Buoyancy, Density and pressure recap

Density
1. ρ = m/V
  1. Units
    1. 1000 kg/m3 = 1000 g/l = 1 g/cm3
    2. SI unites = kilogram per meter cubed
      1. kg/m3
    3. Gaussian unit = gram per cubic centimeter
      1. equivalent to a gram per milliliter
        1000 kg/m3 = 1 g/cm3 = 1g/ml
  2. m = mass. V = volume
2. http://physics.info/density/ for selected densities
3. The 'compactedness' of an object
  1. Materials have density It has no direction. Mass in a continuous system
4. Specific gravity
  1. Unitless
  2. ratio of the density of a substance to the density of a standard substance.
    1. standard substance
      1. Water
        density of liquid water under typical conditions on earth is approximately 1000 kg/m3
        Soilds
        Liquids
        Relative density
        The ratio of substance to the density of the water at 4C
        No units (because it is a ratio
      2. Gasses
        Air
        density of air at room temperature near the surface of the earth is approximately 1.2 kg/m3.
5. To make something less dense you need to make the mass smaller or the volume bigger
Pressure
1. P = F / A
  1. The force exerted per unit area
  2. kgm/s2 / m2 = kilograms per meter per second2
  3. kg / ms2
  4. Units
    1. pascal (Pa)
      1. 1 atm = 1.013 x 10^5 Pa
        Patm = atmospheric pressure
    2. N / m2 = Newtons per m2
    3. 1 bar = 10^5 Pa
2. http://physics.info/pressure/ for selected pressures including blood pressure etc
3. various types
  1. Gauge pressure
    1. measured relative to atmospheric pressure. 0 means there is no pressure inside the gauge compared to the atmospheric pressure on the outside
    2. Negative gauge pressure is also called vacuum pressure
    3. Measured using a manometer
      1. Pressure is dependent on depth
        http://www.efunda.com/formulae/fluids/manometer.cfm - Monometer pressure
        p- p(atm) / g x density x height
  2. Absolute pressure
    1. Pressure in relative to a perfect vaccum
      1. Equal to gauge pressure +1 atmosperic pressure
    2. Measured using a barometer
  3. Differential pressure
    1. The difference in pressure of 2 points
4. Pascals principle
  1. Most often applied to incompressible fluids
  2. http://www.grc.nasa.gov/WWW/k-12/WindTunnel/Activities/Pascals_principle.html - pascals principle and hydrolics
  3. any change of pressure of a contained liquid is distributed evenly
  4. Hydrstatic pressure
  5. Blaise Pascal 1623 - 1662
5. Pressure is the ratio of force times area
  1. Continuous system
Density and buoyancy http://www.tclauset.org/20_ESbk/ch05.pdf
Buoyancy
1. Archimedes (287 - 212 BC)
  1. Father of Forensics
  2. Archimedes Principle
    1. The weight of fluid displaced in a body of water is equal to the buoyant force on an immersed object
      1. When an object is partially or toatllly emersed in fluid it experienes an upthrust that equal to weight of fluid displaced
        Upthrust (buoyancy) F(b)
        Force acting upward that reduces the weight of the object underwater
        Apparent weight : measured when immersed in fluid
        bouyant force is equal to the apparant weight loss
        Effect on object in fluid
        F(b) > W
        object will rise
        F(b) = W
        Object will float
        Weight of fluid displaced = weight of the object
        F(b) < W
        Object will sink
        Volume of liquid displaced = weight of object
    2. EXAMPLES and applications
      1. Hydrometer
        measures relative density of liquids
        Tube containing lead shots in a bulb at the end (to weigh it down) enough for it to float vertically
        less dense
        larger volume of water must re displaced for bouyant force to equalize
        more hydrometer is submerged
        more dense
        smaller volume of water must be displaced for buoyant forces to equalize
        less hydrometer submerged
      2. Submarine
        Sinking
        Ballast tanks fill with water so that the weight of the submarine is larger than the volume of water displaced
        rising
        ballast tank fills with air to make the weight of the submarine lsmaller than the volume of water displaced
      3. Hot air balloon
      4. Ship
        A ship will float because it has a large buoyant force acting upon it despite being crafted of metal (which has a larger density than water. The shape is hollow so that the overall density will be less than the density of the fluid it is in
        Immersion variation
        Effect of temprature on object submersion
        warm water is more buoyant than cold is that its molecules have more energy and are moving around more. This makes warm water less dense and it will rise above denser, colder water.
        Effect of liquid on submersion
        Salt water has a higher density
        Floating in the dead sea
        ship may sink further if it enters freshwater and is overloaded
        plimsoll line
        indicates maximum weight
  3. Had a Eureka moment when he observed that the level of the water in his bath increased when he got in and realized he felt lighter and used it to discover the quality of the crown of King Hiero II of Syracuse
    1. Density of gold, 19.32 g/cm3 Density of silver 10.5 g/cm3
    2. if a certain weight of silver had been substituted for the same weight of gold, the crown would occupy a larger space than an identical one of pure gold.
  4. http://www.physics.arizona.edu/physics/gdresources/documents/13_Archimedes.pdf

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