Phy 102: Fundamentals of Physics II

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

2. 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”

3. 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

4. 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

5. 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

6. Buoyant force Buoyant force Buoyant force weight weight weight 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 Float Rise Sink

7. 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

8. 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

9. 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

10. Examples of Surface Tension

11. 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!