a. at 500 mph at 35,000 ftb. at 200 mph at sea levelThe wing area is 2400 ft2.
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12.2 Find a velocity profile for the laminar boundary layer of the form...when the pressure gradient is not zero.
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12.3 There is fluid evaporating from a surface at which vx|y=0 = 0, but vx|y=0 ≠ 0. Derive the von Kármán momentum relation.
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12.4 The drag coefficient for a smooth sphere is shown below. Determine the speed at the critical Reynolds number for a 42-mm-diameter sphere in air....
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12.5 Estimate the drag force on a 3-ft radio antenna with an average diameter of 0.2 in. at a speed of 60 mph.
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12.6 Estimate the normal force on a circular sign 8 ft in diameter during a hurricane wind (120 mph).
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12.7 A 1998 Lexus LS400 has a drag coefficient of 0.28 and a reference area of 2.4m2. Determine the horsepower required to overcome drag when driving at 70 mph at sea level.
a. On a hot summer day T≅100°F
b. On a cold winter day T≅0°F
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12.8 Golfball “dimples” cause the drag drop (see Figure 12.4 and the illustration for Problem 12.7) to occur at a lower Reynolds number. The table below gives the drag coefficient for a rough sphere as a function of the Reynolds number. Plot the drag for a 1.65-in.-diameter sphere as a function of velocity. Show several comparison points for a smooth sphere.
| Re · 10–4 | 7.5 | 10 | 15 | 20 | 25 |
| CD | 0.48 | 0.38 | 0.22 | 0.12 | 0.10 |
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12.9 If the vertical velocity at the wall is not zero such as would be the case with suction or blowing, what modifications occur to equation (12-33)?... (12-33)
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12.10 In a house, water flows through a copper tube with a 0.75-in. ID, at a flow rate of 2 gpm. Determine the Reynolds number for
a. hot water (T ≅ 120°F)b. cold water (T ≅ 45°F)
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12.11 For the fully developed flow of water in a smooth 0.15-m pipe at a rate of 0.006m3/s, determine the thickness of
a. the laminar sublayerb. the buffer layerc. the turbulent core
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12.12 For a thin a plate 6 in. wide and 3 ft long, estimate the friction force in air at a velocity of 40 fps, assuming
a. turbulent flowb. laminar flowThe flow is parallel to the 6-in. dimension
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12.13 Estimate the friction drag on a wing by considering the following idealization. Consider the wing to be a rectangular flat plate, 7 ft by 40 ft, with a smooth surface. The wing is flying at 140 mph at 5000 ft. Determine the drag, assuming
a. a laminar boundary layerb. a turbulent boundary layer
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12.14 Use the one-seventh power-law profile and compute the drag force and boundary layer thickness on a plate 20 ft long and 10 ft wide (for one side) if it is immersed in a flow of water of 20 ft/s velocity. Assume turbulent flow to exist over the entire length of the plate. What would the drag be if laminar flow could be maintained over the entire surface?
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12.15 Evaluate the velocity derivative, ..., for the power-law velocity profile at y=0 and y=R.
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12.16 Air, water, and glycerin, each at 80°F, are flowing through separate 0.5-in. diameter tubes at a velocity of 40 ft/s. Determine, for each case, whether the follow is laminar or turbulent.
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12.17 Water at 20°C is flowing along a 5-m-bng flat plate with a velocity of 50 m/s. What will be the boundary layer thickness at a position 5 m from the leading edge? Is the boundary layer flow at this location laminar, or turbulent? If each of the plate surfaces measures 500 m2, determine the total drag force if both sides are exposed to the flow....
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