Answer:
The mass of the liquid = 10538 kg
Explanation:
The pressure in a liquid is
P = ρgh ......................... Equation 1
ρ = P/gh ...................... Equation 2
Where P = pressure, ρ = density, g = acceleration due to gravity, h = height.
Given: p = 1.3 atm, h = 2.0 m, g = 9.81 m/s²
If, 1 atm = 1.013×10⁵ N/m²
Then, P = 1.3×1.013×10⁵ N/m² = 1.3169×10⁵ N/m²
Substituting in equation 2,
ρ = 1.3169×10⁵/(9.81×2)
ρ = 1.3169×10⁵/19.62
ρ = 6712.03 kg/m³.
But Density,
ρ = m/v
m = ρ × v........................ Equation 3
Where m = mass of the liquid, v = volume of the liquid in the vat
v = πd²h/4, where d = diameter = 1.0 m, h = 2.0 m.
v = 3.14(1)²×2/4
v = 1.57 m³ also, ρ = 6712.03 kg/m³.
Substituting into equation 3
m = 1.57×6712.03
m = 10537.887 kg
m ≈ 10538 kg.
Thus the mass of the liquid = 10538 kg
