Question

A hemispherical container, 26 inches in diameter, is filled with a liquid at 20C and weighed. The liquid weight is found to be 1617 ounces.Required:a. What is the density of the fluid, in kg/m³? b. What fluid might this be? Assume standard gravity, g = 9.807 m/s².

Answer 1

The answer is below

Step-by-step explanation:

a) Density is the ratio mass of a substance to the total volume it occupies. The SI unit of density is kg/m³. The formula for density is:

Density = mass / volume

1 ounce = 0.0283495 kg

1 inch = 0.0254 m

The mass of liquid = 1617 ounces =
`1617\ ounce * 0.0283495(kg)/(ounce) =45.84\ kg`

diameter of container (d) = 26 inches =
`26\ inches*0.0254(m)/(inch)=0.66\ m`

Radius = d/2 = 0.66/2 = 0.33 m

The volume of a hemisphere = (2/3)πr³

Volume =
`(2)/(3)*\pi*(0.33)^3 =0.075\ m^3`

Density = mass / volume = 45.84 kg / 0.075 m³ = 609.04 kg/m³

b) Specific weight = density × acceleration due to gravity = 609.04 kg/m³ × 9.807 m/s² = 5972.83 N/m³