Elasticity & Fluid Mechanics

• Elasticity


  The property of a body which enables it to resist deformation and to cover after removal of the deforming force.
• Elongation


  State of an elastic body being lengthened.
• Deformation


  State of an elastic body being deformed.
• Stress (σ)


  A force exerted when one body tends to stretch, squeeze, or twist another body.
• Strain

  Deformation of the body under the action of applied forces.
• Tensile and Compressive Stress (𝜎)


  When a force is applied to an elastic body, the body deforms. The way in which the body depends upon that type of force applied to it. A compression force makes the body shorter while a tensile force makes the body longer.
• Tensile Stress and Compressive Strain (𝜀)


  When a force is applied to an elastic body, the body deforms. The deformation per unit of the original length under a stress is called strain.
• 1 N/m^2 = 1 Pascal = 0.021 lb/ft^2
• 1 lb/in^2 = 1 psi = 144 lb/ft^2
• 1 atm = 760 mmHg = 101.3 kPa = 14.7 lb/in^2
• Pressure

  Force / Area
• Liquid (Gauge) Pressure


  Pressure exerted by a liquid.
• Liquid Pressure Formula

  P = p x g x h
• Absolute Pressure


  Pressure exerted by the liquid and the atmosphere.
• Absolute Pressure

  Po + p x g x h
• Pascal's Principle


  Any change in pressure applied to a completely enclose fluid is transmitted undiminished to all parts of the fluid and the enclosing walls
• Pascal's Principle


  P1 = P2
• Pascal's Principle


  F1/A1 = F2/A2
• Hydraulic Lift


  A device that used a confined fluid to transfer pressure from one platform (input) to another (output)
• Density


  Defined to be mass per volume.
• Archimedes' Principle


  Any object completely or partially submerged in a fluid experiences a buoyant force (Fb) equal in magnitude to the weight of the fluid displaced by the object.
• Archimedes' Principle

  Fb = mf x g = pf x g x Vf
• Pobject < Pliquid


  Object FLOATS on liquid.
• Pobject > Pliquid

  Objects SINKS in liquid.
• Pobject = Pliquid

  Object is FULLY SUBMERGED in the liquid
• Common Units for Mass Density

  1.) g/cm^3

  2.) kg/m^3
• For objects FULLY SUBMERGED in fluid


  1.) Vdisplaced fluid = Vobject

  2.) Fg = Fb

  3.)Fb = Wair - Wfluid
• 1 g/cm^3 = 1000 kg/m^3
• Constant Value of Atmospheric Pressure (Po)

  1.013 x 10^5 Pa
• Density of Liquid

  1000 kg/m^3
• Acceleration due to gravity (g)

  9.8 m/s^2
• Specific Gravity

  Psubstance / Pwater