Comprehensive Lecture on Fluid Statics and Hydrostatic Principles

Comprehensive Lecture on Fluid Statics and Hydrostatic Principles

• 1.
  Lecture 4 Fluid Static
• 2.
  Introduction  Fluid statics(also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics.  The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium.
• 3.
   In fluidstatics, there is no relative motion between adjacent fluid layers.  Therefore, there is no shear stress in the fluid trying to deform it.  The only stress in fluid statics is normal stress  Normal stress is due to pressure  Variation of pressure is due only to the weight of the fluid → fluid statics is only relevant in presence of gravity fields.  Applications: Forces on submerged bodies, water dams and gates, liquid storage tanks, etc.
• 4.
  The force exertedby a static fluid on an object is always perpendicular to the surfaces of the object
• 5.
   Pressure isdefined as a normal force exerted by a fluid per unit area.  Units of pressure are N/m2 , which is called a Pascal (Pa).  Since the unit Pa is too small for pressures encountered in practice, kilopascal (1 kPa = 103 Pa) and Mega Pascal (1 MPa = 106 Pa) are commonly used.  Other units include bar, atm, psi.
• 7.
  HYDROSTATIC FORCE AND PRESSURE Suppose that a thin plate with area A m2 is submerged in a fluid of density ρ kg/m3 at a depth h meters below the surface of the fluid. h
• 8.
  HYDROSTATIC FORCE AND PRESSURE The fluid directly above the plate has volume  Vol = Ah  So, weight of fluid:  F =W = ϒ(Vol) = ϒ Ah w h
• 9.
  HYDROSTATIC PRESSURE  Thepressure P on the plate is defined to be the force per unit area: F Ah P h gh A A       h
• 11.
  HYDROSTATIC PRESSURE  Forinstance, if the density of water is ρ = 1000 kg/m3 , the pressure at the bottom of a swimming pool 2 m deep is: 3 2 1000kg/m 9.8m/s 2m 19,600Pa 19.6kPa P gd       
• 15.
  w Since, W =ϒ. vol W = ρ. g. (dx.dy.dz) / 2
• 18.
  A H W FTOP FBOTTOM Forces in aSTATIC fluid (at rest)  W is the weight = mg of this volume  FTOP is the force on the top of the volume exerted by the fluid above it pushing down  FBOTTOM is the force on the volume due to the fluid below it pushing up  For this volume not to move (Static fluid) we must have that FBOTTOM = FTOP + mg
• 19.
  FBOTTOM - FTOP= mg = (density x Vol) x g FBOTTOM - FTOP =  A H g Since pressure is Force / area, Force = P x A PBottom A – PTop A =  A H g, or Variation of pressure with depth PBottom – PTop =  H g The pressure below is greater than the pressure above.
• 23.
  2 2 1 1 A F F A      
• 35.
  Absolute, gage, andatmospheric pressures
• 40.
  Backup slides
• 41.
  Applications of Pascal’sLaw: •Hydraulic Lift: The image you saw on slide 25---30 of this article is a simple diagram of a hydraulic lift. This is the principle of working of hydraulic lift. It works based on the principle of equal pressure transmission throughout a fluid (Pascal’s Law). •The construction is such that a narrow cylinder (in this case A) is connected to a wider cylinder (in this case B). They are fitted with airtight pistons on either end. The inside of the cylinders are filled with an incompressible fluid. •Pressure applied at piston A is transmitted equally to piston B without diminishing, on use of an incompressible fluid. Piston B effectively serves as a platform to lift heavy objects like big machines or vehicles. Few more applications include a hydraulic jack and hydraulic press and forced amplification is used in the braking system of most cars.
• 42.
   Let say,at the surface of a body of water the pressure is  1 atm = 100,000 Pa  As we go down into the water at what depth does the pressure double, from 1 atm to 2 atm or 200,000 Pa  Want  g h = 100,000 Pa 1000 kg/m3 x 10 x h = 100,000  So h = 10 meters or about 30 feet 100,000 Pa h How much does P increase
• 43.
  a). Pg =588KPa; Pa = 160.1 KPa b). Pg = 205.8 Kpa; Pa = 307.1 KPa Problem solve by yourself