Problem 4.101[Difficulty: 3]CS x cy 2h dGiven:Data on flow in 2D channelFind:Maximum velocity; Pressure dropSolution:Basic equations: Continuity, and momentum flux in x directionAssumptions: 1) Steady flow 2) Neglect frictionGiven dataw25mm⋅=h50mm⋅=Q0.025m3s⋅=ρ750kgm3⋅=From continuityQU12⋅h⋅w⋅=U1Q2w⋅h⋅=U110.0ms=Alsoρ−U1⋅A1⋅Aρu2⋅⌠⎮⎮⌡d+0=U12⋅h⋅w⋅wh−hyumax1y2h2−⎛⎜⎝⎞⎠⋅⌠⎮⎮⎮⌡d⋅=wumax⋅hh−()−h3h3−⎛⎝⎞⎠−⎡⎣⎤⎦−⎡⎣⎤⎦⋅=max⋅43⋅h⋅=Henceumax32U1⋅=umax15ms=For x momentump1A⋅p2A⋅−V1ρ1−V1⋅A⋅⋅A2ρ2u2⋅u2⋅⌠⎮⎮⌡d+=Note that there is no Rx(no friction)p1p2−
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.