
Fluids
 Liquids and gases are fluids.
 Density, specific gravity
 Density: ρ=m/V, where ρ is density, m is mass, and V is volume.
 The density of water is ρ_{water} = 1 g/mL = 1 g/cm^{3} = 1 kg/L.
 Specific gravity is the density of something compared to water.
 Specific gravity = ρ/ρ_{water}.
 The specific gravity of water is 1.
 Buoyancy, Archimedes' principle

 Archimedes' principle: buoyant force on an object = weight of the fluid displaced by the object.
 F_{B} = weight_{displaced} = m_{displaced}g =ρ_{fluid}V_{submerged}g
 The volume of an object that is submerged = the volume of fluid displaced by the object.
 Things float when F_{B} = Weight.
 Things will rise upward when F_{B} > Weight.
 Things will sink when F_{B} < Weight.
 Hydrostatic pressure
 Pascal's law: if you apply pressure on a liquid, the pressure is transmitted equally to all parts of the liquid.

 F_{1}/A_{1} =F_{2}/A_{2}
 The pressure input at one end is the same as the pressure output at the other.
 You apply a small force over a small area, and the output force at the end with the larger area will be greater.
 A_{1}d_{1}=A_{2}d_{2}, where d is the distance that the end moves.
 The work done on one end is the same as the work output at the other.
 P = pgh (pressure vs. depth)
 P=ρgh
 P is pressure, ρ is the density of the fluid; g is the gravitational constant, h is the height from the surface, or depth that the object is submerged.
 Pressure at the surface is 0 because h = 0.
 Pressure at a depth of h is ρgh.
 ρgh is the gauge pressure because it ignores the atmospheric pressure above the fluid.
 Absolute pressure of something submerged in the ocean = ρgh + atmospheric pressure.
 Viscosity: Poiseuille flow
 When a viscous fluid flows through a pipe, the flow has a front that is shaped like a parabola bulging outward.
 Continuity equation (A·v = constant)
 The volume flow rate of a fluid is constant.
 dV/dt = constant, where dV/dt is volume flow rate.
 dV = A·dL
 A·dL/dt = A·v = constant, where v is linear flow rate (velocity).
 Concept of turbulence at high velocities
 Low velocity > laminar flow.
 High velocity > turbulent flow, forms eddies.
 Surface tension
 Surface tension gives the surface of a liquid the ability to support things that are very light.
 For example, insects can walk on water due to surface tension.
 Surface tension is due to the attraction between the molecules of the solvent.
 Bernoulli's equation
 P + ½ρv^{2} + ρgh = constant
Solids
 Density: ρ=m/V, where m is mass and V is volume.
 Elastic properties (elementary properties)

 Stress: the pressure exerted on an object. σ = stress = F/A.
 Strain: the deformation of the object in the direction of the applied force divided by the original length. ε = strain = ΔL/L_{0}.
 Young's modulus = stress / strain.
 Young's modulus, the ratio between stress and strain, is constant until you reach the elastic limit, where things get permanently deformed.
 Elastic limit: The maximum stress something can handle before it breaks or become permanently deformed.
 Thermal expansion coefficient
 Things expand when temperature rises, and contract when temperature falls.
 ΔL = αL_{0}ΔT
 ΔL is the change in length, L_{0} is the initial length, ΔT is the change in temperature, and α is the coefficient of linear expansion.
 In the same fashion as linear expansion, the equations for volume and area expansions are below.
 ΔV = βV_{0}ΔT
 ΔA = γA_{0}ΔT
 Shear

 Shear = stress / shear ratio.
 Shear ratio = ΔL/L_{0}.
 When ΔL is very small compared to L_{0}, Shear ratio is approximately the same as the shear angle.
 Shear angle = tan^{1}ΔL/L.
 Note: ΔL and L are perpendicular to each other.
 Compression: solids and liquids are generally not compressible. Gasses are compressible.

