Practice city guilds model questions vol1 engineering 2021 Past Questions

Question 1 View Details

A centrifugal pump has a head‑flow characteristic given by $H = 70 - 0.02 Q^{2}$ where $H$ is in metres and $Q$ is the flow rate in litres per second. The pump is driven by a 5 kW electric motor whose efficiency is $85\%$. The pump efficiency is assumed to be $70\%$. Determine the maximum flow rate that can be delivered without exceeding the motor's rated power. Then state whether a required flow of 150 L min⁻¹ at a total head of 30 m can be achieved, and identify which component (pump or motor) limits the system.

Correct A. Maximum flow ≈ 4.35 L s⁻¹ (≈261 L min⁻¹); the required 150 L min⁻¹ is achievable, and the motor power is the limiting factor.

B. Maximum flow ≈ 3.80 L s⁻¹ (≈228 L min⁻¹); the required 150 L min⁻¹ is achievable, and the pump efficiency is the limiting factor.

C. Maximum flow ≈ 5.10 L s⁻¹ (≈306 L min⁻¹); the required 150 L min⁻¹ cannot be achieved, and the motor power is the limiting factor.

D. Maximum flow ≈ 4.35 L s⁻¹ (≈261 L min⁻¹); the required 150 L min⁻¹ is achievable, and the pump is the limiting component.

Correct Answer: A

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Question 2 View Details

A steel column has a rectangular cross‑section 100 mm wide and 50 mm deep. If an axial load of 12 kN is applied, calculate the average normal stress in the column. Express your answer in megapascal (MPa).

A. 2.0 MPa

B. 1.8 MPa

C. 3.0 MPa

Correct D. 2.4 MPa

Correct Answer: D

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Question 3 View Details

A gear train consists of four gears. Gear A (20 teeth) drives gear B (40 teeth) which is mounted on the same shaft as gear C (30 teeth). Gear C drives gear D (60 teeth). The input shaft (gear A) rotates at 1500 rpm and the input torque is 5 Nm. Assuming the overall mechanical efficiency of the train is 95 %, determine the output speed of gear D and the torque it delivers.

A. 300 rpm and 20 Nm

B. 750 rpm and 9.5 Nm

Correct C. 375 rpm and 19 Nm

D. 500 rpm and 15 Nm

Correct Answer: C

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Question 4 View Details

A piece of equipment has an exponential time‑to‑failure distribution with a mean time between failures (MTBF) of 2000 h. A corrective failure requires 8 h of downtime and costs $\$1500$. A preventive maintenance action takes 2 h of downtime, costs $\$800$, and restores the equipment to "as‑good‑as‑new". Preventive maintenance is performed at regular intervals of $T$ hours. Determine the smallest preventive interval $T$ (in hours) that will keep the overall equipment availability at least 95 %. (Availability $A = 1 - \frac{\text{average downtime per hour}}{1}$.)

A. ≈30 h

B. ≈50 h

C. ≈60 h

Correct D. ≈44 h (or any longer interval)

Correct Answer: D

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Question 5 View Details

A unidirectional composite is made from fibres with modulus $E_f = 230$ GPa and density $\rho_f = 2.5$ g cm⁻³, and a matrix with modulus $E_m = 3.5$ GPa and density $\rho_m = 1.2$ g cm⁻³. Using the rule of mixtures for longitudinal modulus $E_c = V_f E_f + (1-V_f)E_m$, determine the fibre volume fraction $V_f$ required to obtain a composite modulus of 60 GPa. Then calculate the density of the resulting composite.

A. V_f ≈ 0.35 (35 %); density ≈ 1.66×10³ kg m⁻³

B. V_f ≈ 0.45 (45 %); density ≈ 1.80×10³ kg m⁻³

C. V_f ≈ 0.15 (15 %); density ≈ 1.38×10³ kg m⁻³

Correct D. V_f ≈ 0.25 (25 %); density ≈ 1.52×10³ kg m⁻³

Correct Answer: D

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Question 6 View Details

An AC supply of (230\ \text{V}\) RMS at (50\ \text{Hz}\) drives a series circuit consisting of a resistor (R\ (\Omega)\) and an ideal inductor (L\ (\text{H})\). The RMS current measured is (5\ \text{A}\) and the power factor is (0.8\) lagging. Determine the resistance (R\) (to one decimal place) and the inductance (L\) (to three decimal places).

Correct A. R = 36.8 Ω, L = 0.088 H

B. R = 30.5 Ω, L = 0.095 H

C. R = 40.0 Ω, L = 0.075 H

D. R = 36.8 Ω, L = 0.100 H

Correct Answer: A

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Question 7 View Details

An L‑shaped steel plate is formed by joining two rectangular sections as shown: Section A is 200 mm long and 100 mm high; Section B is 150 mm long and 80 mm high and is attached to the top of Section A, sharing the left edge. Assuming uniform thickness and material, determine the coordinates $(\bar{x},\ \bar{y})$ of the centroid of the composite shape measured from the outer corner O (the right‑angle corner of the L). Give your answers to two decimal places.

A. x̄ = 85.40 mm, ȳ = 90.12 mm

Correct B. x̄ = 90.63 mm, ȳ = 83.75 mm

C. x̄ = 95.20 mm, ȳ = 78.60 mm

D. x̄ = 90.63 mm, ȳ = 80.00 mm

Correct Answer: B

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Question 8 View Details

A mechanical drawing of a gear assembly is drawn at a scale of 1 : 25. In the drawing, the centre distance between two gears is measured as 48 mm. The pitch diameters of the gears are shown as 30 mm and 42 mm respectively, and the numbers of teeth are 20 and 28. Determine the actual centre distance (in mm), the actual pitch diameters of the two gears (in mm), and the common module of the gears (in mm).

A. Centre distance = 960 mm; pitch diameters = 600 mm and 840 mm; module = 30 mm

Correct B. Centre distance = 1200 mm; pitch diameters = 750 mm and 1050 mm; module = 37.5 mm

C. Centre distance = 1150 mm; pitch diameters = 720 mm and 1008 mm; module = 36 mm

D. Centre distance = 1300 mm; pitch diameters = 800 mm and 1120 mm; module = 40 mm

Correct Answer: B

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Question 9 View Details

Solve for (x\): $\frac{2}{x}+\frac{3}{x+1}=1$. State all real solutions, giving each to three decimal places.

Correct A. x = 4.449 or x = -0.449

B. x = 5.000 or x = -1.000

C. x = 2.449 or x = -2.449

D. x = 3.732 or x = -0.732

Correct Answer: A

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Question 10 View Details

A solid rectangular bar has dimensions (10\ \text{cm}\times5\ \text{cm}\times4\ \text{cm}\) and a mass of 540 g. Calculate its density and state whether the material is consistent with aluminium, whose typical density is (2.70\ \text{g/cm}^3\).

A. Density = 3.00 g\/cm³; not consistent with aluminium

B. Density = 2.70 g\/cm³; not consistent with aluminium

C. Density = 2.16 g\/cm³; not consistent with aluminium

Correct D. Density = 2.70 g/cm³; consistent with aluminium

Correct Answer: D

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Question 11 View Details

A line AB is inclined at $30^{\circ}$ to the horizontal plane. In the orthographic projection the front view is drawn at a scale of 1:2, and the projected length of AB on the front view measures $40$ mm. Determine the true length of AB in real size (to two decimal places).

A. 100.00 mm

Correct B. 92.38 mm

C. 76.45 mm

D. 84.00 mm

Correct Answer: B

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Question 12 View Details

For the function $f(x)=\frac{x^{2}-9}{x-3}$: (a) state the value of $x$ at which $f$ is undefined; (b) simplify $f(x)$ for all other values of $x$.

Correct A. Undefined at x = 3; simplified expression f(x) = x + 3 for x ≠ 3

B. Undefined at x = 3; simplified expression f(x) = (x^2 - 9)/(x - 3) for x ≠ 3

C. Undefined at x = 3; simplified expression f(x) = x - 3 for x ≠ 3

D. Undefined at x = 0; simplified expression f(x) = x + 3 for x ≠ 0

Correct Answer: A

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Question 13 View Details

A 1045 carbon‑steel component is to be hardened. The Ac3 temperature for a carbon steel can be approximated by $Ac3 = 910 - 203C$ (°C), where $C$ is the carbon fraction. For 1045 steel, $C = 0.45\%$. (a) Calculate the Ac3 temperature. (b) The austenitising temperature must be at least $30^{\circ}$C above Ac3. Determine the minimum austenitising temperature. (c) The austenitising holding time $t$ (minutes) is given by $t = 0.02 D^{1.5}$, where $D$ is the largest section thickness in mm. If the component's maximum thickness is $40$ mm, compute the required holding time (to one decimal place).

A. Ac3 ≈ 909°C; minimum austenitising temperature ≈ 945°C; holding time ≈ 5.1 min

B. Ac3 ≈ 909°C; minimum austenitising temperature ≈ 940°C; holding time ≈ 4.8 min

Correct C. Ac3 ≈ 909°C; minimum austenitising temperature ≈ 940°C; holding time ≈ 5.1 min

D. Ac3 ≈ 912°C; minimum austenitising temperature ≈ 942°C; holding time ≈ 5.1 min

Correct Answer: C

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Question 14 View Details

A stepped shaft is shown in a sectional drawing. The distance between two keyways is indicated as $30$ mm on the drawing, which is at a scale of 1:4. The shaft has a uniform taper of $2^{\circ}$ over a real length of $100$ mm. (a) Find the actual distance between the keyways. (b) Determine the change in diameter of the shaft over the 100‑mm length due to the taper (to one decimal place).

Correct A. Actual distance = 120 mm; diameter change ≈ 7.0 mm

B. Actual distance = 125 mm; diameter change ≈ 7.0 mm

C. Actual distance = 120 mm; diameter change ≈ 6.5 mm

D. Actual distance = 115 mm; diameter change ≈ 7.0 mm

Correct Answer: A

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Question 15 View Details

A bench grinder is equipped with a 125‑mm diameter wheel that rotates at 3500 rpm. Safety standards limit the peripheral speed of a grinding wheel to 20 m·s$^{-1}$. (a) Calculate the peripheral speed of the wheel in m·s$^{-1}$ (to one decimal place). (b) State whether the wheel complies with the safety limit.

A. 20.0 m·s⁻¹; complies with the safety limit

B. 19.5 m·s⁻¹; complies with the safety limit

Correct C. 22.9 m·s⁻¹; does not comply with the safety limit

D. 25.0 m·s⁻¹; does not comply with the safety limit

Correct Answer: C

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Question 16 View Details

A storage tank consists of a right circular cylinder surmounted by a right circular cone. The tank has a total height of $20$ m and a total internal volume of $800$ m³. The radius of both the cylinder and the cone is $5$ m. Determine, to two decimal places, the height (in metres) of the cylindrical portion of the tank.

Correct A. 5.28

B. 6.12

C. 7.45

D. 4.73

Correct Answer: A

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Question 17 View Details

A gear blank must have a final mass of 2 kg and a minimum yield strength of 200 MPa. Three manufacturing processes are available:\n\n- Casting: material waste 30 %, cost = ₦800 per kg, yield strength = 150 MPa.\n- Forging: material waste 10 %, cost = ₦1200 per kg, yield strength = 300 MPa.\n- Machining: material waste 5 %, cost = ₦1500 per kg, yield strength = 250 MPa.\n\nThe total production cost must not exceed ₦3000. Identify which process(es) satisfy all the requirements and state the total cost (rounded to the nearest naira) for each feasible process.

A. Casting, total cost = 2286

Correct B. Forging, total cost = 2667

C. Machining, total cost = 3158

D. Forging, total cost = 2800

Correct Answer: B

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Question 18 View Details

During a 1000‑hour production run three machines require preventive maintenance:\n\n- Machine A: one maintenance of 8 h after every 200 h of operation.\n- Machine B: two maintenances of 5 h each after every 250 h of operation.\n- Machine C: one maintenance of 6 h after every 300 h of operation.\n\nAt most two machines can be under maintenance at the same time, and any overlapping period reduces the effective downtime by 20 % of the overlapped duration (i.e., an overlapped hour counts as 0.8 h of downtime). Determine the minimal total effective downtime (in hours) for the plant over the 1000‑hour period.

A. 20

B. 26

Correct C. 22

D. 24

Correct Answer: C

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Question 19 View Details

A $120$ V supply feeds a circuit where resistor $R_{1}$ is in series with the parallel combination of $R_{2}$ and $R_{3}$. The total current drawn from the supply is $2$ A. It is known that $R_{2}=2R_{3}$ and that resistor $R_{3}$ dissipates $30$ W. Find the resistance values of $R_{1}, R_{2}, R_{3}$ in ohms, giving each answer to two decimal places.

A. R1=45.00 Ω, R2=30.00 Ω, R3=15.00 Ω

B. R1=50.00 Ω, R2=35.00 Ω, R3=17.50 Ω

Correct C. R1=48.75 Ω, R2=33.75 Ω, R3=16.88 Ω

D. R1=46.20 Ω, R2=31.40 Ω, R3=15.70 Ω

Correct Answer: C

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Question 20 View Details

A workshop risk assessment lists three hazards with the following annual probabilities and severity ratings (on a scale of 1-5):\n\n- Electric shock: probability = 0.02, severity = 5.\n- Fire: probability = 0.01, severity = 4.\n- Chemical spill: probability = 0.03, severity = 3.\n\nThe risk rating for a hazard is defined as probability × severity. The overall risk rating is the sum of the individual ratings. Safety policy requires the overall risk rating to be at most 0.15. If a mitigation measure can be applied to a hazard, its probability is reduced by half. Identify the minimal set of hazards that must be mitigated to meet the policy requirement.

A. Electric shock and fire

B. Fire and chemical spill

Correct C. Electric shock and chemical spill

D. Electric shock only

Correct Answer: C

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Question 21 View Details

A cantilever beam of rectangular cross‑section has a width of 50 mm and an unknown height $h$ (in mm). The beam is 1.2 m long and is fixed at one end. A vertical load of 5 kN is applied at the free end, producing a bending moment $M = P L$. The material is steel with a yield strength of 300 MPa and a factor of safety of 3. Determine the minimum integer value of $h$ (in mm) such that the combined normal stress $\sigma = \frac{P}{A} + \frac{M c}{I}$ does not exceed the allowable stress.

A. 78 mm

Correct B. 86 mm

C. 92 mm

D. 84 mm

Correct Answer: B

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Question 22 View Details

In an orthographic projection of a line segment, the projected lengths are 48 mm on the front view, 36 mm on the top view, and 24 mm on the side view. The drawing is made at a scale of 1 : 2. Determine the actual (true) length of the line segment in millimetres, correct to one decimal place.

A. 119.6 mm

B. 124.5 mm

C. 132.8 mm

Correct D. 129.2 mm

Correct Answer: D

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Question 23 View Details

A motor supplies a mechanical power of 5 kW at a speed of 1500 rpm. It drives a belt‑and‑pulley system where the driver pulley has a radius of 0.15 m and the driven pulley a radius of 0.45 m. The overall efficiency of the transmission is 85 %. Calculate (a) the torque available at the driven shaft (in N·m, to one decimal place) and (b) the rotational speed of the driven shaft (in rpm).

Correct A. 81.2 N·m, 500 rpm

B. 90.0 N·m, 500 rpm

C. 71.5 N·m, 500 rpm

D. 81.2 N·m, 450 rpm

Correct Answer: A

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Question 24 View Details

Water flows steadily through a horizontal pipe that narrows from a diameter of 200 mm to a diameter of 100 mm. The pressure upstream is 250 kPa and downstream is 200 kPa. Assuming incompressible, frictionless flow, determine the velocity of the water in the narrower section (in m s$^{-1}$, to one decimal place). Take the density of water as $1000\; \text{kg m}^{-3}$.

Correct A. 10.3 m/s

B. 12.0 m/s

C. 9.1 m/s

D. 7.5 m/s

Correct Answer: A

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Question 25 View Details

A steel rod 1.5 m long at $20^{\circ}\text{C}$ is fixed at one end. Its coefficient of linear expansion is $12\times10^{-6}\; \text{°C}^{-1}$. The free end is attached to a spring of stiffness $200\;\text{kN m}^{-1}$ that is initially pre‑loaded with a tensile force of 50 N. The rod is uniformly heated to $120^{\circ}\text{C}$. Find the total tensile force in the spring after heating (in newtons, nearest integer).

A. 440 N

B. 380 N

C. 470 N

Correct D. 410 N

Correct Answer: D

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