Chapter 9 Fluids

Objectives for Today Hydrostatic Pressure; P = rgh Buoyancy; Archimedes’ Principle Fbuoyancy = rg(Volume displaced) Pascal’s Equation P=F/A = f/a Continuity Equation A1V1=A2V2 Bernoulli’s Equation P +1/2 rv2 + rgh = constant

Density The density of a substance of uniform composition is defined as its mass per unit volume: Units are kg/m3 (SI) or g/cm3 (cgs) 1 g/cm3 = 1000 kg/m3

Pressure The force exerted by a fluid on a submerged object at any point if perpendicular to the surface of the object

Variation of Pressure with Depth If a fluid is at rest in a container, all portions of the fluid must be in static equilibrium All points at the same depth must be at the same pressure Otherwise, the fluid would not be in equilibrium (Think weather)

Pressure and Depth Examine the darker region, assumed to be a fluid It has a cross-sectional area A Extends to a depth h below the surface Three external forces act on the region

Pressure and Depth equation Po is normal atmospheric pressure = 101.3 kPa = 14.7 lb/in2 The pressure does not depend upon the shape of the container

Pressure Units One atmosphere (1 atm) = 760 mm of mercury 101.3 kPa 14.7 lb/in2

Pressure Calculation Hoover Dam Average Head Max Pressure; ??? Worksheet #1 Hoover Dam Average Head 158.5 meters of water Max Pressure; ???

Pressure Calculation P = Po + rgh h=158.4 meters r = 1000 kg/m3 Po + rgh = 101.3KPa + 1000 x 9.8 x 158.5 Pa = 101.3 KPa + 1,553,300 Pa = 1655 KPa

Why Black and White?

Power turbines P stays about the same v doesn’t change much either, the turbines convert (rho g h)*flow rate to electrical power

Downstream

Video Clip Achilles kills WWF guy What to do with Physics? Homer’s Iliad inspired the inventor of the greek writing, How would we do Physics without the Greek Alphabet? The lesson is: If you’re a great greek warrior You’ll inspire someone to invent writing to tell your story Brad Pitt and Colin Farrel will star in movies about you. If you’re a great Greek geek, we’ll name an equation after you.

Archimedes' Principle Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object.

Buoyant Force The upward force is called the buoyant force The physical cause of the buoyant force is the pressure difference between the top and the bottom of the object

Archimedes’ Principle: Totally Submerged Object The upward buoyant force is B=ρfluidVobjg The downward gravitational force is w=mg=ρobjVobjg The net force is B-w=(ρfluid-ρobj)gVobj

Totally Submerged Object The object is less dense than the fluid The object experiences a net upward force

Totally Submerged Object The object is more dense than the fluid The net force is downward The object accelerates downward

Archimedes’ Principle: Floating Object Fbuoyancy = rg(Volume displaced) The object is in static equilibrium. The upward buoyant force is balanced by the downward force of gravity. Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level.

Buoyancy in action Worksheet #2 Ship displacement 810 million N! 332 meters long How many cubic meters are displaced?

Got milk? Vdisp = 82600 cubic meters or 22 million gallons! Ship weighs 810 x 106 N = B Density of water = 1000 kg/m3 Volume of water displaced is B=(810 x 106 )=Vdisp x (1000 x 9.8) Vdisp = 82600 cubic meters or 22 million gallons! B=rfluidgVdisp Vdisp=Wship/rwaterg

Pascal’s Principle A change in pressure applied to an enclosed fluid is transmitted undimished to every point of the fluid and to the walls of the container.

Pascal’s Principle The hydraulic press is an important application of Pascal’s Principle Also used in hydraulic brakes, forklifts, car lifts, etc.

Application Worksheet #3a

Fluids in Motion: Streamline Flow every particle that passes a particular point moves exactly along the smooth path followed by particles that passed the point earlier also called laminar flow Streamline is the path different streamlines cannot cross each other the streamline at any point coincides with the direction of fluid velocity at that point

Characteristics of an Ideal Fluid The fluid is nonviscous There is no internal friction between adjacent layers The fluid is incompressible Its density is constant The fluid is steady Its velocity, density and pressure do not change in time The fluid moves without turbulence No eddy currents are present

Equation of Continuity A1v1 = A2v2 The product of the cross-sectional area of a pipe and the fluid speed is a constant Speed is high where the pipe is narrow and speed is low where the pipe has a large diameter Av is called the flow rate – what are its units?

Application Worksheet #3b

Bernoulli’s Equation Let’s take a minute to show how much you already know about this equation! Do a dimensional analysis -

Bernoulli’s Equation What do the second and third terms look like? What happens we multiply by Volume?

Conservation of energy States that the sum of the pressure, the kinetic energy per unit volume, and the potential energy per unit volume has the same value at all points along a streamline.

Application Worksheet #4

Applications of Bernoulli’s Principle: Venturi Meter Shows fluid flowing through a horizontal constricted pipe Speed changes as diameter changes Can be used to measure the speed of the fluid flow Swiftly moving fluids exert less pressure than do slowly moving fluids

Prairie Dogs Build burrows with two openings One is even with ground, the other built up, why?

Prairie Dogs He wants his family to have fresh air. Apply Bernoulli’s Eq’n to a breeze over both holes. Breeze

Prairie Dogs How will the pressures over each hole compare? What will this do the air in the tunnel? Breeze

Questions? Hydrostatic Pressure; P = rgh Buoyancy; Archimedes’ Principle Fbuoyancy = rg(Volume displaced) Pascal; F/A=f/a Continuity Equation A1V1=A2V2 Bernoulli’s Equation P + 1/2 rv2 + rgh = constant

Greek or Geek? Troy burning What to do with Physics? Homer’s Iliad inspired the inventor of the greek writing, How would we do Physics without the Greek Alphabet? The lesson is: If you’re a great greek warrior You’ll inspire someone to invent writing to tell your story Brad Pitt and Colin Farrel will star in movies about you. If you’re a great Greek geek, we’ll name an equation after you.

Greek or Geek? Archimedes

Greek or Geek?

Greek or Geek?

Greek or Geek?

Video Clip Troy burning What to do with Physics? Homer’s Iliad inspired the inventor of the greek writing, How would we do Physics without the Greek Alphabet? The lesson is: If you’re a great greek warrior You’ll inspire someone to invent writing to tell your story Brad Pitt and Colin Farrel will star in movies about you. If you’re a great Greek geek, we’ll name an equation after you.