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

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

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

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

  2. 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

  3. Resolve stress into any three perpendicular directions • Stress tensor is a mathematical tool to handle a real three dimensional physics Fluid Element Fluid Body Stress Tensor Stress Analysis in Fluid Statics

  4. 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

  5. z g y 0 x 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

  6. g z 0 y x 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

  7. 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:

  8. 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

  9. Example of Basic Equation

  10. Example of Basic Equation

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