1.060 Engineering Mechanics II Spring 2006Recitation 8 - ProblemsApril 20th and 21stProblem 1Water flows in a long straight channel whose trapezoidal cross section shown in Figure 1.The horizontal bottom is finished concrete and the sides are weedy. The bottom slope isS0= 0.001. The water depth over the horizontal bottom is 1 m.a) Determine the discharge, Q.b) Determine the corresponding mean velocity, V .c) Determine the Froude number, Fr, of the flow.d) Is the flow super- or subcritical?Figure 1: Trapezoidal channel in Problem 1.Problem 2A long glass-walled laboratory flume has a rectangular cross-section of width 1 m, a slopeof S0= 10−4, and it discharges water at a flowrate Q = 0.5 m3/s.a) Find the critical depth, hc.b) Find the normal depth, hn, corresponding to steady uniform flow.c) Does the normal depth correspond to super- or subcritical flow?Recitation 8-1Recitation 8-2Values of the Manning Coefficient, n (Ref 5)Wetted PerimeternNatural ChannelsClean and straightSluggish with deep poolsMajor riversFloodplainsPasture, FarmlandLight brushHeavy brushTreesExcavated Earth ChannelsCleanGravellyWeedyStony, CobblesArtifically lined channelsGlassBrassSteel, SmoothSteel, PaintedSteel, RivetedCast ironConcrete, FinishedConcrete, UnfinishedPlaned WoodClay tileBrickworkAsphaltCorrugated metalRubble masonry0.0300.0400.0350.0350.0500.0750.150.0220.0250.0300.0350.0100.0110.0120.0140.0150.0150.0160.0220.0250.0130.0120.0120.0140.014Table by MIT OCW.Recitation 8-20.050.040.030.020.0150.010.0080.0060.0040.0020.0010.00080.00060.00040.00020.00010.000.050.000.010.090.080.070.060.050.040.030.0250.020.0150.010.0090.0081051041031061072(103) 2(104) 2(105) 2(106) 2(107)4 53 46 68 8 4 5 6 83 4 5 6 83 4 5 6 833VDυ2 4 6 8 10 20 40 60 100 200 400 600 800 1000 2000 4000 6000800010000 20,000 40,000 60,00080,000100,0000.100.1 0.2 0.4 0.6 0.8 1 2 4 6 8 10 20 40 60 80 100 200 400 600 800 1000 2000 4000 6000800010,000Laminar FlowCriticalZoneTransitionZoneComplete turbulence rough pipesSmooth PipesLaminar Flow64ReRe5Reynolds Number Re = εDRelative roughness=ε/(4Rh)εD=0.000.005εD=0.000.001Friction factor f - hLDV22gD = 4Aρ= 4RhVDυ υRe = = υ(4Rh)Values of (VD') for atmospheric air at 60oValues of (VD') for water at 60o F (velocity, ft/s, diameter.in)The Moody chart for pipe friction with smooth and rough walls. This chart is identical to Eq. (6.64) for turbulent flow. f.Graph by MIT