Chapter 9 Solids, Liquids, & Gases The Barometer: The atmospheric pressure is related to the height of fluid in the tube by the relation .   Gauge Pressure: Absolute pressure (P) is the sum of the gauge and atmospheric pressure. (5)   Pascal's Principle: An external pressure applied to a fluid confined within a closed container is transmitted undiminished throughout the entire fluid.   Hydraulic Machines: The force divided by the area of the piston determines the pressure. Different piston areas and forces produce the same pressure. (6) If you look at the change in height: (7)   Example 10 In a car lift used in a service station, compressed air exerts a force on a small piston that has a circular cross section and a radius of 5.00 cm. This pressure is transmitted by a liquid to a piston that has a radius of 15.0 cm. What force must the compressed air exert to lift a car weighing 13300 N? What air pressure produces this force?   Solution:   Buoyant Force:   Archimedes's Principle: Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object. (8)     Example 11 Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold. Legend has it that he solved this problem by weighing the crown first in air and then in water as shown. Suppose the scale read 7.84 N in air and 6.86 N in water. What should Archimedes have told the king?   Solution: First find the bouyant force: Then find the volume of the crown: Then find the density of the crown: Compare to the density of gold (): The denisty is much less therefore either hollow or not made of pure gold.   Example 12 A raft is constructed of wood having a density of . Its surface area is , and its volume is . When the raft is placed in fresh water of density , to what depth does the raft sink in the water?   Solution: The buoyant force must equal the weight of the raft. Then find the weight of the raft: Then solve for the height (h) and substitute the values:   On to Fluid Dynamics