Illinois Mechanical Engineer
Examination Advanced 100-Question
Practice Exam 2026 | Questions &
Answers with Detailed Rationales |
Complete Exam Prep & Study Guide
1. A steel pressure vessel is subjected to an internal pressure of 2.0 MPa. Its
internal diameter is 1.2 m and wall thickness is 12 mm. Assuming a thin-
wall cylinder, what is the approximate circumferential stress?
A. 50 MPa
B. 75 MPa
C. 100 MPa
D. 150 MPa
Answer: 100 MPa
Rationale: For a thin cylindrical vessel, hoop stress is ς = pD/(2t). Substituting
2.0 MPa × 1200 mm/(2 × 12 mm) gives 100 MPa.
2. A centrifugal pump increases the pressure head of water by 30 m while
operating at 0.20 m³/s with an overall efficiency of 78%. What shaft power
is approximately required?
,A. 58 kW
B. 65 kW
C. 75 kW
D. 92 kW
Answer: 75 kW
Rationale: Hydraulic power is ρgQH = 1000(9.81)(0.20)(30) = 58.9 kW. Dividing
by 0.78 gives approximately 75.5 kW.
3. For steady, incompressible flow through a horizontal pipe with negligible
losses, which condition follows directly from Bernoulli's equation?
A. Static pressure is always constant
B. Velocity is always constant
C. Total mechanical energy per unit weight remains constant
D. Density decreases as velocity increases
Answer: Total mechanical energy per unit weight remains constant
Rationale: Bernoulli's equation states that pressure head, velocity head, and
elevation head sum to a constant when pumps, turbines, and losses are absent.
4. A refrigeration system operates with an evaporator temperature of −10°C
and condenser temperature of 35°C. For an ideal reversed Carnot
refrigerator, the COP is approximately:
A. 2.5
B. 4.0
C. 5.84
D. 7.1
Answer: 5.84
Rationale: COP = Te/(Tc − Te), using absolute temperatures. Te = 263.15 K and Tc
= 308.15 K, giving 263.15/45 ≈ 5.85.
, 5. A beam is subjected to a bending moment of 12 kN·m. Its section modulus
is 600 cm³. What is the maximum bending stress?
A. 10 MPa
B. 20 MPa
C. 30 MPa
D. 40 MPa
Answer: 20 MPa
Rationale: Bending stress is ς = M/S. Converting 12 kN·m to 12 × 10⁶ N·mm and
600 cm³ to 600,000 mm³ gives 20 N/mm², or 20 MPa.
6. In a heat exchanger, the hot fluid enters at 180°C and leaves at 100°C. The
cold fluid enters at 30°C and leaves at 80°C. What is the log-mean
temperature difference for counterflow operation?
A. 75°C
B. 82°C
C. 85°C
D. 95°C
Answer: 85°C
Rationale: The terminal differences are 180 − 80 = 100°C and 100 − 30 = 70°C.
LMTD = (100 − 70)/ln(100/70) ≈ 84.7°C.
7. A simply supported beam carries a concentrated load at its midpoint. If the
span is doubled while the load remains unchanged, the maximum bending
moment becomes:
A. Half as large
B. Unchanged
C. Twice as large
D. Four times as large
Answer: Twice as large
, Rationale: For a central point load, Mmax = PL/4. Therefore, doubling L doubles
the maximum moment.
8. Which failure theory is generally most appropriate for predicting yielding of
a ductile metal under a multiaxial stress state?
A. Maximum principal stress theory
B. Maximum principal strain theory
C. Maximum distortion-energy theory
D. Coulomb-Mohr brittle theory
Answer: Maximum distortion-energy theory
Rationale: The von Mises distortion-energy criterion is widely used for ductile
metals because yielding correlates well with distortional strain energy.
9. A shaft transmits 100 kW at 1,500 rpm. What is the approximate torque?
A. 318 N·m
B. 637 N·m
C. 955 N·m
D. 1,273 N·m
Answer: 637 N·m
Rationale: T = P/ω. With ω = 2π(1500)/60 = 157.1 rad/s, T = 100,000/157.1 ≈ 637
N·m.
10.Increasing the diameter of a solid circular shaft while keeping torque
constant primarily reduces torsional shear stress because:
A. Polar moment decreases
B. Polar moment increases strongly with diameter
C. Modulus of elasticity increases
D. Poisson's ratio decreases
Answer: Polar moment increases strongly with diameter
Examination Advanced 100-Question
Practice Exam 2026 | Questions &
Answers with Detailed Rationales |
Complete Exam Prep & Study Guide
1. A steel pressure vessel is subjected to an internal pressure of 2.0 MPa. Its
internal diameter is 1.2 m and wall thickness is 12 mm. Assuming a thin-
wall cylinder, what is the approximate circumferential stress?
A. 50 MPa
B. 75 MPa
C. 100 MPa
D. 150 MPa
Answer: 100 MPa
Rationale: For a thin cylindrical vessel, hoop stress is ς = pD/(2t). Substituting
2.0 MPa × 1200 mm/(2 × 12 mm) gives 100 MPa.
2. A centrifugal pump increases the pressure head of water by 30 m while
operating at 0.20 m³/s with an overall efficiency of 78%. What shaft power
is approximately required?
,A. 58 kW
B. 65 kW
C. 75 kW
D. 92 kW
Answer: 75 kW
Rationale: Hydraulic power is ρgQH = 1000(9.81)(0.20)(30) = 58.9 kW. Dividing
by 0.78 gives approximately 75.5 kW.
3. For steady, incompressible flow through a horizontal pipe with negligible
losses, which condition follows directly from Bernoulli's equation?
A. Static pressure is always constant
B. Velocity is always constant
C. Total mechanical energy per unit weight remains constant
D. Density decreases as velocity increases
Answer: Total mechanical energy per unit weight remains constant
Rationale: Bernoulli's equation states that pressure head, velocity head, and
elevation head sum to a constant when pumps, turbines, and losses are absent.
4. A refrigeration system operates with an evaporator temperature of −10°C
and condenser temperature of 35°C. For an ideal reversed Carnot
refrigerator, the COP is approximately:
A. 2.5
B. 4.0
C. 5.84
D. 7.1
Answer: 5.84
Rationale: COP = Te/(Tc − Te), using absolute temperatures. Te = 263.15 K and Tc
= 308.15 K, giving 263.15/45 ≈ 5.85.
, 5. A beam is subjected to a bending moment of 12 kN·m. Its section modulus
is 600 cm³. What is the maximum bending stress?
A. 10 MPa
B. 20 MPa
C. 30 MPa
D. 40 MPa
Answer: 20 MPa
Rationale: Bending stress is ς = M/S. Converting 12 kN·m to 12 × 10⁶ N·mm and
600 cm³ to 600,000 mm³ gives 20 N/mm², or 20 MPa.
6. In a heat exchanger, the hot fluid enters at 180°C and leaves at 100°C. The
cold fluid enters at 30°C and leaves at 80°C. What is the log-mean
temperature difference for counterflow operation?
A. 75°C
B. 82°C
C. 85°C
D. 95°C
Answer: 85°C
Rationale: The terminal differences are 180 − 80 = 100°C and 100 − 30 = 70°C.
LMTD = (100 − 70)/ln(100/70) ≈ 84.7°C.
7. A simply supported beam carries a concentrated load at its midpoint. If the
span is doubled while the load remains unchanged, the maximum bending
moment becomes:
A. Half as large
B. Unchanged
C. Twice as large
D. Four times as large
Answer: Twice as large
, Rationale: For a central point load, Mmax = PL/4. Therefore, doubling L doubles
the maximum moment.
8. Which failure theory is generally most appropriate for predicting yielding of
a ductile metal under a multiaxial stress state?
A. Maximum principal stress theory
B. Maximum principal strain theory
C. Maximum distortion-energy theory
D. Coulomb-Mohr brittle theory
Answer: Maximum distortion-energy theory
Rationale: The von Mises distortion-energy criterion is widely used for ductile
metals because yielding correlates well with distortional strain energy.
9. A shaft transmits 100 kW at 1,500 rpm. What is the approximate torque?
A. 318 N·m
B. 637 N·m
C. 955 N·m
D. 1,273 N·m
Answer: 637 N·m
Rationale: T = P/ω. With ω = 2π(1500)/60 = 157.1 rad/s, T = 100,000/157.1 ≈ 637
N·m.
10.Increasing the diameter of a solid circular shaft while keeping torque
constant primarily reduces torsional shear stress because:
A. Polar moment decreases
B. Polar moment increases strongly with diameter
C. Modulus of elasticity increases
D. Poisson's ratio decreases
Answer: Polar moment increases strongly with diameter
