A large open tank is filled with fresh water to a uniform depth of 4.0 m. Three small holes are drilled at the same horizontal distance from the tank wall, so the effect of curvature of the wall can be ignored.
• Point P is 0.50 m below the water surface.
• Point Q is 2.0 m below the water surface.
• Point R is 4.0 m below the water surface (just above the bottom).
Assume the density of fresh water is 1.00×103kgm−3 and atmospheric pressure is the same at all exposed surfaces of the water.
(a) Rank the magnitudes of the absolute pressures at points P, Q, and R from greatest to least. If any are equal, state so explicitly.
(b) Provide a qualitative explanation for your ranking that refers to appropriate physical principles. Your explanation should include a discussion of how depth influences the pressure in a stationary incompressible fluid and why atmospheric pressure does or does not affect the ranking.
(c) The tank is now emptied and refilled to the same 4.0 m depth with oil of density 0.80×103kgm−3. Rank the gauge (fluid only) pressures at points that are again 0.50 m, 2.0 m, and 4.0 m below the oil surface. Explain how and why, if at all, this ranking differs from the ranking you found for water.