Chapter 9 Fluid Mechanics

9-2 Fluid Pressure and TemperaturePressure – a measure of how much force is

applied over a given area. Formula: P = F/A

Pressure = Force (N) / area (m2)

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.

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 1000000 Pa

Conversions: All equivalent units

14.7 pounds per square inch (psi) = 29.92 in Hg = 760 mm Hg = 101.3 kPa = 1.00 atm

Example: Convert 232 psi to kPa232 p.s.i ● 101.3 kPa 14.7 psi= 1599 kPa

Example: Convert 3.50 atm to mm Hg

3.50 atm ● 760 mm Hg 1 atm

= 2660 mm Hg

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 ● Tn = number of molesR = 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

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 = 8.31 kPa x L / mol x K)n = ?Ideal Gas Law -- P ● V = n ● R ● T

n = 0.25 mol

Boyles’ Law: The pressure and volume of a gas at constant temperature are inversely proportional. Increase one – decrease the other.

Formula: P1 ● V1 = P2 ● V2

• Increasing pressure on a gas (compressible) - decreases volume.

Boyles’ Law: A graph of an inverse relationship

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

P1 ● V1 = P2 ● V2

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

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

“Combined Gas Law”P1V1 = P2 V2

T1 T2

Always convert temperature to Kelvin.

Gay-Lussac’s Law: •The pressure of a gas is directly proportional to the Kelvin temperature if the volume is held constant.

Direct relationship

P1 / T1 = P2 / T2

Question: The air temperature at an altitude of 10 km is a chilling ----35 0C. 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.