1. Chapter 9 Fluid Mechanics

2. 9-2 Fluid Pressure and Temperature
Pressure – a measure of how much force is applied over a given area.
Formula: P = F/A
Pressure = Force (N) / area (m2)

3. Fluids – ability to flow – gases and liquids
Our atmosphere – “ocean of gas”
Density of our atmosphere decreases with altitude
The atmosphere exerts pressure –
atmospheric pressure – caused by the
weight (in Newtons) of the air.

4. Barometer Measures atmospheric pressure or “barometric pressure”
The SI unit for measuring Pressure = pascal (Pa) = 1 N/m2
1 square meter at sea level = 100,000 N -- so 100,000 N/m2
Average atmospheric pressure at sea level is 101.3kPa
Or Pa

5. Conversions: All equivalent units 14
Conversions: All equivalent units 14.7 pounds per square inch (psi) = in Hg = 760 mm Hg = kPa = 1.00 atm
Example: Convert psi to kPa
p.s.i ● kPa
14.7 psi
= 1599 kPa
Example: Convert atm to mm Hg
3.50 atm ● 760 mm Hg
1 atm
= 2660 mm Hg

6. 9-4 Properties of Gases
Ideal gas Law – relates gas volume, pressure and temperature.
For a given Volume of Gas at a given Pressure and a given Temperature there should be a consistent # of molecules/atoms, n
Formula: P ● V = n ●R ● T
n = number of moles
R = universal gas constant = 8.31 J / (mol ● K)
K = SI unit of temperature Kelvin (0C + 273)
Avogadro: said that it doesn’t matter what gas it is,
1 mole = 22.4 L of gas (6.02 x 1023 particles) at STP
(standard temp/press) = 00C and 1 atm of pressure

7. Example:
How many moles of carbon dioxide gas (CO2) are contained in a 6.2 L tank at 101 kPa and 30 0C?
Given: V = 6.2 L P = 101 kPa T = 30 oC (303 K)
And,
Constant R = kPa x L / mol x K)
n = ?
Ideal Gas Law -- P ● V = n ● R ● T
n = 0.25 mol

8. Increasing pressure on a gas (compressible) - decreases volume.
Boyles’ Law: The pressure and volume of a gas at constant temperature are inversely proportional. Increase one – decrease the other.
Increasing pressure on a gas (compressible) decreases volume.
Formula: P1 ● V1 = P2 ● V2

9. Boyles’ Law: A graph of an inverse relationship
P1 ● V1 = P2 ● V2
Example: A volume of gas at 1.10 atm was measured at 326 cm3. What will be the volume if the pressure is adjusted to 1.90 atm?
Given: P1 = 1.10 atm, V 1 = 326 cm3, V2 = ? , P2 = 1.90 atm
Answer V2 = 189 cm3

10. Charles’s Law: at constant pressure, the volume of a gas is directly proportional to its Kelvin temperature
Increase one, increase the other.
Formula: V1T2 = V2T1 proportional to its Kelvin temperature
or V1 = T1 V2   T2
Direct relationship

11. Example: The gas in a balloon occupies 2. 25 L at 298 K
Example: The gas in a balloon occupies 2.25 L at 298 K. At what temperature will the balloon expand to 3.50 L?
Given: V1 = 2.25 L T1 = 298 K T2 = ? V2= 3.50 L
T2 = 464 K

12. “Combined Gas Law” T1 T2 P1V1 = P2 V2
Always convert temperature to Kelvin.

13. Gay-Lussac’s Law: P1 / T1 = P2 / T2
The pressure of a gas is directly proportional to the Kelvin temperature if the volume is held constant.
Direct relationship
P1 / T1 = P2 / T2

14. Question: The air temperature at an altitude of 10 km is a chilling C. Cabin temperatures in airplanes flying at this altitude are comfortable because of air conditioners rather than heaters. Why?
Answer: Airliners have pressurized cabins. The process of stopping and compressing outside air to near sea-level pressures would normally heat the air to a roasting 55 0C (130 0F). So air conditioners must be used to extract heat from the pressurized air.