HOMEWORK ASSIGNMENT #7

ME 303 FLUID DYNAMICS/ WESTPHAL/ WSU/ FALL 2000

• Follow the Homework Guidelines for preparing your submission.
• You are encouraged to work together with other students, but the work you submit cannot be a machine-produced duplication of another student's work - it must be an original, but can represent your version of a collaborative effort.
• Late work not accepted!

The assignment consists of the problems given below.

1. A student in this class, Peter Omel, is studying the flight of an archer's arrow. The arrow's launch speed is 90 m/s in air at 101 kPa (abs) and 20 deg C, its length is 76.7 cm, and diameter is 7.5 mm. Treating the arrow as a flat plate and assuming Re(critical)=0.5 x 10⁶, calculate the following at the given launch condition:
   • Reynolds number based on length,
   • friction drag coefficient,
   • friction drag force experienced by the arrow.
   You may OMIT DISCUSSION for this problem.
   
   
2. The wing of a Cessna 152 airplane is, approximately, a smooth 10.2 m wide (the "span" dimension") by 1.5 m long (the "chord" dimension) flat plate. At its 55 m/s cruise speed under standard sea level conditions and assuming Re(critical)=0.5 x 10⁶, find:
   • friction drag force on the wing (BOTH SIDES!);
   • power required just to overcome the friction drag on the wing;
   • transition location, expressed as percent of chord;
   • boundary layer thickness at wing trailing edge calculated assuming the flow is entirely turbulent.
   You may OMIT DISCUSSION for this problem.
   
   
3. A former student in this class, Justin Nichols, is involved in evaluating the performance of a new "catamaran" style hull to be used for ferries in Puget Sound. For his evaluation, a 1/6 (one-sixth) scale model test is to be done. The total wetted hull area for the model is 100 square feet, and the waterline length of the model is 25 feet. Estimate the viscous (friction) drag on the model if it is tested at a speed of 15 knots (0.869 knots = 1 mile per hour) in 15 deg C fresh water. If the entire model hull surface is very smooth, where will transition occur? HINT: Use figure 9.13; in so doing, you are assuming that the hull behaves approximately as a flat plate for purposes of calculating the friction drag. DISCUSSION: suppose the model surface is roughened slightly so that turbulence occurs right at the bow... would you expect much change in the friction drag?
   
   
4. 11.20 DISCUSSION: How would the added power requirement change if there were a 5 m/s headwind?
   
   
5. 11.22 OMIT DISCUSSION
   
   
6. Hollow cylindrcal support towers, really just a pipe with a ladder inside, have become popular for modern wind turbines. A nearby 25 MW (rated) project has 38 turbines on such towers of 1.5 m diameter and 55 m height. Calculate the moment at the tower base and vortex shedding frequency expected for both rated (10 m/s) and severe (30 m/s) winds. Assume standard sea level atmospheric conditions. Use figure 11.10 to get the Strouhal number for the vortex shedding. DISCUSSION: Why would we care about the vortex shedding?
   
   
7. 11.43 DISCUSSION: How does terminal velocity vary with diameter?
   
   
8. 11.52 OMIT DISCUSSION