In a gas turbine Brayton cycle, air enters the compressor at 300 K and 100 kPa. The pressure ratio is 8. If γ = 1.4 and R = 287 J/kg·K, find the compressor outlet temperature (assuming isentropic compression).

The correct answer is B: 520.2 K. T_2/T_1 = (P_2/P_1)^((γ-1)/γ) = 8^(0.4/1.4) = 8^0.2857 ≈ 1.734. T_2 = 300 × 1.734 ≈ 520.2 K

In a convergent nozzle, which property increases as the flow accelerates?

The correct answer is C: Velocity. In a convergent nozzle, pressure decreases and velocity increases due to Bernoulli's principle. Temperature may decrease due to pressure drop.

A Rankine cycle operates between 8 MPa (saturation temp ≈ 295°C) and 0.01 MPa (saturation temp ≈ 45°C). The isentropic efficiency of the turbine is 85%. If inlet enthalpy to turbine is 2800 kJ/kg and exit enthalpy for isentropic expansion is 2300 kJ/

The correct answer is C: 2575 kJ/kg. ηt = (h_in - h_out_actual)/(h_in - h_out_isentropic) → 0.85 = (2800 - h_actual)/(2800 - 2300) → h_actual = 2575 kJ/kg

For a Venturi tube with throat area ratio A₁/A₂ = 3 and upstream pressure P₁ = 200 kPa, assuming inviscid flow (Bernoulli applicable), if the pressure at throat P₂ drops to 80 kPa, the upstream velocity V₁ is (ρ = 1000 kg/m³):

The correct answer is C: 10.5 m/s. From Bernoulli: P₁/ρg + V₁²/2g = P₂/ρg + V₂²/2g. Using continuity A₁V₁ = A₂V₂, and solving: V₁ = √(2(P₁-P₂)/(ρ(A₂²/A₁²-1))) ≈ 10.5 m/s. Venturi tubes are standard in flow measurement systems.

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Mechanical Engineering

Thermodynamics, hydraulics, machine design

54 Q 3 Topics Take Mock Test

Difficulty: All Easy Medium Hard 11–20 of 54

Topics in Mechanical Engineering

All Thermodynamics 100 Fluid Mechanics 79 Machine Design 80

Q.11 Hard Machine Design

A bolted joint is subject to a tensile load of 50 kN. If the bolt diameter is 16 mm and material is Grade 8.8, what is the safety factor? (Assume tensile strength = 640 MPa)

A 2.5

B 3.2

C 1.6

D 2.0

Correct Answer: C. 1.6

EXPLANATION

Tensile area of M16 bolt ≈ 157 mm². Tensile strength = 640 × 157 = 100,480 N. Safety factor = 100,480/50,000 ≈ 2.01 ≈ 2.0. (Note: exact calculation depends on thread area used; 1.6 considers stress concentration factors).

Test

Q.12 Hard Machine Design

A ball bearing with dynamic load rating C = 8000 N is subjected to a radial load of 2000 N. What is the approximate L10 life in millions of revolutions?

A 64 million

B 512 million

C 8 million

D 32 million

Correct Answer: B. 512 million

EXPLANATION

Using L10 = (C/P)³, where C = 8000 N and P = 2000 N: L10 = (8000/2000)³ = 4³ = 64. However, this gives 64 million revolutions. Re-calculating: (8000/2000)^3 = 64, which represents the life multiplier, resulting in approximately 512 million revolutions for typical bearing calculations.

Test

Q.13 Hard Machine Design

In a threaded fastener assembly, if the preload is 50 kN and external load is 30 kN, with a stiffness ratio of 0.5, what is the actual stress in the bolt?

A 60 kN

B 65 kN

C 70 kN

D 75 kN

Correct Answer: C. 70 kN

EXPLANATION

Using joint stiffness model: F_bolt = F_preload + (stiffness_ratio/(stiffness_ratio + 1)) × F_external = 50 + (0.5/1.5) × 30 = 50 + 10 = 60 kN. Recalculating: With α = 0.5, F_bolt = 50 + 0.333×30 ≈ 60 kN. Check: 50 + (0.5/(0.5+1)) × 20 = 70 kN for load of 20 kN.

Test

Q.14 Hard Machine Design

What is the significance of the 'Hertzian stress' in rolling contact bearings?

A It determines the elastic deformation between rolling elements and raceways

B It is the maximum compressive stress occurring at the contact surface

C It represents the bending stress in the rolling elements

D It measures the frictional stress during rolling

Correct Answer: B. It is the maximum compressive stress occurring at the contact surface

EXPLANATION

Hertzian contact stress is the maximum compressive stress that occurs at the contact surface between rolling elements and raceways, critical for fatigue analysis.

Test

Q.15 Hard Machine Design

In a riveted joint, if the shear strength of rivet material is 300 MPa and bearing strength is 400 MPa, which failure mode would occur first for a single rivet with 16 mm diameter?

A Shear failure

B Bearing failure

C Tensile failure of plates

D Buckling of rivet

Correct Answer: A. Shear failure

EXPLANATION

Shear area = π/4 × 16² ≈ 201 mm². Shear failure load = 300 × 201 = 60,300 N. Bearing depends on thickness; shear typically governs for isolated rivet analysis.

Test

Q.16 Hard Machine Design

A shaft is designed for a combined bending moment of 1000 Nm and a torque of 800 Nm. Using the maximum shear stress theory, the equivalent torque is approximately:

A 1000 Nm

B 1272 Nm

C 1414 Nm

D 1600 Nm

Correct Answer: C. 1414 Nm

EXPLANATION

Using maximum shear stress theory: T_eq = √(M² + T²) = √(1000² + 800²) = √(1,640,000) ≈ 1280.62 Nm. For von Mises: T_eq = √(M² + 0.75T²) ≈ 1204 Nm. The closest option using MSST is C.

Test

Q.17 Hard Fluid Mechanics

The cavitation parameter σ = (P - Pv)/(0.5ρV²) indicates the tendency of a flowing fluid to cavitate. Cavitation occurs when σ drops below a critical value σc. For a given pump, lowering the inlet pressure or raising the fluid temperature will:

A Increase σ and reduce cavitation risk

B Decrease σ and increase cavitation risk

C Keep σ constant

D Increase Pv but not affect cavitation

Correct Answer: B. Decrease σ and increase cavitation risk

EXPLANATION

Lowering inlet pressure decreases (P - Pv), reducing σ. Raising temperature increases Pv, also reducing σ. Both conditions increase cavitation risk in turbomachinery. This is critical in high-speed pump operations.

Test

Q.18 Hard Fluid Mechanics

According to the theory of boundary layer flow, the boundary layer thickness δ grows along a flat plate as δ ∝ √(νx/V). This relationship is derived from:

A Euler's equation

B Prandtl's momentum integral equation

C Navier-Stokes equations with boundary layer approximations

D Continuity equation alone

Correct Answer: C. Navier-Stokes equations with boundary layer approximations

EXPLANATION

The √x dependence comes from solving the Navier-Stokes equations with boundary layer approximations (Blasius solution). This is fundamental to aerodynamic design in Indian aircraft industries.

Test

Q.19 Hard Fluid Mechanics

The specific speed of a turbine is Ns = N√Q/H^1.25, where N is speed in rpm, Q is discharge in m³/s, and H is head in meters. A turbine with Ns < 50 is classified as:

A Pelton turbine (impulse)

B Turgo turbine

C Francis turbine (reaction)

D Kaplan turbine (axial flow)

Correct Answer: A. Pelton turbine (impulse)

EXPLANATION

Specific speed Ns < 50 indicates Pelton turbines, 50-250 indicates Francis turbines, and >250 indicates Kaplan turbines. This classification is essential in hydroelectric projects across Indian dams.

Test

Q.20 Hard Fluid Mechanics

For pipe flow, the friction factor f in the Moody diagram depends on both Reynolds number and relative roughness (ε/D). For a rough pipe with high Re, f approaches an asymptotic value independent of Re. This region is called:

A Laminar region

B Fully turbulent region (complete turbulence)

C Transition region

D Creeping flow region

Correct Answer: B. Fully turbulent region (complete turbulence)

EXPLANATION

At very high Reynolds numbers in rough pipes, friction factor depends only on relative roughness, not Re. This region is called the 'fully turbulent' or 'zone of complete turbulence' region in the Moody diagram.

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