FDSCI 200 Energy in the 21st Century Homework 8 Hydroelectricity Name _________________ 20 points (2 pts) Show your work. 1- A spring above your remote cabin is delivering water at a rate of 1000 gallons per minute through a 13 inch pipe with 10 feet of head. How fast is the water traveling in feet per second? How many kW is the system capable of producing with an 80% efficiency? 2. The radius of this pipe is 45 cm and the length is 14 feet with 30 feet head. A flow meter mounted on the pipe reports the velocity to be at 8 feet per second. What is the discharge (Q)? How many 200 watt solar panels is this equal to? The generator has 75% efficiency. 3. A rectangular concrete channel or flume is 3 feet wide and the water depth is 24 inches. The discharge is 14 feet per second. What is the velocity in feet per second? 4. A stream flowing at 5 feet per second has a cross-sectional area of 34 square feet. How many gallons per minute is discharge? 5. Poseidon is willing to provide math tutoring for this class if you can beat him in a race across a 1 mile (5280 feet) wide lake. He can swim at a rate of 5 feet per second. You can swim the distance in 16 minutes. What will the result be? 6. The spring near your gold mine is producing 800 gpm through an 8 inch pipe and dropping 75 feet. Your buddy has an 84% efficient generator he will sell. You are making about $5000 in gold revenue per year. You are buying electricity for 0.15/KwH and can sell it to the power company for 0.10/KwH. Is it more economical for you to mine gold or convert your water power entirely to hydroelectrical production? 7. A hydroelectric plant in receives water from a penstock with 45 feet head. The Q is 250 cfs. The turbine was recently upgraded to a .90 efficient unit. In 2014, the average annual electricity consumption for a U.S. residential utility customer was 10,932 kilowatt hours (kWh), an average of 911 kWh per month. Louisiana had the highest annual consumption at 15,497 kWh per residential customer, and Hawaii had the lowest at 6,077 kWh per residential customer. How many people can be served by this plant if it was located in Louisiana?__________Hawaii? ________ 8. Your microhydro penstock provides 1500 gallons per minute through a 4 inch pipe into your Pelton wheel. The bearings in your generator are rated for water traveling no faster than 25 fps. Do you have a problem or is this system matched well? 9. A stream is 8 feet wide. The following depth measurements were made at 1 foot intervals. 1.2 1.3 1.67 2.3 3.2 3.3 1.8 0.76 An orange was used to measure the velocity of flow over a 100 foot distance and repeated three times for the same stream. The time of travel was 45 seconds 47 seconds 52 seconds What is the Q for the stream? 10. A stream flowing at 5 feet per second has a cross-sectional area of 34 square feet. How many gallons per day is discharged