Unformatted text preview:

Elementary Mechanics of FluidsTable A.2PHYSICAL PROPERTIES OF GASES AT STANDARD ATMOSPHERIC PRESSURE AND 15ºC (59ºF)Example (2.4)Example (2.8)Elasticity (Compressibility)Example (2.45)Vapor PressureSurface TensionCapillary RiseExample (2.51)Examples of Surface TensionExample (2.47)Example (2.48)Bug ProblemCE 319 FDaene McKinneyElementary Mechanics of FluidsIntroduction &Fluid Properties(continued)Table A.2PHYSICAL PROPERTIES OF GASES AT STANDARD ATMOSPHERIC PRESSURE AND 15ºC (59ºF)Example (2.4)• Given: Natural gas–Time 1: T1=10oC, p1=100 kPa–Time 2: T2=10oC, p2=200 kPa• Find: Ratio of mass at time 2 to that at time 1– Ideal gas law (p is absolute pressure)212121ppVRTpVRTpMM==VRTpVM ==ρ5.120030012==kPakPaMMExample (2.8)• Estimate the mass of 1 mi3of air in slugs and kgs• Assume ρair= 0.00237 slugs/ft3, the value at sea level for standard conditionskgxMslugskgslugsxMslugsxMVMair98831009.5/59.14*1049.31049.3)280,5(*00237.0=====ρElasticity (Compressibility)• Deformation per unit of pressure change•For water Ev= 2.2 GPa, 1 MPa pressure change = 0.05% volume changeWater is relatively incompressibleρρ// ddpVdVdpEv=−=Example (2.45)3339601.999909.01000909.01000102.2102/cmVVVVcmcmPaxPaxVEpVVVpEfinalfinalvv=−=∆+=−=−=∆−=∆∆∆−=• Given: Pressure of 2 MPa is applied to a mass of water that initially filled 1000-cm3volume. • Find: Volume after the pressure is applied.• Solution: E = 2.2x109Pa (Table A.5)Vapor Pressure• Pressure at which a liquid will boil for given temp.• Vapor pressure increases with temperature– Increasing temperature of water at sea level to 212 oF, increases the vapor pressure to 14.7 psia and boiling occurs– Boiling can occur below 212 oF if we lower the pressure in the water to the vapor pressure of that temperatureVapor Press. vs. Temp.0204060801001200 102030405060708090100Temperature (oC)Vapro Pressure (kPa)• At 50 oF, the vapor pressure is 0.178 psia• If you reduce the pressure in water at this temperature, boiling will occur (cavitation)Surface Tension• Below surface, forces act equally in all directions• At surface, some forces are missing, pulls molecules down and together, like membrane exerting tension on the surface• If interface is curved, higher pressure will exist on concave side • Pressure increase is balanced by surface tension, σ•σ = 0.073 N/m (@ 20oC)waterairNo net forceNet forceinwardInterfaceCapillary Rise• Given: Water @ 20oC,d = 1.6 mm• Find: Height of water• Solution: Sum forces in verticalAssume θsmall, cosθÆ 1 σFW0)4)((cos02,=∆−=−dhdWFzπγθσπσmmhxdh6.18106.1*9790073.0*443=∆==∆−γσExample (2.51)• Find: Capillary rise between two vertical glass plates 1 mm apart.σ= 7.3x10-2N/ml is into the page•Solution:tσσθhmmhmhxthhltlFvertical9.140149.09810*001.0103.7*220202=====−=∑−γσγσExamples of Surface TensionExample (2.47)• Find: The formula for the gage pressure within a spericaldroplet of water?•Solution: Surface tension force is reisited by the force due to pressure on the cut section of the droprprrpσσππ22)(2==Example (2.48)• Given: Sperical bubble, inside radius r, film thickness t, and surface tension σ.•Find: Formula for pressure in the bubble relative to that outside.•Solution:PapxprprrpF0.73004.0103.7*440)2(2022=∆=∆=∆=−∆=∑−σσππBug Problemθ FF=surface tension on 1 side of legCross-sectionof bug


View Full Document

UT CE 319F - Elementary Mechanics of Fluids

Download Elementary Mechanics of Fluids
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Elementary Mechanics of Fluids and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Elementary Mechanics of Fluids 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?