Hydroelectric power is a major source of electricity in both California and the United States. In 2008 6.2% of the electricity in America was generated using hydroelectric power (11.6% in CA). [1] This electricity is typically generated by large scale dam projects that block rivers and pass water over turbines. In this fashion, the amount of electricity that can be generated ranges from a few kilowatts to hundreds of megawatts. The streams and rivers effectively funnel the amount of rainfall covering a huge land area into a concentrated flow with enough kinetic and potential energy to justify large infrastructure projects to power a large number of households. This webpage looks to describe the energy generating potential of a single US household using only the amount of precipitation falling on their home and compares it to the annual household electric usage of about 6000-10000kWh per year. [2,3]
Any body of mass that has been raised above the Earth's surface has a potential energy relative to the same mass on the Earth's surface. As explained above, by running elevated water over a turbine, some of this potential energy can be converted into kinetic and electrical energy. In the water cycle, water evaporates via solar energy and gains potential energy that is then lost again when the water precipitates. This cycle of evaporation, rain, turbine, provides a mechanism for the conversion of solar into electrical energy. At best, the amount of electrical energy that can be generated is equal to the potential energy of the rain.
This gravitational potential energy is simply equal to the product of mass, height, and gravitational constant (9.81 m/s2). For example, the potential energy of a cubic meter of water (1000kg) in a stratus cloud at 2000 m of elevation is about 20 MJ, or 5.5 kWh. This means that in a region where the average amount of rain is about 0.40 m, the total amount of rain potential energy lost over a 1 km2 plot of land is about 7.8 x 1012 J, 2.18 x 106 kWh, or enough energy for about 220 homes. Unfortunately, the vast majority of this energy is lost via friction with the air during the rain fall. The next section looks at the total amount of kinetic energy that is still present when the rain hits the ground.
In order to account for the total amount of amount of potential energy that practically be used, assume that the rain is funneled (via home gutters) and then stored into a tank located about roof level, say, 7 m off the ground. The total amount of potential energy of the rain water in the tank would be equal to about 70 kJ per cubic meter of water. As an example, if the total roof space were about 185 m2 (2000 sq feet), the amount of potential energy would be 130 kJ (0.036 kWh) per cm of rain. In a college town where the amount of rain is only about 43 cm/year, this amounts to only about 1.5k Wh. Even in the rainiest place on earth (13.3m in Lloro, Colombia) the amount of energy generated would be 48kWh. [7] In order to capture enough rain for a years worth of energy, the amount of surface area at 7 m and exposed to 100 cm of rain per year would need to be about 515000 m2. This assumes a perfectly efficient generator, which does not exist.
|
||||||||||||||||||||||||||||||||
| Table 1: Examples of the potential energy of rain on the roof of two buildings and into the Columbia River Basin | ||||||||||||||||||||||||||||||||
Instead of relying entirely on rainfall to fill the tank of water on top of the house, a home owner could have a similarly sized tank (or pool) at ground level and build a mechanism catching water that rises due to evaporation. This would be the same conversion of solar thermal energy into electricity as explained above. The average amount of water that can be evaporated per unit of surface varies in California, with a peak of 404 cm in Death Valley and a value of about 182 cm in the San Francisco area. [8] If the evaporation was taking place from a pool of the same size as the roof tank (185 m2 to a tank 7 m high) above, the total amount of energy harvested would be about 6.42 kWhr at Stanford and 14.3 kWr in Death Valley. Again, not nearly enough to power a home.
Finally, another (obviously horrible) idea is to fill the potential energy tank on top of house via a garden hose. Since the homeowner does not directly run/pay for the water pump, this would not be a net electricity loss when looked at from the home's perspective. Assuming a garden hose can output 6 gallons per minute (456 x $10-6 m3/s) onto the rooftop, the total amount of power generated is about 31W. Running this hose for an hour would generate about $0.003 worth of electricity while consuming 360 gallons, or about $1, of water (approximately 2000x more expensive).
Studying the total amount of rainfall on an entire river valley, yields vastly different results. For example, the size of the Columbia River basin is about 668 x 109 m2. Making (my own) estimate that half of this land drains upstream of the the Grand Coulee Dam, this means that the exposed surface area for rain collection is about 334 x 109 m2. The Grand Coulee dam itself is about 170 m high and generates 21 x 109 kWh per year. [9] This means that, on average, 14 cm of rain that falls in the upper basin needs to reach the dam in order to provide it with enough potential energy (assuming perfect conversion) to generate its electricity. As a final limit, if all the rain that fell in the United States (an area of 9.62 x 1012 m2 and depth of 76.2 cm) was passed over a structure the height of the dam, a total of 3.4 x 1012 kWh could be produced. While this number is still only 80% of the total US electrical production, it is worth mentioning that the US hydroelectric production is already at 7.5% of this number. [1]
As shown above, trapping rain, storing it, and running it past a turbine is one mechanism of converting the energy of rainfall into electricity. Another option that can be used in tandem is to capture the kinetic energy of the rain directly. This can be done using piezoelectricity, where crystals convert mechanical motion into electricity.
Again making the unrealistic assumption of perfect conversion, the amount of kinetic energy in a object is half the mass times the velocity squared. The velocity of rain is limited by air resistance and typically has a maximum of around 8 m/s [4]. Doing the calculation, the amount of kinetic energy falling on a 185 m2 roof is about 59.2 kJ (0.016 kWh) per cm of rain. This is only about 1.6 kWh of energy per year in an area that receives a meter of rain per year. As an unrealizable limit, the total amount of rain kinetic energy over the USA is about 65 billion kWh (a quarter of the total energy use).
There are practical applications that arise from this effect, however. Recent research has demonstrated how this effect can power small sensors that use only a little amount of energy and are inconvenient to power by other means. [5,6]
This article shows basic calculations and estimates for the amount of energy that could potentially be harvested from rain. In moderate scales, there is little potential for energy generation using either the potential or kinetic energy of falling water. In the gigantic scale, however, where nature has carved out a large basin to catch rainfall, dams and turbines can be installed to produce significant amounts of electricity. On small sensors, the kinetic energy of rain can provide enough energy in order to sustain operation. Overall, using precipitation to generate electricity can be used situationally to compliment other technologies, but is not an end solution.
© Curt Harting. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] M. Bowles, State Electricity Profiles 2008," US Energy Information Administration," DOE/EIA 0348(01)/2, March 2010.
[2] O. Dzioubinski and R. Chipman, "Trends in Consumption and Production: Household Energy Consumption," United Nations Department of Economic and Social Affairs, ST/ESA/1999/DP.6, April 1999.
[3] R. Brown and J. Koomey, "Electricity Use in California: Past Trends and Present Usage Patterns," Energy Policy 31, 849 (2003).
[4] R. Gunn and G. D. Kinzer, "The Terminal Velocity of Fall for Water Droplets in Stagnant Air," J. Atmosph. Sci. 6, 243 (1949).
[5] R. Guigon et al. "Harvesting Raindrop Energy: Experimental Study," Smart Materials and Structures 17, 015039 (2008).
[6] R. Guigon et al. "Harvesting Raindrop Energy: Theory," Smart Materials and Structures 17, 091038 (2008).
[7] P. F. Krause and K. L. Flood "Weather And Climate Extremes," US Army Corps of Engineers, Technical Report TEC-0099, September 1997.
[8] R. Farnsworth and E. Thompson, "Mean Monthly, Seasonal, and Annual Pan Evaporation for the United States," U.S. national Oceanic and Atmospheric Administration, NOAA Technical Report NWS 34, December 1982.
[9] L. Ortolano and K. Kao Cushing, "Grand Coulee Dam and the Columbia Basin Project, USA," World Commission on Dams, November 2000.