MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 2

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MECH 221 FLUID MECHANICS(Fall 06/07)Tutorial 2
FLUID STATICS
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Two Basic Properties of Fluid Statics

• There is no shear stress in a fluid at rest
• The pressure/normal stress at a point in a fluid
  at rest is same in all direction
• Please refer to chapter two lecture notes or text
  book for above two properties proofs

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Stress Analysis in Fluid Statics
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Stress Analysis in Fluid Statics

• The two basic properties in fluid statics is
  converted into mathematical form by stress tensor
• Mathematical form is more accurate or rigorous
• Engineering is quantitative science
• Then we can use these two basic properties to
  calculate fluid pressure engineering problem
  accurately

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Basic Equation of Fluid Statics

• Fluid static pressure is due to the gravity (g)
  in our daily life
• For fluid at rest the pressure change pre unit
  distance (gradient) in the vertical direction at
  any point in a fluid depends ONLY on the specific
  weight ( ) of the fluid at that point

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Basic Equation of Fluid Statics

• This implies that there is no pressure change pre
  unit distance in the horizontal direction
  (perpendicular to body force g direction)
• If we set the z-axis of coordinate system in a
  same direction to the body force g, the sign of
  the left hand side equation will change from
  negative to positive

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Basic Equation of Fluid Statics

• For incompressible fluid (density is constant)
  and not a very large vertical distance variation,
  the basic equation is reduced to
• For many kind medium across z direction

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Basic Equation of Fluid Statics

• If we select the horizontal level across the two
  sides of U tube and the medium is same in the
  enclosed end section, then the two tubes pressure
  on the horizontal level are same

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Example of Basic Equation
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Example of Basic Equation