1. Fluid Mechanics Why is the electricity produced at the bottom of dams?
When you catch a deep-sea fish, why does its eyes pop-out?
Why do your ears pop on an airplane or up in the mountains?

2. Fluid Mechanics
The study of how fluids flow and how forces and energy are transferred through fluids
Liquids and gases have the ability to flow
They are called fluids
There are a variety of “LAWS” that fluids obey
Need some definitions

3. Defining a Fluid
A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid.
Both liquids and gases are considered fluids because they can flow and change shape.
Liquids have a definite volume; gases do not.

4. Density
Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space

5. Pressure A measure of the amount of force exerted on a surface area
Pressure is measured in pascals (pa)

6. Pressure = Force/surface area
Pressure = Newtons (Kg x m/s2)
meters2
Units are in N/m² or Pascals (Pa)

7. Pressure in a Fluid
The pressure is just the weight of all the fluid above you
Atmospheric pressure is just the weight of all the air above on area on the surface of the earth
In a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water)

8. Pressure in a Fluid
So, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE you
The deeper you go, the more weight above you and the more pressure
Go to a mountaintop and the air pressure is lower

9. Pressure in a Fluid
Pressure acts perpendicular to the surface and increases at greater depth.

10. Pressure in a Fluid
Remember that when we are considering the pressure of a fluid:
At any given point the pressure exerted by the fluid is equal in all directions
In other words a fluid will exert the same pressure in every direction relative to the force acting on the fluid (that is the weight above the fluid)

11. Pressure in a Fluid

12. Buoyancy Net upward force is called the buoyant force!!!
Easier to lift a rock in water!!

13. Factors Affecting Fluid Pressure
Fluid density
Depth
Weight
NOT:
Shape or volume of the container

14. Hydrostatic Pressure
Water pressure due to depth alone

16. Instruments Used to Measure Pressure
Barometer
Mercury
Aneroid
Gauges
Gauge Pressure
Measures system pressure relative to the atmospheric pressure, 0 gauge pressure indicates the system is at atmospheric pressure
Absolute Pressure
Measures pressure relative to a perfect vacuum

17. Specific Gravity
(s.g.)= The comparison of the density of a substance to the density of water
s.g.= density of substance
density of water

18. Displacement of Water
The amount of water displaced is equal to the volume of the object displacing the water.

19. Archimedes’ Principle
An immersed body is buoyed up by a force equal to the weight of the fluid it displaces.
If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float
The apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force

20. Archimedes’ principle:
Buoyant Force on an object immersed in a liquid equals the weight of the liquid displaced and the weight of the object if it floats.

22. Flotation
A floating object displaces a weight of fluid equal to its own weight.

23. Flotation

24. Pascal's Principle
When a force is applied to a confined fluid, the increase in pressure is exerted equally to all parts of the fluid.

25. Transmitting Pressure in a Fluid
When force is applied to a confined fluid, the change in pressure is transmitted equally to all parts of the fluid.

26. Hydraulic Machines
In a hydraulic machine, a force applied to one piston increases the fluid pressure equally throughout the fluid.

27. Hydraulic Devices
By changing the size of the pistons, the force can be multiplied.

29. Flowing Fluids: Liquid
A fluid flows because a fluid will exert an equal force in all directions.
When a fluid is contained the fluid remains within its boundaries (Newton’s 1st law)
When an opening is made the fluid will flow through that opening (Newton’s 3rd law) (a substance will flow where there is least resistance)

30. Flowing Fluids: Gases
“Gases flow because of difference in pressure as well, but their behavior is also influenced much more by the way they diffuse and are compressed” –pg 184
Gases are more susceptible to compressibility and diffuse more readily than liquids
Think of how a storm forms:
When low pressure winds are surrounded by high pressure winds the winds form a circular effect.
Low pressure is formed from the warm air rising from the ground, they reach the cooler air (high pressure) in the atmosphere. When these warm and cool airs combine we get a storm

31. The whole system is a low pressure, but it dramatically decreases towards the eye of the hurricane.
Very Low pressure
Pressure always flows from high to low, which creates the high velocity winds.
Higher Pressure

32. Barometric Pressure The barometer is used to forecast weather.
Decreasing barometer means stormy weather and an increasing barometer means warmer weather.

33. Atmospheric Pressure Just the weight of the air above you
Unlike water, the density of the air decreases with altitude since air is compressible and liquids are only very slightly compressible
Air pressure at sea level is about 105 newtons/meter2

34. Barometers

36. Bernoulli's Principle
The pressure exerted by a moving stream of fluid is less than its surrounding fluid.
Therefore, as the speed of the fluid increases its pressure decreases.
The sum of the water’s pressure, kinetic energy and potential energy, is equal at all points

37. Bernoulli’s Principle
Flow is faster when the pipe is narrower
Put your thumb over the end of a garden hose
Energy conservation requires that the pressure be lower in a gas that is moving faster
Has to do with the work necessary to compress a gas

38. Bernoulli’s Principle

39. Bernoulli’s Principle
When the speed of a fluid increases, internal pressure in the fluid decreases.

40. Bernoulli’s and Baseball
A non-spinning baseball or a stationary baseball in an airstream exhibits symmetric flow. A baseball which is thrown with spin will curve because one side of the ball will experience a reduced pressure. This is commonly interpreted as an application of the Bernoulli principle. The roughness of the ball's surface and the laces on the ball are important! With a perfectly smooth ball you would not get enough interaction with the air.
                                                        
Bernoulli’s and Baseball

41. Bernoulli’s and Air Foil
Bernoulli's Principle says that increased air velocity produces decreased pressure.
                                   
Lift is produced by an airfoil through a combination of decreased pressure above the airfoil and increased pressure beneath it.
The principle states that "the pressure of a fluid [liquid or gas] decreases as the speed of the fluid increases." Within the same fluid (air in the example of aircraft moving through air), high-speed flow is associated with low pressure, and low-speed flow is associated with high pressure.

43. The Condă Effect
Condă effect is the phenomena in which a fluid (mainly jet flow) attaches itself to a nearby surface and remains attached even when the surface curves away from the initial fluid/air (jet) direction.

44. Gases
The primary difference between a liquid and a gas is the distance between the molecules
In a gas, the molecules are so widely separated, that there is little interaction between the individual moledules
IDEAL GAS
Independent of what the molecules are

45. Kinetic theory of gases and …
Compressibility of Gases
Boyle’s Law
P a collision rate with wall
Collision rate a number density
Number density a 1/V
P a 1/V
Charles’ Law
Collision rate a average kinetic energy of gas molecules
Average kinetic energy a T
P a T

46. Physical Characteristics of Gases
Gases assume the volume and shape of their containers.
Gases are the most compressible state of matter.
Gases will mix evenly and completely when confined to the same container.
Gases have much lower densities than liquids and solids.

47. Buoyancy in a Gas
An object surrounded by air is buoyed up by a force equal to the weight of the air displace.
Exactly the same concept as buoyancy in water. Just substitute air for water in the statement
If the buoyant force is greater than the weight of the object, it will rise in the air

48. Buoyancy in a Gas
Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons don’t rise forever!!!

49. Atmospheric Pressure at Sea Level:
Force
Area
Barometer
Pressure =
Units of Pressure
1 pascal (Pa) = 1 N/m2
Atmospheric Pressure at Sea Level:
1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa

50. Gas Laws
Boyle’s Law- states that volume and pressure of a confined gas are inversely related
As the temperature remains constant the pressure will decrease when the volume increases.
Charles’ Law- states that the volume of a fixed amount of gas is directly proportional to its absolute temperature when the pressure is constant.
As the pressure remains constant the volume will increase as the temperature increases

51. 10 miles
0.2 atm
4 miles
0.5 atm
Sea level
1 atm

52. Boyle’s Law P a 1/V Constant temperature P x V = constant
Constant amount of gas
P x V = constant
P1 x V1 = P2 x V2

53. As P (h) increases
V decreases

54. Boyle’s Law
This defines an inverse relationship: when one goes up, the other comes down.
p1 * V1 = p2 * V2
p1 = initial pressure
V1 = initial volume
p2 = final pressure
V2 = final volume
If you know three of the four, you can calculate the fourth.

55. Boyle’s Law Density is mass divided by volume.
Halve the volume and you double the density and thus the pressure.

56. Boyle’s Law
At a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant

57. A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?
P1 x V1 = P2 x V2
P1 = 726 mmHg
P2 = ?
V1 = 946 mL
V2 = 154 mL
P1 x V1 V2
726 mmHg x 946 mL
154 mL =
P2 =
= 4460 mmHg

58. The relationship between temperature and volume
Charles's Law
The relationship between temperature and volume

59. As T increases
V increases

60. Variation of gas volume with temperature
at constant pressure.
Charles’ Law
V a T
Temperature must be
in Kelvin
V = constant x T
V1/T1 = V2/T2
T (K) = t (0C)

61. Kelvin = C° + 273 Celsius = K - 273
Temperature (T)
The temperature of a gas is generally measured with a thermometer in Celsius.
All calculations involving gases should be made after converting the Celsius to Kelvin temperature.
Kelvin = C° + 273
Celsius = K - 273

62. Kelvin Practice
What is the approximate temperature for absolute zero in degrees Celsius and kelvin?
Calculate the missing temperatures
0C = _______ K 100C = _______ K
100 K = _______ C – 30C = _______ K
300 K = _______ C 403 K = _______ C
25C = _______ K 0 K = _______ C
Absolute zero is – 273C or 0 K
273
373
– 173
243 27
130
298
– 273

63. A sample of carbon monoxide gas occupies 3. 20 L at 125 0C
A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?
V1/T1 = V2/T2
V1 = 3.20 L
V2 = 1.54 L
T1 = K
T2 = ?
V2 x T1 V1
1.54 L x K
3.20 L =
T2 =
= 192 K

64. A sample of gas occupies 3. 5 L at 300 K
A sample of gas occupies 3.5 L at 300 K. What volume will it occupy at 200 K?
V1 = 3.5 L, T1 = 300K, V2 = ?, T2 = 200K
Using Charles’ law: V1/T1 = V2/T2
3.5 L / 300 K = V2 / 200 K
V2 = (3.5 L/300 K) x (200 K) = 2.3 L
If a 1 L balloon is heated from 22°C to 100°C, what will its new volume be?
V1 = 1 L, T1 = 22°C = 295 K
V2 = ?, T2 = 100 °C = 373 K
V1/T1 = V2/T2, 1 L / 295 K = V2 / 373 K
V2 = (1 L/295 K) x (373 K) = 1.26 L