Water has a density of 1.94 slug/ft^3. What is this density expressed in SI units (kg/m^3)?

• A. 31.1 kg/m^3
• B. 99.4 kg/m^3
• C. 124.0 kg/m^3
• D. 99.0 kg/m^3

Answer: (B)

Verified step by step guidance

1. Identify the given density and its units: 1.94 slug/ft^3. Our goal is to convert this to kg/m^3, the SI unit for density.
2. Recall the conversion factors needed: 1 slug = 14.5939 kg, and 1 ft = 0.3048 m. Since the density is per cubic foot, we will cube the length conversion for volume.
3. Convert the density from slug/ft^3 to kg/m^3 using the formula: \(\text{density in kg/m}^3 = \text{density in slug/ft}^3 \times \frac{14.5939 \text{ kg}}{1 \text{ slug}} \times \left(\frac{1 \text{ ft}}{0.3048 \text{ m}}\right)^3\).
4. Calculate the volume conversion factor by cubing the length conversion: \(\left(\frac{1}{0.3048}\right)^3\) to convert ft^3 to m^3.
5. Multiply the given density by the mass conversion factor and the volume conversion factor to find the density in kg/m^3.