_ice x (0 - T_ice), with Lf = 335 kJ/kg, cp of water 4.187 and cp of ice 2.093 kJ/kg-K. The latent term dominates, so subcooling the ice a few degrees adds far less load than the freezing itself.

Only at saturation, where relative humidity is 100%. The wet-bulb depression, the gap between dry-bulb and wet-bulb, is what fixes the air's state on a psychrometric chart; a zero depression means the air can absorb no more moisture.

SHF = sensible heat / (sensible heat + latent heat). It sets the slope of the room process line on the psychrometric chart, so a low SHF from crowded rooms or kitchens calls for a coil that dehumidifies as much as it cools.

Every run is sized for the same pressure drop per unit length, so velocity falls naturally toward the ends of the system. It does not self-balance runs of unequal length, so dampers or the static-regain method are still needed on long duct systems.

Sum = -b / a and product = c / a. The discriminant b^2 - 4ac then classifies them: positive gives two distinct real roots, zero a repeated root, negative a conjugate complex pair.

Dividing f(x) by (x - a) leaves the remainder f(a), and if f(a) = 0 then (x - a) is a factor. This turns root-hunting into simple evaluation, and synthetic division returns the remainder and the depressed polynomial in one pass.

log(MN) = log M + log N, log(M/N) = log M - log N, log(M^p) = p log M, and the change of base log_b M = ln M / ln b. Only the change-of-base rule lets a calculator evaluate bases other than 10 or e.

c^2 = a^2 + b^2 - 2ab cos C solves side-angle-side and side-side-side triangles. The law of sines, a / sin A = b / sin B, suits angle-angle-side but produces the ambiguous case for side-side-angle, where two triangles may satisfy the data.

a^2 - b^2 = (a - b)(a + b); a^3 - b^3 = (a - b)(a^2 + ab + b^2); a^3 + b^3 = (a + b)(a^2 - ab + b^2). In the cube forms the middle term's sign is opposite the binomial's, which is the detail most often reversed under time pressure.

V = (h / 6)(A1 + 4Am + A2), where Am is the area of the mid-section, not the average of the two ends. One expression covers prisms, pyramids, frustums, cones and spheres, which makes it the fastest route through mensuration items.

d = |A x0 + B y0 + C| / square root of (A^2 + B^2) for the line Ax + By + C = 0. Drop the absolute value and the sign reveals which side of the line the point lies on, which is also how the distance between two parallel lines is obtained.

Effective annual rate = (1 + r/m)^m - 1, with r the nominal annual rate and m the compounding periods per year. 12% compounded monthly is effectively 12.68%, so comparing alternatives on nominal rates understates the cost of frequent compounding.

Either compare annual worth directly, or compare present worth over a study period equal to the least common multiple of the lives. Comparing present worths taken over different lives is the standard trap because it flatters the shorter-lived option.

In rank order, Professional Mechanical Engineer, Mechanical Engineer, and Certified Plant Mechanic (Section 13). Only a Professional Mechanical Engineer may sign and seal mechanical designs, plans and specifications, and proposals for pressurised piping rated at 70 kPa or more (Sections 33 and 35).

One mole holds 6.022 x 10^23 particles and, for an ideal gas at 0 degC and 101.325 kPa, occupies 22.4 litres. That volume is tied to standard temperature and pressure; at 25 degC the same mole fills about 24.5 litres.

N = N0 x (1/2)^(t / t_half), equivalently N = N0 x e^(-lambda t) with lambda = 0.693 / t_half. Decay is exponential, so activity approaches but never reaches zero, and no chemical or thermal treatment alters the half-life.

v = f x lambda. When a wave crosses into a new medium its frequency is unchanged because the source fixes it, while speed and wavelength both change, and that mismatch is what produces refraction.

v is about 331 + 0.6t m/s with t in degrees Celsius, so roughly 343 m/s at 20 degC. Sound level in decibels = 10 log(I / I0) with I0 = 10^-12 W/m^2, so each 10 dB step is a tenfold change in intensity.

delta = P x L / (A x E), valid only below the proportional limit where Hooke's law holds. E is a material property and cannot be designed around, so doubling cross-sectional area halves the stretch while doubling the length doubles it.

eta = 1 - TL / TH, with both temperatures absolute in kelvin or rankine. No engine operating between the same two reservoirs can beat it, so any computed efficiency above the Carnot value points to an arithmetic error or a Celsius temperature left unconverted.

p / (rho g) + v^2 / (2g) + z = constant along a streamline. It assumes steady, incompressible, frictionless flow, so real piping problems extend it into the energy equation by adding head loss hf plus any pump or turbine head.