CENEVAL EGEL Plus Ingeniería Mecánica Eléctrica (EGEL Plus IME)

A solid circular drive shaft of diameter d = 50 mm transmits a steady torque of T = 1,200 N·m. What is the maximum torsional shear stress (τ_max) developed on the outer surface of the shaft?

• A48.9 MPa
• B391.1 MPa
• C97.8 MPa
• D24.4 MPa

A structural steel tie rod with an elastic modulus E = 200 GPa, length L = 2.5 m, and cross-sectional area A = 400 mm² is subjected to an axial tensile force of P = 80 kN. What is the total elastic elongation (δ) of the rod?

• A1.25 mm
• B2.50 mm
• C1.00 mm
• D5.00 mm

A simply supported steel beam of rectangular cross section (width b = 80 mm, height h = 150 mm) is subjected to a maximum bending moment of M = 18 kN·m. What is the maximum flexural bending stress (σ_max) in the outer fibers of the beam?

• A30.0 MPa
• B60.0 MPa
• C40.0 MPa
• D800 MPa

In mechanical design against fatigue failure under fluctuating cyclic loading, which criterion connects the alternating stress amplitude (σ_a) and mean stress (σ_m) to the material ultimate tensile strength (S_ut) and fatigue endurance limit (S_e)?

• ASoderberg line
• BGoodman line
• CGerber parabolic curve
• DASME elliptic criterion

A standard spur gear set consists of a 20-tooth pinion rotating at 1,800 rpm that drives an 80-tooth gear. What is the rotational speed of the driven gear and the gear ratio (m_g)?

• A450 rpm and gear ratio of 4:1
• B7,200 rpm and gear ratio of 1:4
• C600 rpm and gear ratio of 3:1
• D360 rpm and gear ratio of 5:1

In a flat belt drive with tight side tension F_1, slack side tension F_2, coefficient of friction μ, and wrap angle θ (in radians), what fundamental equation governs the maximum torque transmission limit without slipping?

• AF_1 / F_2 = 1 + μ·θ
• BF_1 / F_2 = e^(μ·θ)
• CF_1 - F_2 = μ·θ·(F_1 + F_2)
• DF_1 / F_2 = e^(μ/θ)

An ideal steam Rankine power cycle operates with steam entering the turbine at h_1 = 3,100 kJ/kg and exiting to the condenser at h_2 = 2,100 kJ/kg. The feedwater leaves the condenser as saturated liquid at h_3 = 192 kJ/kg, and the boiler feed pump requires w_pump = 3 kJ/kg (so h_4 = 195 kJ/kg entering the boiler). What is the thermal efficiency (η_th) of this Rankine cycle?

• A32.2%
• B34.3%
• C52.4%
• D65.7%

In CNC machining programmed with ISO 6983 G-codes, what motion does the command G02 produce?

• ALinear interpolation at the programmed feed rate
• BCircular interpolation in the counterclockwise direction
• CRapid positioning at maximum traverse speed without cutting
• DCircular interpolation in the clockwise direction

Steam at a pressure of 2.0 MPa has a saturation temperature of 212.4 °C. At this pressure, the specific enthalpy of saturated liquid is h_f = 908.8 kJ/kg and the enthalpy of vaporization is h_fg = 1,890.7 kJ/kg. If a steam sample has a measured enthalpy of h = 2,422.3 kJ/kg, what is its dryness fraction (vapor quality, x)?

• A0.54
• B0.87
• C0.80
• D0.20

In a counter-flow shell-and-tube heat exchanger, hot oil is cooled from 140 °C to 80 °C by cooling water that enters at 20 °C and leaves at 50 °C. What is the Log Mean Temperature Difference (LMTD, ΔT_lm) across the exchanger?

• A73.9 °C
• B60.0 °C
• C75.0 °C
• D64.9 °C

Water at 20 °C (density ρ = 1,000 kg/m³, dynamic viscosity μ = 1.0 × 10⁻³ Pa·s) flows through a commercial steel pipe of internal diameter D = 0.10 m at a mean velocity v = 2.0 m/s. What is the Reynolds number (Re) and flow regime?

• ARe = 20,000; laminar flow
• BRe = 200,000; fully turbulent flow
• CRe = 2,000; transitional flow
• DRe = 500,000; turbulent flow

A water main of length L = 800 m and internal diameter D = 0.25 m carries flow at a mean velocity v = 1.5 m/s. With a Darcy friction factor f = 0.018 and g = 9.81 m/s², what is the major head loss (h_f) due to friction?

• A4.40 m
• B6.61 m
• C13.21 m
• D26.42 m

According to the centrifugal pump affinity laws, if the impeller rotational speed is increased by 20% (speed ratio n_2 / n_1 = 1.20), how do the volumetric flow rate (Q), developed head (H), and required shaft power (P) scale, assuming constant impeller diameter?

• AQ increases by 20%, H increases by 44%, P increases by 72.8%
• BQ increases by 20%, H increases by 20%, P increases by 44%
• CQ increases by 44%, H increases by 72.8%, P increases by 107%
• DQ increases by 20%, H increases by 40%, P increases by 60%

A centrifugal water pump draws water at 20 °C (vapor pressure P_vap = 2.34 kPa, density ρ = 1,000 kg/m³) from an open atmospheric sump at sea level (P_atm = 101.3 kPa). The pump suction eye is situated 2.50 m above the free water level (suction lift z_s = 2.50 m). Total suction piping head losses are h_fs = 1.20 m. With g = 9.81 m/s², what is the Net Positive Suction Head Available (NPSHa)?

• A3.89 m
• B8.89 m
• C6.39 m
• D11.39 m

In a long hydraulic pipeline carrying fluid with density ρ and acoustic wave propagation speed c, a valve is closed rapidly, reducing the flow velocity from v_0 to 0. According to the Joukowsky equation, what is the maximum pressure surge (ΔP) produced by water hammer?

• AΔP = ρ·c·v_0
• BΔP = (1/2)·ρ·v_0²
• CΔP = ρ·c² / v_0
• DΔP = 2·ρ·c·v_0²

A plane stress element is subjected to normal stresses σ_x = 100 MPa, σ_y = 40 MPa, and shear stress τ_xy = 40 MPa. What is the maximum in-plane shear stress (τ_max) determined by Mohr's circle?

• A30.0 MPa
• B50.0 MPa
• C70.0 MPa
• D40.0 MPa

A slender structural column of length L and flexural rigidity E·I has both ends pinned. If the end conditions are modified so that both ends are fixed against rotation, how does the Euler critical buckling load (P_cr) change?

• AIt doubles (increases by a factor of 2)
• BIt quadruples (increases by a factor of 4)
• CIt remains unchanged
• DIt increases by a factor of √2

A composite industrial furnace wall consists of 100 mm of firebrick (k_1 = 1.0 W/(m·K)) and 50 mm of insulating fiber (k_2 = 0.10 W/(m·K)). What is the total conductive thermal resistance per unit area (R''_th) of this wall?

• A0.15 m²·K/W
• B0.60 m²·K/W
• C1.50 m²·K/W
• D0.40 m²·K/W

In psychrometric analysis of an industrial air conditioning system, what happens to dry-bulb temperature, relative humidity, and specific humidity during a pure sensible heating process?

• ADry-bulb temperature increases, relative humidity decreases, specific humidity remains co…
• BDry-bulb temperature increases, relative humidity increases, specific humidity increases
• CDry-bulb temperature decreases, relative humidity decreases, specific humidity remains co…
• DDry-bulb temperature increases, relative humidity remains constant, specific humidity inc…

An industrial vapor-compression refrigeration plant absorbs Q_L = 120 kW of heat in its evaporator while the compressor consumes W_in = 30 kW of electrical power. What is the Coefficient of Performance (COP_R) of this refrigeration system?

• A0.25
• B3.00
• C4.00
• D5.00

In hydrodynamic journal bearings, which dimensionless number combines journal radius r, radial clearance c, dynamic viscosity μ, rotational speed N (rev/s), and unit load P to evaluate film thickness and operating regime?

• AReynolds number
• BSommerfeld number
• CMach number
• DPrandtl number

A steam turbine expands steam from inlet enthalpy h_1 = 3,400 kJ/kg to condenser pressure where the ideal isentropic exit enthalpy is h_2s = 2,400 kJ/kg. If the actual turbine exit enthalpy is measured as h_2a = 2,550 kJ/kg, what is the isentropic efficiency (η_t) of the turbine?

• A85.0%
• B117.6%
• C90.0%
• D80.0%

An engineer performs a tensile test on a steel that shows no distinct yield point on its stress-strain curve. How is its yield strength determined in standard practice?

• AAs the maximum engineering stress reached before necking begins
• BAs the stress at which the specimen fractures
• CAs the stress where a line parallel to the elastic portion, offset by 0.2% strain, inters…
• DAs the stress at the end of the proportional limit, where Hooke's law first stops holding…

In transient heat conduction, the lumped capacitance method is valid only when the internal conductive thermal resistance of a solid body is negligible compared to the external convective thermal resistance. What condition on the Biot number (Bi = h·L_c / k) must be satisfied?

• ABi > 10.0
• BBi < 0.10
• CBi = 1.0
• D0.50 < Bi < 2.0

Two identical pipes in parallel, each of length L = 100 m, diameter D = 0.10 m, and Darcy friction factor f = 0.020, connect two common manifolds. If a total water flow rate of Q_total = 0.0314 m³/s enters the manifold, what is the head loss across the parallel pipe network (g = 9.81 m/s²)?

• A4.08 m
• B8.16 m
• C16.31 m
• D2.04 m

A 3-phase, 4-pole, 60 Hz squirrel-cage induction motor runs at a full-load speed of 1,746 rpm. What is the per-unit slip (s) and the frequency of the rotor induced currents (f_r)?

• As = 0.030 and f_r = 1.8 Hz
• Bs = 0.054 and f_r = 3.24 Hz
• Cs = 0.030 and f_r = 60.0 Hz
• Ds = 0.015 and f_r = 0.9 Hz

When a three-phase synchronous generator connected to an infinite grid is overexcited (field current I_f increased above normal excitation), how does its operating condition change?

• AIt absorbs reactive power from the grid, operating at a leading power factor
• BIt delivers lagging reactive power (vars) to the grid, operating at a lagging power factor
• CIt increases its active power output without changing reactive power
• DIts rotational speed increases above synchronous speed

In a standard NEMA Design B squirrel-cage induction motor, what does the 'breakdown torque' (pullout torque) represent on the torque-speed curve?

• AThe torque developed at zero rotor speed (locked rotor)
• BThe continuous torque developed at rated full-load speed
• CThe maximum torque the motor can develop before abruptly stalling as speed decreases belo…
• DThe minimum torque developed during the motor acceleration period

In an open-circuit (no-load) test performed on a single-phase power transformer, rated voltage is applied to the low-voltage winding while the high-voltage winding remains open. Which equivalent circuit parameters and losses are primarily determined by this test?

• ACore magnetization branch parameters (R_c and X_m) and no-load core iron losses (hysteres…
• BSeries winding resistance (R_eq) and leakage reactance (X_eq)
• CFull-load copper I²R losses and percent impedance voltage
• DDielectric breakdown strength of the mineral insulating oil

During the short-circuit test of a power transformer, a reduced voltage is applied to the high-voltage winding with the low-voltage terminals short-circuited to circulate rated current. What are the primary quantities determined from the wattmeter and voltmeter readings?

• ACore hysteresis and eddy current losses and no-load power factor
• BEquivalent series winding resistance (R_eq), leakage reactance (X_eq), and full-load copp…
• CMagnetizing shunt admittance and turns ratio
• DInsulation resistance between primary and secondary windings

A machine controlled by G90 (absolute) programming has its tool at X20 Y10. The next block is 'G91 G01 X15 Y-5 F200'. Where is the tool after this block is executed?

• AX15 Y-5
• BX35 Y5
• CX5 Y15
• DX35 Y15

A three-phase induction motor delivers 75 kW of shaft mechanical power while connected to a 440 V, 60 Hz line. At rated load, its efficiency is 92.0% and its power factor is 0.85 lagging. What is the line current (I_L) drawn by the motor?

• A98.4 A
• B125.8 A
• C218.0 A
• D72.7 A

According to NOM-001-SEDE-2012 (Article 430-22), what minimum ampacity rating must branch-circuit conductors supplying a single continuous-duty electric motor have relative to the motor full-load current (FLC) rating?

• ANot less than 100% of the motor full-load current rating
• BNot less than 115% of the motor full-load current rating
• CNot less than 125% of the motor full-load current rating
• DNot less than 150% of the motor full-load current rating

According to NOM-001-SEDE-2012 Table 310-15(b)(2)(a), what temperature correction factor must be applied to copper conductors with 75 °C insulation (THW) installed in an industrial area where the ambient temperature reaches 45 °C (reference ambient 30 °C)?

• A0.82
• B0.87
• C0.71
• D0.58

Under NOM-001-SEDE-2012 Table 310-15(b)(3)(a), when 4 to 6 current-carrying conductors are installed in the same conduit or raceway without maintained spacing, what adjustment factor must be applied to their allowable ampacities?

• A0.70 (70%)
• B0.80 (80%)
• C0.50 (50%)
• D0.90 (90%)

According to NOM-001-SEDE-2012 Table 430-52, what maximum percentage of motor full-load current (FLC) is permitted for sizing an inverse-time circuit breaker providing branch-circuit short-circuit and ground-fault protection for a standard squirrel-cage induction motor?

• A125%
• B175%
• C250%
• D300%

A brake press motor retrofit costs MXN 60,000 and reduces energy consumption by 12,000 kWh per year. At an average energy price of MXN 2.50/kWh, what is the simple payback period of the investment?

• A5.0 years
• B0.5 years
• C2.0 years
• D12.0 years

A 500 kVA, 13.2 kV / 480 V distribution transformer has a no-load core loss of 1,800 W and a full-load copper loss of 4,200 W. What is its operational efficiency when supplying an 80% load at a 0.80 lagging power factor?

• A98.62%
• B98.16%
• C99.44%
• D98.89%

In a three-phase power system with a base voltage of V_base = 13.8 kV (line-to-line) and a three-phase base apparent power of S_base = 10 MVA, what is the base impedance (Z_base) of the system?

• A1.38 Ω
• B19.04 Ω
• C33.00 Ω
• D57.13 Ω

In power transformer differential protection (ANSI 87T), why is a second-harmonic restraint feature incorporated into the protective relay algorithm?

• ATo detect high-resistance winding-to-ground faults
• BTo prevent relay tripping during transformer steady-state overexcitation
• CTo prevent false tripping caused by magnetizing inrush current during transformer energiz…
• DTo compensate for CT phase angle shifts across star-delta connections

In an industrial electrical installation governed by NOM-001-SEDE-2012 Article 250, what is the primary safety purpose of the main bonding jumper (puente de unión principal) at the service entrance?

• ATo provide a backup lightning path directly into the earth rod
• BTo connect the equipment grounding conductor to the grounded neutral conductor, establish…
• CTo equalize voltage between the three live line phases during unbalanced loads
• DTo isolate the transformer neutral from metallic equipment enclosures

Under the general tariff rules of Comisión Federal de Electricidad (CFE) for industrial medium and high voltage supply, at what power factor threshold does billing switch between a bonus credit and a penalty surcharge?

• A0.90 (90%)
• B0.85 (85%)
• C0.95 (95%)
• D1.00 (100%)

A nonlinear industrial load generates harmonic currents. If the fundamental current is I_1 = 100 A and the RMS sum of all higher harmonic currents is √(∑ I_h²) = 25 A, what is the Total Harmonic Current Distortion (THD_I) according to IEEE 519 and the Mexican Grid Code (Código de Red)?

• A4.0%
• B12.5%
• C25.0%
• D33.3%

An industrial facility absorbs an active power of P = 600 kW at a lagging power factor of 0.75 (tan θ_1 = 0.8819). To avoid low power factor charges from CFE, plant engineering installs a capacitor bank to raise the power factor to 0.95 lagging (tan θ_2 = 0.3287). What is the required reactive power rating (Q_c in kVAr) of the capacitor bank?

• A120 kVAr
• B197 kVAr
• C332 kVAr
• D529 kVAr

An equipment item's maintenance records show a mean time between failures (MTBF) of 190 hours and a mean time to repair (MTTR) of 10 hours. What is its inherent availability?

• A95.0%
• B94.7%
• C5.0%
• D105.3%

According to NOM-001-SEDE-2012 Article 110-14(c), for circuits rated 100 amperes or less, or marked for conductors from 2.08 mm² to 42.4 mm² (14 to 1 AWG), which temperature column of Table 310-15(b)(16) must be used to size conductors unless the equipment terminals are listed and marked for a higher temperature?

• A90 °C
• B60 °C
• C75 °C
• D105 °C