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

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 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 z y x g 0

6 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 z y x g 0

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