7.27 A thin smooth disk of diametd., D is immersed parallel to a uniform stream of velocity U. Assuming laminar flow and using flat-plate theory as a guide, develop an approximate formula for the drag of the disk.
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- A Savonius rotor can be approximatedby the two open half-tubes in Fig mounted ona central axis. If the drag of each tube is similar to thatin Table 7.2, derive an approximate formula for therotation rate Ω, as a function of U, D, L, and the fluidproperties (ρ, μ).Assume the stabilizer of an airplane is a flat plate. If the transition /critical RN 750,000, what is the skin-friction drag of a rectangular stabilizer having a span of 1.73 m and a chord of 0.81 m at a speed of 44.7 meters per second? Assume standard sea level conditions.-round off to 4 decimal places-show complete solutionIcebergs can be driven at substantial speeds by the wind.Let the iceberg be idealized as a large, flat cylinder, D >> L,with one-eighth of its bulk exposed, as in Fig.. Letthe seawater be at rest. If the upper and lower drag forcesdepend on relative velocities between the iceberg and thefluid, derive an approximate expression for the steady icebergspeed V when driven by wind velocity U.
- The main cross-cable between towers of a coastal suspensionbridge is 60 cm in diameter and 90 m long. Estimatethe total drag force on this cable in crosswinds of 50 mi/h.Are these laminar flow conditions?Consider Mach 4 flow at standard sea level conditions over a flat plateof chord 5 in. Assuming all laminar flow and adiabatic wall conditions,calculate the skin-friction drag on the plate per unit span.Suppose that the solid-propellant rocket isbuilt into a missile of diameter 70 cm and length 4 m. Thesystem weighs 1800 N, which includes 700 N of propellant.Neglect air drag. If the missile is fi red vertically fromrest at sea level, estimate ( a ) its velocity and height at fuelburnout and ( b ) the maximum height it will attain.
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- Determine the velocity required for take off for an aircraft with the following characteristics.Aircraft mass: 7200 kgWingspan: 15 mWing shape: rectangularWing chord length: 1.8 mWing airfoil: NACA 4415Wing angle of attack: 7× 0.5 + 5 degreesHint: Check NACA charts for required parameters.The original Flettner rotor ship was approximately 100 ftlong, displaced 800 tons, and had a wetted area of 3500 ft2. Assketched in Fig. , it had two rotors 50 ft high and 9 ft indiameter rotating at 750 r/min, which is far outside the range. The measured lift and drag coefficients for eachrotor were about 10 and 4, respectively. If the ship is mooredand subjected to a crosswind of 25 ft/s, as in Fig. whatwill the wind force parallel and normal to the ship centerlinebe? Estimate the power required to drive the rotors.Air equivalent to one of a standard height of 4000 m flows at 450 mi/h over a wing with a thickness of 18 cm, a chord of 1.5 m, and a wingspan of 12 m. What is the appropriate value of the Reynolds number to correlate lift and drag on this wing?