Individual Submissions
Read carefully the Reference section and the Competition Rules for the Wind Turbine Project and answer the following.
1. The 20-inch box fan used in Project 1 consumes about 85 watts of electricity (on high setting) and delivers a useful stream of air moving with the maximum velocity of about 15 feet per second. Estimate the mechanical power of wind (or the kinetic power of the moving air) from equation 3 2 1 Pwind = ρAVwind (in watts). Assume that the fan generates a ‘tube' of wind 20 inches in diameter and with uniform wind speed of 15 ft/s. What is the efficiency of the power conversion in the fan (in percent)? Convert all non-SI units to SI units.
2. In real wind turbines mechanical power of wind Pwind is first converted to shaft power of the turbine rotor Protor, then the a gear box converts it to shaft power of an electric generator Pgenerator , finally the generator converts it into electric power Pelectric. If the efficiency of the three power conversion steps are ηblades = 30% , ηgearbox = 88% and ηgenerator = 95% , respectively, what is the overall power conversion efficiency of the whole wind turbine? Draw a block schematic showing the flow of power into and out of each power conversion stage.
3. If an 18-inch diameter turbine rotor spins at 90 revolutions per minute (or rpm), and the wind speed is 15 ft/s, what is the resulting tip speed ratio VtipVwindΩ=/? Perform your calculations in US Customary units (do not convert to SI). Examining the Reference section, what levels of power coefficient CP can you expect from the turbine you are building in the Wind Turbine Project? Note that the power coefficient CP is synonymous with ηblades discussed in Problem 2.
Format for Technical Homework Assignments:
Given: (Brief statement of the problem and given information) Required: (State the required results) Solution: (Solve the problem. Failure to follow the listed instructions can cost you points!)
1. Use of 8.5"x11" quadrille paper (grid on back side paper) is recommended. Unlined 8.5" x 11" white paper or regular grid paper is permitted. Write on one side only and staple your homework at the top left hand corner. Use the heading as shown above and number all pages in the top right-hand corner.
2. It is permissible to solve more than one problem per page. However, problems MUST be clearly distinguished by drawing a solid line to separate the end of one problem from the start of the next problem. In general, provide ample space so that your work is easy to follow.
3. Use pencil (not pen) for your solutions.
4. Include neat, proportionate, clear drawings showing all quantities involved. Use of a ruler or straight edge is highly recommended. Neat freehand drawings are acceptable.
5. List any assumptions necessary for obtaining the solution.
6. Draw any diagrams which can explain your solution method (such as energy flow, wiring diagram, free body diagrams, etc...).
7. State clearly the equation/s used in your solution. The solution must be based on the fundamental principles of the topic.
8. Follow appropriate rules of algebra to manipulate equations.
9. Specify and check the units of each quantity as you proceed.
10. Your numerical answers should not have more than 4 significant figures, unless specified by the solution method.