Fluids

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CHAPTER-14

• Fluids

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Ch 14-2, 3 Fluid Density and Pressure

• Fluid a substance that can flow
• Density ? of a fluid having a mass m and a volume
  V is given by ? m/V (uniform density)
• Density Units kg/m3
• Density of a compressible material such as gases
  depends upon the pressure P, where P is given by
• PF/A

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Ch 14-4 Fluid at Rest

• Hydrostatic Pressure
• (Pressure due to fluid at rest)
• The pressure at a point in a fluid in static
  equilibrium depends upon the depth of that point
  but not on any horizontal dimension of the fluid
  or container.
• Consider the imaginary water cylinder with
  horizontal base , with weight mg, enclosed
  between two depths y1 and y2.The cylinder has a
  volume V, face area A and height y1-y2, Water is
  in static equilibrium. Three forces F1, F2 and mg
  acts such that F2-F1-mg0 F2F1mg
• But p1F1/A p2F2/A m?Vg ?A(y1-y2)
• p2p1?g(y1-y2)

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Ch 14-4 Absolute Pressure and Gauge Pressure

• p2p1?g(y1-y2)
• If p2p p1p0 and y10 y2-h
• pp0?gh
• ?p p-p0?gh
• P is Absolute pressure
• ?p is Gauge pressure

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Ch 14-4 Absolute Pressure and Gauge Pressure
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Ch 14-6 Pascals Principle

• Pascals Principle A change in the pressure
  applied to a an enclosed incompressible fluid is
  transmitted undiminished to every portion of the
  fluid and to the walls of its container.
• A change in pressure ?P at input of hydraulic
  lever is converted to change in pressure ?P at
  output of hydraulic lever
• ?PFi/AiFo/Ao Fo Ao(Fi/Ai),Fo?Fi
• If input piston moves through a distance di
  and then output piston moves through a smaller
  distance do because VAidiAodo
• With a hydraulic lever, a given force applied
  over a given distance can be transformed to a
  greater force applied over a smaller distance

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Ch 14-7 Archimedes Principle

• Archimedes Principle
• Buoyant Force FB Upward force on an fully or
  partially submerged object by the fluid
  surrounding the object , magnitude of the force
  FB equal to weight of the displaced fluid mfg
  ?Vfg. Vf is volume of the displaced fluid.
• Floating Object When an object floats in a
  fluid, the magnitude of FB is equal to magnitude
  of the gravitational force Fg (mg). Then
• FB Fg mg mfg ?Vfg
• A floating object displaces its own weight of
  fluid
• For objects submerged in a fluid, its Apparent
  weight Wapp is less than true weight W
• Apparent weight Wapp W-FB

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Ch 14-8 Ideal Fluid in Motion

• Four assumptions related to ideal flow
• Steady flow the velocity of the moving fluid at
  any fixed point does not change with time
• Incompressible Flow Fluid has constant density
• Nonviscous flow an object can move through the
  fluid at constant speed- no resistive force
  within the fluid to moving objects through it
• Irrotational flow Objects moving through the
  fluid do not rotate about an axis through its
  center of mass

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Ch 14-9 Equation of Continuity

• Equation of Continuity A relation between the
  speed v of an ideal fluid flowing through a tube
  of cross sectional area A in steady flow state
• Since fluid is incompressible, equal volume of
  fluid enters and leaves the tube in equal time
• Volume ?V flowing through a tube in time ?t is
• ?V A?x Av?t
• Then ?V A1v1?t A2v2?t
• A1v1A2v2
• RVA1v1constant (Volume flow rate)
• Rm?A1v1constant (Mass flow rate)

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Ch 14-10 Bernoullis Equation

• Bernoullis Equation
• If y1,v1 and p1 are the elevation, speed and
  pressure of the fluid entering the tube and and
  y2,v2 and p2 are the elevation, speed and
  pressure of the fluid leaving the tube
• Then
• p1 (?v12)/2?gy1p2 (?v22)/2?gy2
• or
• p (?v2)/2?gy constant