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Difficulty: MediumProperties of Fluids

A marine engineer is filling a sealed buoyancy tank with a specialized flotation fluid. The system requires a fluid with a specific gravity of 0.850.85 to provide the correct lift. If the internal volume of the tank is 0.4 m30.4 \text{ m}^3, what must the total mass of the fluid be? (Assume the density of water is 1000 kg/m31000 \text{ kg/m}^3)

Answer: 340 kg

Answer

The correct mass is 340 kg340 \text{ kg}.
The correct answer is found by first converting the unitless specific gravity into an actual density by multiplying it by the density of water (0.85×1000=850 kg/m30.85 \times 1000 = 850 \text{ kg/m}^3). The total mass is then calculated by multiplying this density by the given volume (850×0.4=340 kg850 \times 0.4 = 340 \text{ kg}).

Step-by-Step Solution

1
Calculate the density of the fluid using its specific gravity.
Density = 850 kg/m3850 \text{ kg/m}^3
Specific gravity is defined as the ratio of a fluid's density to the density of water (1000 kg/m31000 \text{ kg/m}^3). Therefore, density equals 0.85×10000.85 \times 1000.
2
Calculate the mass of the fluid using its density and volume.
Mass = 340 kg340 \text{ kg}
Mass is the product of density and volume. 850 kg/m3×0.4 m3=340 kg850 \text{ kg/m}^3 \times 0.4 \text{ m}^3 = 340 \text{ kg}.

Key Concept

The relationship between specific gravity, density, and volume to determine the mass of a fluid.
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Topics

Properties of Fluids

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