Elementary Mechanics of FluidsApproaches to Solving Fluids ProblemsSystemsControl VolumesCV Inflow & OutflowSlide 6Reynolds Transport TheoremSteady vs. Unsteady CVContinuity EquationExample (4.57)Example (4.61)HW (4.80)HW (4.81)HW (4.82)Elementary Mechanics of FluidsCE 319 FDaene McKinneyControl VolumesApproaches to Solving Fluids Problems•Experimental Analysis•Differential Analysis•Control Volume Analysis–Single most valuable tool available (White, Ch. 3)Systems•Laws of Mechanics–Written for systems–System = arbitrary quantity of mass of fixed identity–Fixed quantity of mass, m0dtdmdtmd )( VFdtdWdtdQdtdE•Conservation of Mass–Mass is conserved and does not change•Momentum–If surroundings exert force on system, mass will accelerate•Energy–If heat is added to system or work is done by system, energy will changeControl Volumes•Solid Mechanics–Follow the system, determine what happens to it•Fluid Mechanics–Consider the behavior in a specific region or Control Volume•Convert System approach to CV approach–Look at specific regions, rather than specific masses•Reynolds Transport Theorem–Relates time derivative of system properties to rate of change of property in CV)(extensiveenergymomentum,mass,CVCVdbbdmB)(intensivemassunitperofamount BdmdBbCV Inflow & OutflowArea vector always points outward from CVAVQCSinoutAVAVQQAVAVAV11221122CV Inflow & OutflowCSCSinoutinoutnetmbbmbmbBBBAVBmbinoutttCVttsysinoutttCVttsysBBBBMMMM,,,,Reynolds Transport TheoremCSCVsysnetCVinoutttCVttCVttCVinoutttCVttCVtttsysbdbdtddtdBBdtdBtBBtBBtBBBBtBBdtdBAV0,,0,,0,0limlimlimlimSteady vs. Unsteady CVCSCVsysbdbdtddtdBAVCSsysbdtdBAVContinuity Equation•Reynolds Transport Theorem)(extensivesysMB )(intensive1dmdMdmdBbsysCSCVsysbdbdtddtdBAVCSCVddtdAV0CSAV0Unsteady Case Steady CaseExample (4.57)•Continuity equationsmVgVxAVAVdtdhAAVAVhAdtdddtdininoutoutinintankoutoutinintankCSCV/47.4)0025.0(1*2)0025.0(101.0*1.0)(02AVExample (4.61)•Select a CV that moves up and down with the water surface•Continuity EquationCSVA=2VBVBrisingissurface0)(20;6;32002141412424BBBBBBBABABBABCVCSCVAVdtdhAAVAVdtdhAAAAAAVAVddtdddtdAVhHW (4.80)HW (4.81)HW