Final answer:
The amount of ballast space (BS) in the loading of the ship's hold is calculated by subtracting the volume occupied by the cargo, determined using the stowage factor (SF), from the hold's total volume. With a stowage factor of 1.90 m³/ton and a total weight of 12,000 sacks at 90 kg each, the BS is found to be 448 m³.
Step-by-step explanation:
To calculate the amount of ballast space (BS) in the loading of a ship's hold, we first need to understand the concept of 'stowage factor' (SF), which is the measure of how many cubic meters of space one ton of cargo occupies. In this question, the stowage factor (SF) of the cargo is given as 1.90 m³/ton. The ship's hold has a volume of 2500 m³, and it is filled with 12,000 sacks, each weighing 90 kg.
Firstly, calculate the total mass of the sacks:
- Total mass = number of sacks × weight per sack
- Total mass = 12,000 sacks × 90 kg/sack
- Total mass = 1,080,000 kg
The total mass in tons (since 1 ton = 1000 kg):
- Total mass in tons = 1,080,000 kg / 1000 kg/ton
- Total mass in tons = 1080 tons
Next, to find out how much volume the cargo occupies, we apply the stowage factor:
- Total volume of cargo = Total mass in tons × SF
- Total volume of cargo = 1080 tons × 1.90 m³/ton
- Total volume of cargo = 2052 m³
Finally, subtract the total volume of cargo from the hold's volume to obtain the ballast space:
- Ballast space (BS) = Hold volume - Total volume of cargo
- Ballast space (BS) = 2500 m³ - 2052 m³
- Ballast space (BS) = 448 m³
Therefore, there is 448 m³ of ballast space in the loading.