1. Chapter 9
Fluids

2. 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

3. 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

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

5. 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)

6. 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

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

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

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

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

11. Why Black and White?

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

13. Downstream

14. 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.

15. 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.

16. 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

17. 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

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

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

20. 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.

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

22. 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 = cubic meters or
22 million gallons!
B=rfluidgVdisp
Vdisp=Wship/rwaterg

23. 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.

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

25. Application
Worksheet #3a

26. 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

27. 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

28. 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?

29. Application
Worksheet #3b

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

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

32. 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.

33. Application
Worksheet #4

34. 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

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

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

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

38. 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

39. 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.

40. Greek or Geek?
Archimedes

41. Greek or Geek?

42. Greek or Geek?

43. Greek or Geek?

44. 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.