Phy 102: Fundamentals of Physics II Chapter 13: Liquids Lecture Notes

Archimedes (287-212 BC) Possibly the greatest mathematician in history Studied circles and geometric shapes Invented an early form of calculus Discovered the Principle of Buoyancy (now called Archimedes’ Principle) Discovered the Principle of Leverage (Torque) and built several machines based on it. Famous quote: “Give me a point of support and I will move the Earth” The inventions of Archimedes’ single-handedly held off the advances of the Roman fleets for several years. When Syracuse was finally overtaken, Archimedes was busy working on geometry. When confronted by a Roman soldier, Archimedes was storied to have said, “not now, I am busy with my circles”. The Roman soldier promptly beheaded Archimedes.

Liquids Substance with a definite volume but indefinite shape Take the shape of their container but always retain their volume Liquids are fluids (they flow) Liquids are difficult to compress

Pressure Force per unit area To calculate pressure: Pressure = force/area Units are SI: N/m2 (pascals or P) Other: lb/in2(psi), lb/ft2, dynes/cm2, kilopascals F = P x A

Liquid Pressure = weight density x depth Pressure in a Liquid When submerged in a liquid, an object experiences liquid pressure due to the weight of the fluid directly above it Liquid Pressure (P) is equal to weight density (r) times depth (H) or Liquid Pressure = weight density x depth or P = r x H The deeper into the liquid you are, the greater the pressure (& force) the liquid exerts on you! H Weight density is weight/volume (or mg/V in N/m2)

Buoyancy & Archimedes’ Principle An object submerged in a liquid experiences a buoyant force The buoyant force acting on an object is equal to the weight of the fluid it displaces The denser the liquid the greater buoyant force it will exert on an object (for the same volume displaced) Floatation occurs when an object displaces the weight of fluid equal to its own weight Buoyant force weight Float Rise Sink Buoyant force weight Buoyant force weight

Floatation In accordance with Archimedes’ Principle: when the buoyant force is less than the weight of liquid displaced, object will sink when the buoyant force is greater than the weight of liquid displaced, object will rise when the buoyant force is the same as the weight of liquid displaced, object will suspend Weight of a liquid/object is proportional to its weight density & volume: Weight = weight density x volume Consequences: It will float on the surface if its density is less than the density of the fluid It will sink to the bottom if its density is more than the density of the fluid It will neither float nor sink if its density is the same as the density of the fluid

Pascal’s Principle A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid The basis for hydraulic machines Discuss work & machines Machines perform work & often multiply force

Surface Tension The tendency of the surface of a liquid to contract in area and behave like a stretched elastic membrane Surface tension is caused by molecular attractions beneath the surface of the liquid Surface tension causes the area of the liquid to be forced into the shape with least surface area: Raindrops are spherical The surface of a pond is flat (when there is no wind or flow to disturb it) The surface of a slightly overfilled glass of beer is slightly circular (near edge) and flat in the center

Examples of Surface Tension

Capillarity Adhesion: the attraction of unlike substances Example: glass and water Cohesion: the attraction of like substances due to molecular “stickiness” The cause of surface tension!