A container weighs 450 lb when filled with 4 ft3 of fluid. If the empty container weighs 50 lb, determine the specific weight, mass density and specific gravity of this fluid.

112.5 lb/ft³

405.93 kg/m³

0.406

Explanation:

given that

Weight of the container, w(c) = 450 lb

Volume of fluid, v(f) = 4 ft³

Weight of empty container, w(e) = 50 lb

Specific weight is said to be the weight per unit volume. Thus, the specific weight of this fluid is

w(s) = 450 / 4

w(s) = 112.5 lb/ft³

Mass density is the ratio of the mass of the fluid, with respect to the volume.

ρ = m/v

Since the question gives us the mass in weight, we'd have to convert it to mass from weight.

mass = weight / acceleration due to gravity

mass = 450 / 9.81

mass = 45.87 kg

Also, since the mass is going to be in kg, the volume also has to be in m³, thus needing a conversion.

4 ft³ = 0.113 m³

Mass density = 45.87 / 0.113

Mass density = 405.93 kg/m³

Specific gravity of the fluid is simply given as mass density / 1000. Therefore,

g(s) = 405.93 / 1000

g(s) = 0.406

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