1. Wednesday(11/17): Fluids, Density, Pressure, Pascal's Principle,

Archimedes' Principle, and Bernoulli's Principle. HW: Read pages 301-313

and solve prob. 2, 8, 12, 20, 26, and 32 on pages 329-331.

2. Thursday(11/18): Applications of Fluid Mechanics. HW: Read pages

313-321 and solve prob. 37, 40, 50, 59, and 67 on pages 331-333.

3. Friday(11/19): Lab on Archimedes' Principle. HW: Process lab

data, Lab Report due Tuesday.

4. Monday(11/22): Post-Lab Discussion and Review of Fluid Mechanics.

HW: Finish Lab Report and Review Problems for Homework.

5. Tuesday(11/23): TEST on Ch.11. HW: Go to web-site for notes

on Ch.12 - Temperature and Heat.

1. Fluid Mechanics is the study of fluids in motion while Fluid Statics is

the study of fluids at rest.

2. A fluid is any material that flows and offers little resistance to change

in shape. Therefore, all liquids and gases are fluids. Recall that the other

two states of matter are solid and plasma.

3. Fluids are described by their density, ρ, (the Greek letter Rho) which is

the ratio of mass to volume. ρ = m/V. The MKS unit is kg/m³. Some

common densities, in kg/m³ , would be: (a) helium .179, (b) steam .598,

(c) ice .917, (d) air, 1.29, (e) carbon dioxide 1.98.

4. Pure water has its greatest density, 1000 kg/m³, at 4 degrees Celsius.

We use this value to compute the Specific Gravity of other substances,

which is  S.G. = Density of the substance/Density of Water at 4^o C .

Some common Specific Gravity values are (a) lead 11.3, (b) mercury 13.6,

(c) gold 19.3 .

5. All densities can change due to variations in pressure and temperature.

We should know that STP (Standard Temperature and Pressure) is 0.0^oC

and 1.0 atm.

6. All fluids also exert pressure, P, which equals force per unit area,

P=F/A.  Combining this equation with the density equation we can easily

compute the pressure exerted by a fluid at any depth, P=ρhg.

7. The MKS unit of pressure is the N/m². This is now called the Pascal (Pa)

in honor of the French mathematician Blaise Pascal (1623-1662). A common

amount of pressure is in terms of 10⁵ Pa, which is known as one bar. Other

units are lb/in² (psi), mm of Hg, meters or feet of water, and Torr.

8. Some accepted values of pressure estimates, for example, are

(a) 1 atm = 1.013x10⁵ Pa at sea level, (b) at 10 km elevation, 1 atm =

2.8x10⁴ Pa, (c) bottom of Pacific, 6x10⁷ Pa, (d) center of Earth, 4x10¹¹ Pa,

(e) best vacuum, 1x10^-12 Pa.

9. Pressure also varies with depth of a fluid, with the absolute pressure

equal to fluid pressure, as a function of its density and height, plus

atmospheric pressure. Therefore, P_abs= P_atm + ρhg .

10. Two well-known pressure gauges are the Mercury Barometer and the

U-tube Manometer. The barometer is useful for measuring atmospheric

pressure, while the Manometer can measure the pressure inside a closed

container.

11. Gauge Pressure is the amount by which the container pressure differs

from atmospheric. Using the above equation we have, for Gauge Pressure,

P_abs - P_atm = ρhg .

12. Pascal's Principle states that the force exerted on a fluid is

transmitted equally throughout the fluid. That is, P₁=P₂ , which means

that F₁/A₁=F₂/A₂. This leads to hydraulics, the study of forces exerted by

fluids.

13. All fluids exert a force on objects partially or completely submerged

in them. This is the Buoyant Force.

14. Archimedes (287-212,BC), of Syracuse, Greece, was probably the

greatest scientist of antiquity. He discovered the method for calculating

the buoyant force and shouted, "Eureka!" as he sprang from his bath.

15. Archimedes' Principle states that the buoyant force of a fluid on a

mass submerged in it equals the weight of the fluid displaced. In other

words F_B = ρVg , but since V =Ah, we also have F_B = ρgAh.

16. Fluids can be classified as steady or unsteady, based on the

behavior of their velocity. An extreme condition would be that of

turbulent flow. Fluids can also be termed compressible (gases), or

incompressible (liquids).

17. A fluid can referred to viscous (does not flow readily) or non-viscous

(flows easily). An incompressible, non-viscous fluid is called an ideal

fluid. 

18. The Equation of Continuity states the fact that mass is conserved.

In simple terms, what flows into one end of a pipe flows out the other

end, assuming that there are no additional exit or entry points in

between.

19. Expressed in terms of mass flow rate, the Equation of Continuity

is ρ₁A₁v₁ = ρ₂A₂v₂ .  If a fluid is incompressible, then the density

cancels out and we have A₁v₁ = A₂v₂ . The product Av = Q, is known

as the volume flow rate. The MKS unit would m³/s, but customary units

are gal/min, or even ft³/min.

20. Daniel Bernoulli (1700-1782), Swiss, derived the principle that bears

his name, "as the velocity of a fluid increases, the pressure exerted by

the fluid decreases."   P + ½ρv² + ρhg = (constant) .

21. His most famous production, Hydrodynamica, was the basis for the

Kinetic Theory of Gases and also explains the phenomenon of lift.

22. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.

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THE AP PHYSICS B ARCHIVES Ch.1: Physics Intro. Ch.2: Linear Motion. Ch.3: 2-Dim Motion. Ch.4&5: Newton's Laws. Ch.6: Work/Energy. Ch.7: Momentum. Ch.8&9: Rotary Motion. Ch.10: SHM. Ch.11: Fluids. Ch.12&13: Temp.&Heat. Ch.14&15: Thermodynamics. Semester Review.