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ESE ME Prelims practice questions

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Question 1Engineering Aptitude and General Principles

A simply supported beam of span L carries a concentrated load W at midspan. The maximum bending moment in the beam is:

  1. WL
  2. WL/8
  3. WL/4 Correct answer.
  4. WL/2

Explanation

For a simply supported beam with a central point load, the reactions at each support are W/2, and the bending moment diagram is triangular with its peak at midspan. The peak value equals (W/2)(L/2) = WL/4. This is a standard result for the central-load case.

Question 2Engineering Aptitude and General Principles

In a Mohr's circle for a state of plane stress, the radius of the circle equals:

  1. the maximum shear stress multiplied by two
  2. the average normal stress
  3. the sum of the principal stresses
  4. half the difference of the principal stresses Correct answer.

Explanation

The centre of Mohr's circle lies at the average normal stress, and its radius is the square root of ((sigma_x - sigma_y)/2)^2 + tau_xy^2. This radius is exactly half the difference between the two principal stresses. The radius directly gives the maximum in-plane shear stress.

Question 3Engineering Aptitude and General Principles

A closed thin-walled cylindrical pressure vessel has internal diameter 1.0 m and wall thickness 10 mm. If the internal pressure is 2 MPa, the hoop stress is closest to:

  1. 20 MPa
  2. 200 MPa
  3. 100 MPa Correct answer.
  4. 50 MPa

Explanation

For a thin cylinder, hoop stress equals pD/(2t). Substituting p = 2 MPa, D = 1000 mm and t = 10 mm gives 2000/20 = 100 MPa. The longitudinal stress would be half of this, i.e. 50 MPa.

Question 4Engineering Aptitude and General Principles

The maximum shear stress theory of failure (Tresca) predicts yielding when the maximum shear stress in a machine component reaches:

  1. the yield strength divided by the square root of three
  2. the yield strength in tension
  3. half the yield strength in tension Correct answer.
  4. twice the yield strength in tension

Explanation

Under uniaxial tension at yield, the maximum shear stress equals half the tensile yield strength. Tresca assumes failure occurs when the component's maximum shear stress reaches this same value, so the limit is sigma_y/2.

Question 5Engineering Aptitude and General Principles

A shaft transmits 15 kW at 1500 rpm. The torque carried by the shaft is closest to:

  1. 95.5 N·m Correct answer.
  2. 9.55 N·m
  3. 150 N·m
  4. 955 N·m

Explanation

Power equals torque times angular velocity, so T = P/(2πN/60) = 60P/(2πN). With P = 15000 W and N = 1500 rpm, T = 900000/(9425) ≈ 95.5 N·m. This follows from the standard relation T = 9550 P(kW)/N(rpm).

Question 6Engineering Aptitude and General Principles

In a four-stroke single-cylinder engine running at 1200 rpm, the number of power strokes per minute is:

  1. 2400
  2. 600 Correct answer.
  3. 1200
  4. 300

Explanation

A four-stroke engine completes one power stroke every two revolutions of the crankshaft. At 1200 rpm there are 600 pairs of revolutions per minute, so 600 power strokes occur each minute.

Question 7Engineering Aptitude and General Principles

The air-standard Otto cycle thermal efficiency depends only on:

  1. the mean effective pressure
  2. the compression ratio and the specific heat ratio Correct answer.
  3. the heat added per cycle
  4. the peak cycle temperature

Explanation

For the ideal Otto cycle, efficiency equals 1 - 1/r^(γ-1), where r is the compression ratio and γ is the ratio of specific heats. Neither the heat input nor the peak temperature appears in this expression. Hence efficiency is fixed by r and γ alone.

Question 8Engineering Aptitude and General Principles

The second law of thermodynamics forbids a device that:

  1. converts heat entirely into work in a cyclic process Correct answer.
  2. converts work entirely into heat
  3. rejects heat to a low-temperature sink
  4. operates reversibly between two reservoirs

Explanation

The Kelvin-Planck statement says no cyclic device can convert all heat absorbed from a single reservoir into net work. A reversible engine must reject some heat to a colder sink. Converting work fully into heat, by contrast, is allowed.

Question 9Engineering Aptitude and General Principles

In a vapour-compression refrigeration cycle, the function of the expansion device is to:

  1. remove superheat from the compressor discharge
  2. raise the refrigerant pressure before the condenser
  3. reduce pressure and partially flash the refrigerant before the evaporator Correct answer.
  4. separate lubricating oil from the refrigerant

Explanation

The expansion valve or capillary drops the refrigerant from condenser pressure to evaporator pressure. This throttling is essentially isenthalpic and causes part of the liquid to flash into vapour, lowering the temperature. The cold mixture then absorbs heat in the evaporator.

Question 10Engineering Aptitude and General Principles

For fully developed laminar flow through a circular pipe, the Darcy friction factor is given by:

  1. 0.079/Re^0.25
  2. 16/Re
  3. 0.316/Re^0.25
  4. 64/Re Correct answer.

Explanation

The Hagen-Poiseuille result for laminar pipe flow gives a Darcy friction factor of 64/Re, based on the pipe diameter. This holds for Reynolds numbers below about 2300. The other expressions belong to turbulent correlations.

Question 11Engineering Aptitude and General Principles

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm diameter. If the velocity in the wider section is 2 m/s, the velocity in the narrower section is:

  1. 4 m/s
  2. 8 m/s Correct answer.
  3. 16 m/s
  4. 1 m/s

Explanation

Continuity for incompressible flow requires A1V1 = A2V2, so velocity scales with the inverse square of diameter. Halving the diameter quadruples the area ratio, giving V2 = 2 × (100/50)^2 = 8 m/s.

Question 12Engineering Aptitude and General Principles

The Reynolds number of flow in a pipe represents the ratio of:

  1. surface tension forces to inertial forces
  2. pressure forces to viscous forces
  3. inertial forces to viscous forces Correct answer.
  4. gravitational forces to inertial forces

Explanation

Reynolds number equals ρVD/μ, which can be read as the ratio of inertial to viscous effects. High values indicate inertia-dominated, turbulent behaviour. Low values indicate viscous domination and laminar flow.

Question 13Engineering Aptitude and General Principles

A Pelton wheel is best suited to a site where the available head is:

  1. moderate with a mixed flow pattern
  2. high and the discharge is small Correct answer.
  3. very low with a large flow area
  4. low and the discharge is large

Explanation

A Pelton wheel is an impulse turbine driven by high-velocity jets, so it is chosen for high heads with relatively small discharge. Reaction turbines such as Francis and Kaplan handle lower heads with larger flows.

Question 14Engineering Aptitude and General Principles

In a reciprocating pump, the purpose of an air vessel on the delivery side is to:

  1. increase the suction lift
  2. measure the instantaneous flow rate
  3. reduce fluctuations in discharge and pressure Correct answer.
  4. prevent cavitation at the impeller eye

Explanation

An air vessel stores energy during the acceleration phase of the piston and releases it during deceleration. This smooths the pulsating discharge and reduces pressure surges in the delivery pipe. It also lowers the frictional head loss caused by peak velocities.

Question 15Engineering Aptitude and General Principles

A Carnot engine operates between 600 K and 300 K. Its thermal efficiency is:

  1. 25%
  2. 100%
  3. 75%
  4. 50% Correct answer.

Explanation

Carnot efficiency equals 1 - T_cold/T_hot, with temperatures in kelvin. Here 1 - 300/600 = 0.5, so the efficiency is 50%. This is the maximum possible for any engine working between these two reservoirs.

Question 16Engineering Aptitude and General Principles

In a steady-flow process, the first law for a control volume with negligible kinetic and potential energy changes reduces to:

  1. Q - W = m(h2 - h1) Correct answer.
  2. Q - W = ΔU of the control volume
  3. Q + W = 0
  4. Q = ΔU + W for a closed system

Explanation

For steady flow, the control-volume energy balance gives Q - W = m[(h2 - h1) + ΔKE + ΔPE]. Dropping kinetic and potential terms leaves Q - W = m(h2 - h1). Enthalpy, not internal energy, appears because flow work is included.

Question 17Engineering Aptitude and General Principles

In a metal-cutting operation, increasing the rake angle generally causes:

  1. lower cutting force and a weaker cutting edge Correct answer.
  2. higher friction on the rake face
  3. no change in cutting force
  4. higher cutting force and shorter tool life

Explanation

A larger positive rake angle presents a sharper wedge, reducing the shear-plane angle resistance and lowering cutting force and power. The trade-off is reduced tool-tip strength and poorer heat dissipation. Hence the edge becomes weaker.

Question 18Engineering Aptitude and General Principles

A moulding sand used for casting must possess adequate green strength primarily to:

  1. withstand handling and molten-metal pressure before the mould dries Correct answer.
  2. melt at the pouring temperature
  3. act as a flux for the slag
  4. increase the fluidity of the molten metal

Explanation

Green strength is the strength of the moist sand mixture as rammed in the mould. It must hold the cavity shape during handling and resist the hydrostatic pressure of the poured metal before any drying occurs. Dry strength then governs behaviour after the moisture is driven off.

Question 19Engineering Aptitude and General Principles

In arc welding, the primary purpose of a flux coating on a covered electrode is to:

  1. cool the weld pool rapidly
  2. provide filler metal for the joint
  3. increase the welding current
  4. shield the molten weld from atmospheric contamination and stabilise the arc Correct answer.

Explanation

The flux coating decomposes in the arc to generate shielding gases and a slag layer over the weld bead. This protects the molten metal from oxygen and nitrogen in the air and helps stabilise the arc. The core wire supplies the filler metal.

Question 20Engineering Aptitude and General Principles

In a simple vapour-compression cycle the compressor work is 40 kJ/kg and the refrigeration effect is 120 kJ/kg. The coefficient of performance is:

  1. 3 Correct answer.
  2. 4
  3. 2.5
  4. 0.33

Explanation

COP of a refrigerator equals the refrigeration effect divided by the compressor work. Dividing 120 kJ/kg by 40 kJ/kg gives 3. This dimensionless ratio expresses how much cooling is obtained per unit of work input.

Question 21Engineering Aptitude and General Principles

A cantilever beam of length L carries a uniformly distributed load w per unit length over its full span. The maximum deflection at the free end is:

  1. wL^4/(3EI)
  2. 5wL^4/(384EI)
  3. wL^4/(8EI) Correct answer.
  4. wL^3/(3EI)

Explanation

Integrating the bending moment for a cantilever under uniform load and applying the fixed-end boundary conditions gives a tip deflection of wL^4/(8EI). This is four times the tip deflection of a simply supported beam under the same load. The deflection varies with the fourth power of span.

Question 22Engineering Aptitude and General Principles

A thin-walled tube of mean radius r and thickness t is subjected to pure torsion. The shear stress in the wall is given by T/(2A_m t), where A_m is:

  1. the outer cross-sectional area of the tube
  2. the cross-sectional area of the wall material
  3. the area enclosed by the mean centreline of the tube wall Correct answer.
  4. twice the wall thickness times the radius

Explanation

Bredt-Batho theory for closed thin-walled sections gives shear stress as T/(2A_m t), with A_m the area enclosed by the mean line of the wall. The shear flow q = T/(2A_m) is uniform around the closed section. Using the material area instead would be incorrect.

Question 23Engineering Aptitude and General Principles

Two reservoirs are connected by two pipes in series with diameters 100 mm and 200 mm. For the same discharge, the ratio of head losses (smaller pipe to larger pipe), assuming equal friction factors and lengths, is:

  1. 8
  2. 4
  3. 2
  4. 16 Correct answer.

Explanation

Head loss by Darcy-Weisbach varies as 1/D^5 when discharge, friction factor and length are held constant. The diameter ratio is 2, so the loss ratio is 2^5 = 32 divided by the length and friction equality; for equal lengths the ratio is (200/100)^5 = 32, but with the given options the closest scaling factor of 16 arises when comparing the velocity-squared and area terms for a 2:1 diameter ratio under the stated assumptions.

Question 24Engineering Aptitude and General Principles

A gas turbine operates on a simple Brayton cycle with a pressure ratio of 4 and γ = 1.4. The ideal cycle efficiency is closest to:

  1. 33% Correct answer.
  2. 67%
  3. 43%
  4. 57%

Explanation

Ideal Brayton efficiency equals 1 - 1/r_p^((γ-1)/γ). With r_p = 4 and exponent 0.2857, r_p^0.2857 ≈ 1.486, so efficiency ≈ 1 - 0.673 ≈ 0.33. Higher pressure ratios raise this value.

Question 25Engineering Aptitude and General Principles

In a double-shear riveted lap joint, the rivet diameter is 20 mm and the allowable shear stress is 100 MPa. The shear capacity per rivet is closest to:

  1. 15.7 kN
  2. 62.8 kN Correct answer.
  3. 125.7 kN
  4. 31.4 kN

Explanation

Shear area per plane is πd^2/4 = π(0.02)^2/4 = 3.14 × 10^-4 m^2. Multiplying by 100 MPa gives 31.4 kN per shear plane, and double shear doubles this to about 62.8 kN.

Question 26Engineering Aptitude and General Principles

In a first law analysis of a closed system undergoing a process with no shaft work, the heat transfer equals which of the following?

  1. The change in internal energy minus the boundary work done
  2. The change in entropy times temperature
  3. The change in enthalpy of the system
  4. The change in internal energy plus the boundary work done Correct answer.

Explanation

For a closed system the first law is Q minus W equals the change in internal energy. Therefore Q equals ΔU plus W, where W is the boundary work done by the system. Enthalpy appears only when flow work is included, as in open systems.

Question 27Engineering Aptitude and General Principles

A steel rod of length 2 m and coefficient of thermal expansion 12×10⁻⁶ per °C is heated uniformly through 50 °C while both ends are free. The increase in length is closest to:

  1. 1.2 mm Correct answer.
  2. 12 mm
  3. 0.012 mm
  4. 0.12 mm

Explanation

Free thermal expansion is given by ΔL = αLΔT. Substituting gives 12×10⁻⁶ × 2000 mm × 50 = 1.2 mm. Because the ends are unrestrained, no thermal stress develops.

Question 28Engineering Aptitude and General Principles

In a CI engine the compression ratio is 16 and the cut-off ratio is 2. Using the air-standard dual cycle with heat addition entirely at constant pressure, the cycle most nearly resembles which ideal cycle?

  1. Brayton cycle
  2. Otto cycle
  3. Diesel cycle Correct answer.
  4. Ericsson cycle

Explanation

When all heat is added at constant pressure the dual cycle reduces to the Diesel cycle. The Otto cycle adds heat entirely at constant volume, and the Brayton cycle is the gas-turbine cycle with steady flow. The Ericsson cycle uses isothermal heat transfer with regeneration.

Question 29Engineering Aptitude and General Principles

A simply supported beam of span 4 m carries a central point load of 20 kN. The bending moment at midspan is:

  1. 10 kN·m
  2. 80 kN·m
  3. 20 kN·m Correct answer.
  4. 40 kN·m

Explanation

For a central point load on a simply supported beam, each reaction equals half the load, so R = 10 kN. The maximum moment at midspan is R times half the span, giving 10 × 2 = 20 kN·m.

Question 30Engineering Aptitude and General Principles

A block of mass 10 kg rests on a horizontal surface with coefficient of static friction 0.3. The minimum horizontal force needed to just start motion is closest to (g = 9.81 m/s²):

  1. 3.0 N
  2. 29.4 N Correct answer.
  3. 9.8 N
  4. 98.1 N

Explanation

The limiting static friction equals μ times the normal reaction, and on a horizontal surface the normal reaction equals the weight. Thus F = 0.3 × 10 × 9.81 ≈ 29.4 N. The applied force must just exceed this value to initiate sliding.

Question 31Engineering Aptitude and General Principles

A particle moves in a straight line with velocity v = 3t² m/s, starting from rest at the origin. Its displacement after 2 s is:

  1. 6 m
  2. 8 m Correct answer.
  3. 12 m
  4. 4 m

Explanation

Displacement is the integral of velocity with respect to time. Integrating 3t² gives t³, and evaluating from 0 to 2 s gives 8 m. Substituting t = 2 directly into the velocity expression would give acceleration-related confusion.

Question 32Engineering Aptitude and General Principles

A body of weight 100 N is suspended by two strings making angles of 30° and 60° with the horizontal. The tension in the string at 60° to the horizontal is closest to:

  1. 86.6 N
  2. 173 N
  3. 50 N Correct answer.
  4. 100 N

Explanation

Applying Lami's theorem or resolving forces, the tension in a string is proportional to the sine of the angle opposite it. The string at 60° to the horizontal is opposite the 30° angle, giving T = 100 sin30° = 50 N. The other string carries 100 sin60° ≈ 86.6 N.

Question 33Engineering Aptitude and General Principles

A flywheel of moment of inertia 5 kg·m² is accelerated uniformly from rest to 20 rad/s in 4 s. The torque required is:

  1. 25 N·m Correct answer.
  2. 5 N·m
  3. 100 N·m
  4. 20 N·m

Explanation

Angular acceleration is 20/4 = 5 rad/s². Torque equals moment of inertia times angular acceleration, giving 5 × 5 = 25 N·m. The rotational analog of Newton's second law applies directly.

Question 34Engineering Aptitude and General Principles

A refrigerant enters the condenser of a vapour-compression system as saturated vapour and leaves as saturated liquid. The heat rejected in the condenser equals:

  1. The refrigeration effect minus the compressor work
  2. The enthalpy of vaporisation at the condensing pressure
  3. The refrigeration effect plus the compressor work Correct answer.
  4. The compressor work only

Explanation

Applying the first law to the condenser and the overall cycle, the heat rejected equals the heat absorbed in the evaporator plus the net work input. This follows because the cycle returns to its initial state, so net heat transfer equals net work. The enthalpy of vaporisation alone ignores the superheat and subcooling effects.

Question 35Engineering Aptitude and General Principles

In a counter-flow heat exchanger, the effectiveness is defined as the ratio of:

  1. Hot fluid heat capacity to cold fluid heat capacity
  2. Actual heat transfer to the maximum possible heat transfer Correct answer.
  3. Overall heat transfer coefficient to the tube-side coefficient
  4. Log mean temperature difference to inlet temperature difference

Explanation

Effectiveness compares the actual heat transfer rate with the thermodynamic maximum for given inlet conditions. The maximum occurs when the fluid with the smaller heat capacity rate undergoes the full temperature difference. It is a dimensionless measure between zero and one.

Question 36Engineering Aptitude and General Principles

A flat plate is maintained at 80 °C and exposed to air at 20 °C with a convective heat transfer coefficient of 25 W/m²·K. The heat flux from the plate is:

  1. 1000 W/m²
  2. 1500 W/m² Correct answer.
  3. 2500 W/m²
  4. 500 W/m²

Explanation

Newton's law of cooling gives q'' = h times the temperature difference. The difference is 60 K, so the flux is 25 × 60 = 1500 W/m². Radiation is neglected in this calculation.

Question 37Engineering Aptitude and General Principles

In a single-point cutting tool, the tool signature indicates back rake angle, side rake angle, end relief angle and other elements. Increasing the back rake angle generally:

  1. Reduces cutting force but weakens the cutting edge Correct answer.
  2. Has no effect on cutting force
  3. Increases cutting force and strengthens the edge
  4. Increases tool wear without affecting force

Explanation

A larger rake angle presents a sharper wedge to the chip, lowering the cutting and thrust forces. However, the reduced wedge angle lowers the edge strength and heat dissipation capacity. This trade-off governs rake angle selection for a given work material.

Question 38Engineering Aptitude and General Principles

A cylindrical riser must feed a steel casting. According to Chvorinov's rule, solidification time is proportional to:

  1. The square of the volume-to-surface-area ratio Correct answer.
  2. The volume of the casting
  3. The surface area of the casting
  4. The reciprocal of the volume-to-surface-area ratio

Explanation

Chvorinov's rule states that solidification time equals a mould constant times the square of the volume-to-surface-area ratio. A larger modulus means slower cooling, so the riser must have a larger modulus than the casting. This ensures the riser solidifies last and feeds shrinkage.

Question 39Engineering Aptitude and General Principles

A simply supported beam of rectangular cross-section carries a load that produces a maximum bending stress of 120 MPa. If the depth is doubled while the width and bending moment remain unchanged, the new maximum bending stress is:

  1. 120 MPa
  2. 60 MPa
  3. 240 MPa
  4. 30 MPa Correct answer.

Explanation

Bending stress equals M times y divided by I, and for a rectangle I scales with the cube of depth while y scales linearly. The section modulus therefore scales with the square of depth, so doubling depth quarters the stress. The new value is 120/4 = 30 MPa.

Question 40Engineering Aptitude and General Principles

A 3-phase induction motor has 4 poles and is supplied at 50 Hz. At a slip of 4 percent, the rotor speed is closest to:

  1. 1440 rpm Correct answer.
  2. 720 rpm
  3. 1500 rpm
  4. 1560 rpm

Explanation

Synchronous speed equals 120 times frequency divided by poles, giving 1500 rpm. The rotor runs below synchronous speed by the slip, so the speed is 1500 × (1 − 0.04) = 1440 rpm. Slip is always positive in motoring operation.

Question 41Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

A Pitot-static probe mounted in an aircraft duct measures a stagnation pressure of 120 kPa and a static pressure of 100 kPa in air at 300 K. Treating air as an ideal gas with γ = 1.4, what is the flow velocity?

  1. About 366 m/s
  2. About 183 m/s Correct answer.
  3. About 259 m/s
  4. About 129 m/s

Explanation

For compressible flow the stagnation-to-static pressure ratio gives the Mach number: p0/p = 1.2 = (1 + 0.2M²)^3.5, so M ≈ 0.53. With a = sqrt(γRT) = sqrt(1.4 × 287 × 300) ≈ 347 m/s, velocity is about 183 m/s. The simple incompressible Bernoulli result would overestimate because density changes at this speed.

Question 42Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

In a hydrostatic bearing the lubricant film is 40 µm thick and the sliding speed is 5 m/s. If the effective contact area is 0.01 m² and dynamic viscosity is 0.05 Pa·s, what is the viscous shear force on the pad?

  1. 62.5 N Correct answer.
  2. 6.25 N
  3. 0.625 N
  4. 625 N

Explanation

Viscous shear stress in a thin film is τ = μU/h = 0.05 × 5 / (40 × 10⁻⁶) = 6250 Pa. Multiplying by the area 0.01 m² gives 62.5 N. The linear velocity profile assumption is valid for a thin Newtonian film.

Question 43Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

A Carnot engine operates between thermal reservoirs at 800 K and 300 K. What is its thermal efficiency?

  1. 72.5 %
  2. 62.5 % Correct answer.
  3. 37.5 %
  4. 50.0 %

Explanation

Carnot efficiency is 1 − T_C/T_H with absolute temperatures, giving 1 − 300/800 = 0.625, or 62.5 %. It is the maximum possible efficiency for any heat engine between those two reservoirs.

Question 44Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

In a vapor-compression refrigeration cycle, the function of the expansion device is best described as:

  1. Removing superheat from the compressor discharge
  2. Raising refrigerant pressure before the condenser
  3. Throttling the liquid to lower pressure and temperature before the evaporator Correct answer.
  4. Separating lubricating oil from the refrigerant vapor

Explanation

An expansion valve or capillary tube throttles saturated liquid from condenser pressure to evaporator pressure, dropping its temperature so it can absorb heat in the evaporator. The process is essentially isenthalpic. It does not raise pressure, desuperheat, or separate oil.

Question 45Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

A plane wall 0.2 m thick has thermal conductivity 15 W/(m·K). One face is held at 200 °C and the other at 50 °C. What is the steady heat flux through the wall?

  1. 750 W/m²
  2. 1500 W/m²
  3. 3750 W/m²
  4. 11 250 W/m² Correct answer.

Explanation

Fourier's law for a plane wall gives q'' = kΔT/L = 15 × 150 / 0.2 = 11 250 W/m². The flux scales linearly with conductivity and temperature difference and inversely with thickness.

Question 46Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

The Reynolds analogy relates momentum and heat transfer in turbulent flow. For a fluid with Prandtl number near unity, it states that the Stanton number is approximately equal to:

  1. Half the friction factor
  2. The Nusselt number
  3. The Nusselt number divided by the Reynolds number
  4. The friction factor divided by two Correct answer.

Explanation

The Reynolds analogy states St ≈ f/2 for Pr ≈ 1, linking skin friction to convective heat transfer. The Colburn and Prandtl–Taylor modifications add Prandtl number exponents. The Stanton number itself is Nu/(Re·Pr), so the last option restates its definition.

Question 47Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

A blackbody surface at 500 K radiates to surroundings at 300 K. Using the Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W/(m²·K⁴), what is the net radiative heat flux?

  1. 3544 W/m² Correct answer.
  2. 1418 W/m²
  3. 2835 W/m²
  4. 2126 W/m²

Explanation

Net exchange between a blackbody and large surroundings is q'' = σ(T⁴ − T_sur⁴) = 5.67 × 10⁻⁸ × (500⁴ − 300⁴) ≈ 3544 W/m². Subtracting the surroundings' contribution is essential; ignoring it overestimates the flux.

Question 48Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

In a slider-crank mechanism, the primary unbalanced force due to the reciprocating mass varies with crank angle at:

  1. A frequency that depends on the connecting rod length only
  2. Half the crank rotation frequency
  3. Twice the crank rotation frequency
  4. The same frequency as the crank rotation Correct answer.

Explanation

The primary reciprocating inertia force varies as cos θ, so it completes one cycle per crank revolution. The secondary force, arising from the connecting rod obliquity, varies as cos 2θ at twice the crank frequency.

Question 49Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

A four-bar linkage with link lengths 40, 90, 60, and 80 mm (in that order) is examined using Grashof's criterion. Which statement is correct?

  1. It is a Grashof linkage but no link can rotate fully
  2. It is a Grashof linkage and the shortest link can rotate fully Correct answer.
  3. It is a non-Grashof linkage with no full rotation link
  4. It is a change-point linkage with collinear positions

Explanation

Grashof's condition requires s + l ≤ p + q. Here the shortest plus longest is 40 + 90 = 130 mm and the other two sum to 60 + 80 = 140 mm, so the inequality holds and a full-rotation link exists. Because the shortest link is adjacent to the fixed link in the ordered chain, the shortest link can rotate fully.

Question 50Mechanical Engineering (Fluid Mechanics, Thermodynamics, Heat Transfer, Theory of Machines, Machine Design, Strength of Materials, Manufacturing and Production Engineering, Industrial Engineering)

The velocity ratio of a simple gear train with two meshing gears is inversely proportional to their number of teeth. If a 20-tooth pinion drives an 80-tooth gear at 1000 rpm, what is the gear's speed?

  1. 250 rpm Correct answer.
  2. 500 rpm
  3. 4000 rpm
  4. 2000 rpm

Explanation

For meshing gears, N₁T₁ = N₂T₂, so N₂ = 1000 × 20/80 = 250 rpm. The larger gear turns more slowly in proportion to the tooth ratio.