Chp. 10: Fluids

Chp. 10: Fluids

1. Pressure and Density

   • Pressure = Force / Area
   • Density = Mass / Volume

2. Fluids and the Effect of Gravity

   • Pressure at the bottom must support pressure at top plus weight of fluid. Therefore, pressure at bottom is greater.
   • ΣFy = Pbot A – Ptop A – m g = 0; P = Po + ρ g h
   • Po = Patm

3. Hydraulics and Pascal's Principle

   • Pascal's Principle: Pressure remains constant throughout all of a fluid in closed container.
   • Hydraulics utilize the fact that pressure remains constant to amplify force.
     • FL = FR (AL / AR)

4. Buoyancy and Archimedes' Principle

   • Buoyancy Force: Force that keeps an immersed object afloat (from below).
     • FB = ρL g V
     • Equal to the weight of displaced fluid.
   • Apparent Weight: True Weight - Buoyant Force

5. Fluids in Motion: Continuity and Bernoulli's Equation

   • Flow rate is conserved in a system.
     • vL AL = vR AR
     • Flow Rate: Q= vA (m^3/2)
   • Bernoulli's Equation puts the idea of fluid Continuity in terms of work and energy.
     • P1 + (1/2) ρ (v1^2) + ρ g h1 = P2 + (1/2) ρ (v2^2) + ρ g h2

6. Exam 3

   • Chp. 11: Simple Harmonic Motion
     • Harmonic Motion
       • Motion which repeats periodically.
         • sin waves
       • Period, T: Time to complete one whole cycle.
       • Frequency, f: Number of oscillations in one unit of time.
       • Position: y = A sin (2πƒt)
         • A = Amplitude
         • θ=ωt =2πƒt
     • Spring-Mass Oscillator, Simple Pendulum
       • Mass on a spring exhibit simple harmonic motion and displays behavior that can be described with wave functions.
       • Pendulums move in simple harmonic motions.
         • Behavior only dependent on frequency or period and Length of string
     • Harmonic Motion and Energy
       • Total mechanical energy is conserved in SHM as potential energy is converted to kinetic energy and vice versa.
       • KEmax = PEmax
     • Hooke's Law
       • Fspring = - k x
         • restoring force
       • Young's Modulus measures stiffness
         • F/A = Y(ΔL / Lo)
           • F/A is stress
           • ΔL / Lo is strain
       • Shear Modulus: F/A = S (Δx/Lo)
   • Chp. 12: Waves
     • A wave transfers energy without transporting matter.
       • "Disturbs" its medium
         • When medium is solid, wave is called "Mechanical Wave"
         • Transverse waves: wave motion is perpendicular to medium motion
         • Longitudinal waves: wave motion is parallel to medium motion.
       • Displacement: y = A sin [ 2 π ƒt - (2π x / λ )]
         • A = amplitude
         • λ = wavelength
       • speed of a wave: fλ
     • Exhibits SHM
     • Waves are functions of space AND time