Pressure in a fluid: A cubical box, 5.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 594 Pa and the gauge pressure on the bottom surface is 1133 Pa. What is the density of the fluid? A) 1000 kg/m³ B) 1100 kg/m³ C) 1220 kg/m³ D) 2340 kg/m³ E) 12,000 kg/m³

Question

Quizplus · Accepted Answer

The difference in gauge pressure between the top and bottom surfaces is due to the weight of the fluid column above the box. The pressure difference is 1133 Pa - 594 Pa = 539 Pa. The height of the box is 0.05 m. Using the formula for pressure difference, ΔP = ρgh, where ρ is the fluid density, g is the acceleration due to gravity (9.81 m/s²), and h is the height, we solve for ρ: ρ = ΔP / (gh) = 539 / (9.81 * 0.05) ≈ 1100 kg/m³.

Pressure in a Fluid: a Cubical Box, 5