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Understanding Fluid Dynamics: Density, Pressure, and Buoyant Forces

This guide delves into fundamental concepts in fluid dynamics, including density, pressure, and buoyancy. Discover the definitions of density (( ho = m/V )) and pressure (( p = F/A )), and understand the principles of buoyancy and fluid flow continuity. We explore Archimedes' Principle, determining the buoyant force on submerged objects, and examine Bernoulli's Theorem, which relates pressure with kinetic and potential energies in fluid flow. Ideal for students and enthusiasts seeking to grasp fluid mechanics in real-world applications.

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Understanding Fluid Dynamics: Density, Pressure, and Buoyant Forces

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Presentation Transcript

  1. Introduction To Fluids

  2. Density •  = m/V • : density (kg/m3) • m: mass (kg) • V: volume (m3)

  3. Pressure • p = F/A • p : pressure (Pa) • F: force (N) • A: area (m2)

  4. Pressure The pressure of a fluid is exerted in all directions. The force on a surface caused by pressure is always normal to the surface.

  5. Specific Gravity of Gases • The Specific Gravity - SG - of a gas is a dimensionless unit defined as the ratio of density of the gas to the density of air at a specified temperature and pressure. • SG = ρ / ρair • ρ = density of the gas • ρair = density of the air

  6. The Pressure of a Liquid • p = gh • p: pressure (Pa) • : density (kg/m3) • g: acceleration constant (9.8 m/s2) • h: height of liquid column (m)

  7. Absolute Pressure • p = po + gh • p: pressure (Pa) • po: atmospheric pressure (Pa) • gh: liquid pressure (Pa)

  8. Piston 25 cm Density of Hg 13,400 kg/m2 Problem Area of piston: 8 cm2 Weight of piston: 200 N A What is total pressure at point A?

  9. Floating is a type of equilibrium

  10. Floating is a type of equilibrium Archimedes’ Principle: a body immersed in a fluid is buoyed up by a force that is equal to the weight of the fluid displaced. Buoyant Force: the upward force exerted on a submerged or partially submerged body.

  11. Calculating Buoyant Force Fbuoy = Vg Fbuoy: the buoyant force exerted on a submerged or partially submerged object. V: the volume of displaced liquid. : the density of the displaced liquid.

  12. Fbuoy = rVg mg Buoyant force on submerged object Note: if Fbuoy < mg, the object will sink deeper!

  13. Fbuoy = rVg mg Buoyant force on submerged object SCUBA divers use a buoyancy control system to maintain neutral buoyancy (equilibrium!)

  14. Fbuoy = rVg mg Buoyant force on floating object If the object floats, we know for a fact Fbuoy = mg!

  15. Fluid Flow Continuity • Conservation of Mass results in continuity of fluid flow. • The volume per unit time of water flowing in a pipe is constant throughout the pipe.

  16. Fluid Flow Continuity • A1v1 = A2v2 • A1, A2: cross sectional areas at points 1 and 2 • v1, v2: speed of fluid flow at points 1 and 2

  17. Fluid Flow Continuity • V = Avt • V: volume of fluid (m3) • A: cross sectional areas at a point in the pipe (m2) • v: speed of fluid flow at a point in the pipe (m/s) • t: time (s)

  18. Announcements8/16/2014 • Lunch Bunch pretest due tomorrow at beginning of regular class. • Engineering seminar announcement.

  19. Bernoulli’s Theorem The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow.

  20. Bernoulli’s Theorem All other considerations being equal, when fluid moves faster, the pressure drops.

  21. Bernoulli’s Theorem • p +  g h + ½ v2 = Constant • p : pressure (Pa) •  : density of fluid (kg/m3) • g: gravitational acceleration constant (9.8 m/s2) • h: height above lowest point (m) • v: speed of fluid flow at a point in the pipe (m/s)

  22. Bernoulli’s Theorem p1 +  g h1 + ½ v12 = p2 +  g h2 + ½ v22

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