Question

The pound-mass (lbm) is a frequently employed unit of mass, equivalent to 0.454 kg. What is the density of water in pound-mass per cubic foot?

a) 62.4 lbm/ft³
b) 31.2 lbm/ft³
c) 15.6 lbm/ft³
d) 7.8 lbm/ft³
e) 3.9 lbm/ft³

Answer 1

The density of water is 62.4 lbm/ft³ after converting the metric density of water 1 g/cm³ to the English system using conversion factors 1 lbm = 0.454 kg and 1 ft³ = 30.48³ cm³.

Step-by-step explanation:

To find the density of water in pound-mass per cubic foot, we must start with the known density of water in metric units, which is 1 g/cm³ or equivalently, 1000 kg/m³. Converting the metric unit to the English system, we use the following conversion factors: 1 lbm = 0.454 kg, and there are 30.48 cm in a foot (therefore, there are 30.48³ cm³ in 1 ft³).

To convert the density of water to lbm/ft³:

1. First convert from grams to pounds: 1 g/cm³ is equivalent to (1/454) lbm/cm³, since there are 454 grams in a pound.
2. Then, convert cubic centimeters to cubic feet: Since there are (30.48³) cm³ in 1 ft³, we multiply (1/454) lbm/cm³ by 30.48³ cm³/ft³.
3. This results in (1/454) * 30.48³ lbm/ft³, which calculates to approximately 62.4 lbm/ft³.

Therefore, the correct answer is a) 62.4 lbm/ft³, which represents the density of water in pound-mass per cubic foot.