A flask with height h and base area A is filled with water. If the hydrostatic pressure is 2 atm halfway between the base and the top, what is the hydrostatic pressure at the base of the flask?

Question

A flask with height h and base area A is filled with water.  If the hydrostatic pressure is 2 atm halfway between the base and the top, what is the hydrostatic pressure at the base of the flask?

Quizplus · Accepted Answer

11ecba2d_1332_e5ab_a3bf_bb60e8554490_MD0008_00 Hydrostatic pressure describes the pressure fluid molecules in a static column of fluid exert on each other and their surroundings. In contrast to osmotic pressure (Π), which causes fluid to migrate from regions of lower Π to regions of higher Π, hydrostatic pressure P causes fluid to move away from areas of higher P toward areas of lower P. Hydrostatic pressure results from the weight of the fluid above a point within the fluid column. This weight is determined by the density of the fluid (ρ), the acceleration gravity (g = 10 m/s²), and the height (h) of fluid above the point: 11ecba2d_1332_e5ac_a3bf_adf8cd6bbf6c_MD0008_00 As a result, container shape does not influence the hydrostatic pressure in a column of a noncompressible fluid with constant density. In this question, a flask with variable cross-sectional area is half filled with water. Because the water is not flowing, it forms a fluid column that generates hydrostatic pressure. The hydrostatic pressure at half the depth of the total flask height is 2 atm, which is twice the atmospheric pressure experienced by objects on Earth's surface at sea level: 11ecba2d_1332_e5ad_a3bf_b1f51bfff8a2_MD0008_00 Therefore, the hydrostatic pressure experienced at the bottom of the flask is: 11ecba2d_1332_e5ae_a3bf_73b98b53f72d_MD0008_00 Converting the units from atmospheres (atm) to millimeters of mercury (mm Hg), which is a unit derived from the height of a mercury barometer at atmospheric pressure, gives: 11ecba2d_1333_0cbf_a3bf_8566ca0be211_MD0008_00 Therefore, the pressure at the bottom of the flask is about 3,000 mm Hg, regardless of the flask widening at the bottom (Choice B). Educational objective: Hydrostatic pressure describes the pressure caused by the weight of static fluid molecules within a column of fluid. The magnitude of hydrostatic pressure depends on the density of the fluid, the acceleration of gravity, and the height of the fluid; it is unrelated to container shape. Atmospheric pressure is 760 mm Hg at sea level.

A Flask with Height H and Base Area a Is