BTEC Level 4 Unit 4003 Engineering Science I Assignment 2, 2026

Unit 4003 Assignment 2

Vocational Scenario

Congratulations! You have been employed by Universal Marine Solutions ltd. (UMS); a fictional company that designs and manufactures ship related structures, such as framing systems, hulls, and decks; and mechanical ships systems, such as propulsion systems, and cargo loading and unloading systems. Your job involves applying fundamental mechanical engineering principles for analysing various mechanical systems produced by UMS.

Task 1: Apply the fundamentals of mechanical engineering systems

AI use for Task 1: This task is completed in a controlled environment designed to exclude AI. Knowledge, understanding, and skills are demonstrated and assessed independently.

1. Your first task involves analysing one of the steel beams in a longitudinal framing system for a river ferry. The beam supports the engine room deck, and spans the distance between the fore end of the stern tube and the fore end of the engine.

Figure 1. Propeller shaft

a) Figure 1 illustrates the propeller shaft, which spans the distance between the aft end of the stern tube, and the fore end bearing (i.e., the bearing on the right). The propeller shaft is suspended above the deck by two bearings; you may assume the bearings act as pinned supports at 1m and 4m from the aft end of the propeller shaft, and that the whole system is in equilibrium. The stern tube does not support the propeller shaft. The propeller hangs from the aft end of the propeller shaft, and has a mass equal to your age in years in kg. For example, if are 32 years old, the propeller is 32kg. The propeller shaft is 200kg. Produce a free body diagram of the propeller shaft, including all the relevant forces, and calculate the reaction forces acting upwards through the bearings. Clearly state your age in years, and justify your chosen methods by showing each step and providing an explanation if necessary.

Figure 2. Engine room beam

b) Figure 2 illustrates the rest of the engine room, depicting the machinery resting on top of the engine room deck beam. Each bearing is 60kg; the gearbox exerts 3430N/m, and the engine exerts 3560N/m on the beam. Assume the propeller shaft is not fixed to the gearbox. The beam itself is 300kg, and the whole system is in equilibrium. Produce a free body diagram of the engine room deck beam, including all the relevant forces, and calculate the reaction forces acting upwards through the two supports underneath the beam. Justify your chosen methods by showing each step and providing an explanation if necessary.

(Tip: remember Newtons first law of motion, every action has an equal and opposite reaction).

2. Your next task involves analysing a derrick used to move TEU containers on and off of a container ship, as depicted in figure 3. The process of moving cargo involves raising a container to a height above the weather deck, in pace with the process of filling the ballast tanks; keeping the ship balanced while the ships centre of buoyancy changes.

Figure 3. Derrick

a) The container illustrated in figure 3 begins at rest, but accelerates to 1.5m/s by the time it reaches the height of the weather deck, then decelerates to 0m/s after reaching 6m above the weather deck. The mass of the container is equal to (your age in years x 100)kg. For example, if you are 32 years old, the container is 3200kg. Produce two fully annotated kinematic free body diagrams that include all unknown values related to the forces at play; the first depicting the acceleration of the container towards the weather deck, and the second depicting the deceleration of the container up to 6m above the weather deck.

b) Determine the force required to act through the derricks cable to raise the container to the height of the weather deck, then the force required to raise the container from the height of the weather deck to the maximum possible height. Justify your chosen methods by showing each step and providing an explanation if necessary.

3. The distance between the top of the weather deck, and the waterline is called the freeboard, and the distance from the waterline to the bottom of the keel is called the draft. It is important to be aware the draft of a ship at lightweight (when a ship is completely unloaded), to determine the maximum safe deadweight of the ship (the total mass of the ship’s cargo, ballast water, fuel, and crew and passengers).

Figure 4. Floating ship hull

a) Determine the draft of the ship hull illustrated in figure 4, given that it is floating in seawater. You may assume the hull is a rectangular cuboid. Justify your chosen method by showing each step and providing an explanation if necessary.

b) Calculate the maximum deadweight of the ship, given that the minimum permitted freeboard distance for this ship is 1.4m. Justify your chosen method by showing each step and providing an explanation if necessary.

4. Seawater is pumped into a ship for multiple reasons, among which is to exchange heat with the engine coolant fluid in a heat exchanger. Coolant fluid is first heated by the engine through a pipe that expands in size to accommodate smaller tubes filled with seawater; exchanging thermal energy with the coolant, forming a heat exchanger. Figure 5 illustrates the flow of engine coolant entering a heat exchanger.

Figure 5. Heat exchanger

a) Determine the volumetric flow rate of the coolant through the heat exchanger necessary to achieve a change in temperature of 33^o Assume the volume of the sea water pipes are negligible. Q = Heat removed by sea water = 25MW ρ = Density of the coolant = 975 kg/m³ V = Volumetric flow rate cp = Specific heat capacity of the coolant = 4180 J/kg·K ΔT = Change in temperature Justify your chosen method by showing each step and providing an explanation if necessary.

b) A pump is used to control the pressure of the coolant passing through the engine. Given that the pressure of the coolant passing through the heat exchanger needs to be 1kPa to achieve your calculated value of volumetric flowrate, calculate what the pressure of the coolant should be before it enters the heat exchanger to account for the pressure drop. Justify your chosen method by showing each step and providing an explanation if necessary.

5. UMS has built a prototype of a new marine diesel engine, and you need to fully analyse the thermodynamic processes occurring in one of the cylinders. The properties of air inside each cylinder changes four times via a cycle of four thermodynamic processes:

State 1 to 2: Isentropic compression (i.e., the cylinder compresses the air)

State 2 to 3: Isobaric heating (i.e., ignition)

State 3 to 4: Isentropic expansion (i.e., the power stroke of the engine)

State 4 to 1: Isochoric cooling (i.e., exhaustion of hot air) The following properties of the air in the cylinder are known:

P₁ = 100kPa (i.e., pressure of the air at state 1).

T₁ = 300K

P₂ = 500kPA T₃ = 1200K

You may assume the air in the cylinder is an ideal gas with the following specific heats:

c_p = 1005 Jkg^-1K^-1 c_v = 718 Jkg^-1K^-1

a) Calculate the ratio of specific heats. Justify your chosen method by showing each step and providing an explanation if necessary.

b) Calculate the values of pressure and temperature of each of the four states, and present the determined values in a table. Justify your chosen methods by showing each step and providing an explanation if necessary.

c) If 60g of air is drawn into the engine cylinder, determine:

i. How much work is done during the isobaric heating process.

ii. How much heat is transferred during the isochoric cooling process.

Justify your chosen methods by showing each step and providing an explanation if necessary.

Learning Outcomes and Assessment Criteria

The tables below reproduce the Pearson criteria covered by this assignment. Use them to check the evidence across your whole submission.

LO2: Apply the fundamentals of mechanical engineering systems

Answer

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