Columns of fluid Density Pressure variation with depth

Columns of fluid • • • Density Pressure variation with depth Pascal’s principle Absolute pressure vs. gauge pressure Columns of fluid

Density •

Densities of materials •

Density calculation •

Pressure •

Pressure variation with Depth • A ρgh. A h P = ρgh

Properties of pressure – Pressure pushes equally all directions. – Perpendicular to surface restraining it. – Equal at common depth

Example 1– swimming pool (w/o air pressure) •

Absolute and gauge pressure • Pa ρgh. A + Pa. A h P = ρgh + Pa

Not even half air pressure!

Example 2– swimming pool with air pressure •

Various units of pressure • We always use Pascals (Pa or k. Pa)

Pascal’s Principle • External pressure distributed uniformly at uniform depth. Pin • Pressure is same at common level. • Thus Fin/Ain = Fout/Aout (if A small F small). • Hydraulic lift. (make up example) Pout

Hydraulic Lift •

Columns of fluid • Ptop ρgh Pbottom

Column of water • Ptop ρgh Pbottom

Column of mercury • Ptop ρgh Pbottom

“Balancing” column of fluid Balancing water with straw 10 m Water Barometer Torricelli Mercury Barometer

Example – Problem 16 • Equate pressure along line a---b

Example – Problem 16 (cont) •