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ENGG 2230 (2)


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ENGG 2230
Bahram Gharabaghi

Chapter 6Viscous Flow in Ducts 61 In flow past a sphere the boundary layer becomes turbulent at about Re25E5 To Dwhat air speed in mih does this correspond to a golf ball whose diameter is 16 in Do the pressure temperature and humidity of the air make any difference in your calculation 3Solution For air at 20C take 12 kgm and 18E5 kgms Convert D16 inches to 00406 m The critical Reynolds number is miVD12V00406m Ans206Re25E5orV92Dh18E5sSince air density and viscosity change with pressure temperature and humidity the calculation does indeed depend upon the thermodynamic state of the air62 Air at approximately 1 atm flows through a horizontal 4cmdiameter pipe a Find a formula for Q the maximum volume flow for which the flow remains laminar and plot maxQ versus temperature in the range 0CT500C b Is your plot linear If not explain maxSolution a First convert the Reynolds number from a velocity form to a volume flow form 4QV d Q thereforeRe2300for laminar flowVd2d d42300d Maximum laminar volume flow is given by aAnsQmax4 andfor air from Table A2 and plot Q versus T C With d004 mconstant get max Fig P62 364 SolutionsManualFluid Mechanics Fifth Edition The curve is not quite linear becauseis not quite linear with T for air in this range Ans b63For a thin wing moving parallel to its chord line transition to a turbulent boundarywhere x is the distance from the leading layer occurs at a local Reynolds number Rexedge of the wing The critical Reynolds number depends upon the intensity of turbulent fluctuations in the stream and equals 28E6 if the stream is very quiet A semiempirical correlation for this case Ref 3 of Ch 6 is 21211132512 Rex2crit000392 is the tunnelturbulence intensity in percent If V20 ms in air at 20C use this wherebetween formula to plot the transition position on the wing versus stream turbulence foris x decreased 50 percent from its value at 0 0 and 2 percent At what value of critSolution This problem is merely to illustrate the strong effect of stream turbulence on 312 kgm and 18E5 kgms Compute the transition point For air at 20C takefrom the correlation and plot xRe20 ms versus percent turbulence Rexcrittrx Fig P63 The value of x decreases by half to 107 meters at 042 Ans crit Chapter 6Viscous Flow in Ducts 365 64 For flow of SAE 30 oil through a 5cmdiameter pipe from Fig A1 for what flow 3h would we expect transition to turbulence at a 20C and b 100C rate in m3Solution For SAE 30 oil take 891 kgm and take 029 kgms at 20C Table A3 and 001 kgms at 100C Fig A1 Write the critical Reynolds number in terms of flow rate Q 344891 VDQkgmQa Re2300critDk g m s m029 005 33mm106QA n ssolve00293ahs344891 VDQkgmQb Re2300crit0010 005 Dk g m s m33mm36solve000101bQA n shs65 In flow past a body or wall early transition to turbulence can be induced by placing a trip wire on the wall across the flow as in Fig P65 If the trip wire in Fig P65 is placed where the local velocity 850 is U it will trigger turbulence if Udwhere d is the wire diameter Ref 3 of Ch 6If the sphere diameter is 20 cm and transition Fig P65 90000 what is the is observed at ReDdiameter of the trip wire in mm Solution For the same U andUdUDRe850Re90000dD Re850d19mmordD200 mm Re90000D 366 A fluid at 20C flows at 850 cms through an 8cmdiameter pipe Determine the entrance length if the fluid is a hydrogen b air c gasoline d water e mercury and f glycerin VD where V4Q Solution Tabulate the kinematic viscosities and compute ReD232D4850E6 ms008 m0169 ms Thus Re016900800135 D
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