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Fluids 7.1 - pressure density pascal depth buoyancy

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Fluids 7.1 - pressure density pascal depth buoyancy Powered By Docstoc
					Pressures in Fluid Systems
     Problem Types / Formulas
•   Density ρ = m/v
•   Pressure    P = F/A
•   Pressure at depth    P = ρhg
•   Buoyancy Force Fb= ρVg
•   Pascal’s     F1/A1 = F2/A2
         States of Matter
The Fluid State:
• gases or liquids
• no definite shape
• flow
The Solid State:
• definite shape
• support a force
               Density
• Density: the mass per unit volume of a
  substance
              ρ = m/V

• Units: kg/m3 or g/cm3
Pressure: A force distributed over an
  area
             P = F/A

   Pressure = force / area

Units = Pascal (N/m2)
          kPa or MPa
               Example
• A 500 kg box is resting on the ground.
  The side touching the ground is 1 m wide
  by 2 m long. What’s the pressure
  exerted by the box on the ground?
  P = F/A
    = ( 500 kg x 9.8 m/s2) / (2m x 1 m)
    = 4900 N / 2 m2
    = 2450 Pa
                 Example
A car weighs 8800 N. Each tire has a contact
patch (footprint) of 15 by 25 cm. What
pressure is exerted by the car on the ground?
     P = F/A
      Area = (0.15 m)∙(0.25 m)∙4 tires
         A= 0.15 m2
         P = 8800 N / 0.15 m2
           = 58,667 Pa
           = 5.9 x 104 Pa
         P = 59 kPa
       Gas or Air Pressure
• Kinetic Molecular Theory: as gas
  particles hit a surface, they apply a
  force over a tiny area.
• Lots of particles = detectable pressure.
• Gage pressure: reads zero at
  atmospheric
• Absolute pressure = 101.3 kPa + Gage
  Pressure
         Pascal’s Principle
• Applying pressure at any point to a fluid
  is transmitted immediately to the rest
  of the fluid.
• Examples:
      Toothpaste
      Squeeze a balloon
      Hydraulic jack
           Hydraulic Jack




Pressure is the same throughout the fluid
               F1 / A1 = F2 / A2
      Pressure Underwater
• Due to weight of column of water
• Use density to simplify to:
               P = ρgh
• Pressure = density x gravity x height or
  depth
• ρ = “rho” = density = mass per unit
  volume
               Buoyancy
• Given an object underwater
• Pressure is less at the top of the object
  than at the bottom.
• Result: net upward force on the object
  = Buoyant Force
           Buoyancy

P = ρgh1
                      Fnet = Fb

P = ρgh2
            Buoyant Force
• Buoyant Force Fb = ρVg
            Fb = (density x volume x gravity)
 Fb = weight of displaced fluid
      (Archimede’s)
• Compare weight of object to Fb to see if
  it sinks.
               Example
A block of aluminum has a volume of 0.5
 m3. If it is suspended by a string in
 water, which has a density of 1000
 kg/m3, and g=9.8 m/s2, what is the
 buoyant force acting on the block?
 Fb = ρVg
     = 1000 kg/m3 x 0.5 m3 x 9.8 m/s2
     = 4900 N

				
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posted:11/26/2011
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