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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)

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phy 102 fundamentals of physics ii

Phy 102: Fundamentals of Physics II

Chapter 13: Liquids

Lecture Notes

archimedes 287 212 bc
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”

liquids
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
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
pressure in a liquid
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

buoyancy archimedes principle

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

floatation
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
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
surface tension
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
capillarity
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!