Assume Patm = 10^5, Pa = 14.7 psi ; ρwater ~ 1000 kg/m3 ; ρair ~ 1.2 kg/m3 ; μwater ~ 10^-3 N•s/m2 ; μair ~ 2 x 10^-5 N•s/m2 ; Vwater ~ 10^-6 m2 /s ; Vair ~ 1.67 x 10^-5 m2 /s ; g = 9.8 m/s^2 .; 1 m/s = 2.24 mph ; 1lbf = 4.45 N ; 1 m^3 = 264 gallons leDOLOFairingShape2. Jom www..wow.www.www.Six-car passenger trainLooD FlutteringflagEmpireState BuildingBikesParachuteAveragepersonPorousparabolicdishRacingOo ooUpright commuterTractor-trailor tucks600 00Gap sealDraftingStreamlined.00TreeStandardWith fairingWithfairing andgap sealU= 10 m/sU = 20 m/sU = 30 m/sDolphinLargebirdsReference areaFrontal areaA=4D²Frontal areaA=4D²StandingSittingCrouchingA =lDFrontal areaFrontal areaA= 5.5 ft2A = 3.9 ft²A = 3.9 ft2A = 5.0 ft²Frontal areaFrontal areaFrontal areaFrontal areaWetted areaFrontal areaDrag coefficientCD1.4Porosity00.2 0.51.42 1.20 0.820.95 0.90 0.80Porosity = open area/total areaCDA = 9 ft²C₂A = 6 ft²CDA=2.5 ft²e/D123 0.15CD0.070.121.41.81.10.880.500.120.960.760.700.430.260.200.0036 at Re = 6 x 105(flat plate has Cpf = 0.0031)0.40FIGURE 9.21 Typical drag coefficients for objects of interest (Refs.4, 5, 11, and 14). Drag, Cyclist. A cyclist in an upright commuter position can generate sufficient power to achieve amaximum speed of 10 m/s on a calm day with no wind, on a flat surface. The total mass of the rider andbike is 100 kg. The rolling resistance for the tires (a constant force) is FR = 10 N. Comparing powerrequirements, using drag data from fig. 9.21, pg. 356: (a) what is the max power for the biker? (b) whatmaximum speed can the cyclist reach in a racing position in still air exerting the same power? (c) what is themaximum speed in a racing position but against a head wind of 5 m/s?Ans OM: (a)~ 10² W; (b)~ 10¹ m/s; (c)~ 10⁰m/sVBVw

Given data: maximum speed with no wind V = 10 m/s Total mass of the rider and bike = 100 kg Rolling resistance for the tires FR= 10 N Find: (a) what is the max power for the biker? (b) what maximum speed can the cyclist reach in a racing position in still air exerting the same power? (c) what is the maximum speed in a racing position but against a head wind of 5 m/s? Solution: (a) what is the max power for the biker? From the above table CD,upright=0.88 and Aupright = 3.9 ft2 max power = Power to account for rolling resistance + power to account for air resistance=FR*V +FD*V= FR*V +12CD,upright ρairV2Aupright*V=10*10+12*1.1*1.2*102*5.5*0.093*10=437.59 W (b) what maximum speed can the cyclist reach in a racing position in still air exerting the same power? From the above table CD,racing=0.88 and Aracing = 3.9 ft2 max power = Power to account for rolling resistance + power to account for air resistance437.59=FR*V +FD*V437.59= FR*V +12CD,racingρairV2Aracing*V437.69=10*V+12*0.88*1.2*V2*3.9*0.093*V437.69=10V+0.1915V3 Solving the above equation we will have V=11.85 m/s (c) what is the maximum speed in a racing position but against a head wind of 5 m/s? for wind speed condition air speed accounting for drag force will be Vair=V+Vwind , so for same maximum powermax power = Power to account for rolling resistance + power to account for air resistance437.59=FR*V +FD*V437.59= FR*V +12CD,racingρair(V+Vwind)2Aracing*V 437.69=10*V+12*0.88*1.2*(V+5)2*3.9*0.093*V Solving the above equation we will haveV=9.101 m/s