106-523: The National Hydropower Association (NHA) represents the interests of the U.S. hydropower industry, which includes all forms of water energy—conventional, hydrokinetic, tidal and ocean. Since 1983, NHA has represented the majority of domestic, non-federal hydroelectric producers. The association has some 200 members which include public utilities, investor-owned utilities, independent power producers, equipment manufacturers, environmental and engineering consultants, and hydropower attorneys from all regions of
212-541: A Sig-Fig Calculator mode in which the calculator will evaluate the count of significant digits of entered numbers and display it in square brackets behind the corresponding number. The results of calculations will be adjusted to only show the significant digits as well. For the HP 20b / 30b -based community-developed WP 34S (2011) and WP 31S (2014) calculators significant figures display modes SIG + n and SIG0 + n (with zero padding) are available as
318-423: A normalized number (i.e., a × 10 with 1 ≤ a < 10 and b as an integer), is rounded such that its decimal part (called mantissa ) has as many significant figures as the significant figures in the normalized number. When taking the antilogarithm of a normalized number, the result is rounded to have as many significant figures as the significant figures in the decimal part of the number to be antiloged. If
424-480: A transcendental function f ( x ) {\displaystyle f(x)} (e.g., the exponential function , the logarithm , and the trigonometric functions ) is differentiable at its domain element 'x', then its number of significant figures (denoted as "significant figures of f ( x ) {\displaystyle f(x)} ") is approximately related with the number of significant figures in x (denoted as "significant figures of x ") by
530-490: A Southern Europe hydropower race. In Italy's Po Valley , the main 20th century transition was not the creation of hydropower but the transition from mechanical to electrical hydropower. 12,000 watermills churned in the Po watershed in the 1890s, but the first commercial hydroelectric plant, completed in 1898, signaled the end of the mechanical reign. These new large plants moved power away from rural mountainous areas to urban centers in
636-443: A billion tonnes of CO2 greenhouse gas a year. This occurs when organic matters accumulate at the bottom of the reservoir because of the deoxygenation of water which triggers anaerobic digestion . People who live near a hydro plant site are displaced during construction or when reservoir banks become unstable. Another potential disadvantage is cultural or religious sites may block construction. A watermill or water mill
742-433: A city might only be known to the nearest thousand and be stated as 52,000, while the population of a country might only be known to the nearest million and be stated as 52,000,000. The former might be in error by hundreds, and the latter might be in error by hundreds of thousands, but both have two significant figures (5 and 2). This reflects the fact that the significance of the error is the same in both cases, relative to
848-407: A decimal (e.g., 1.0) is significant, and care should be used when appending such a decimal of zero. Thus, in the case of 1.0, there are two significant figures, whereas 1 (without a decimal) has one significant figure. Among a number's significant digits, the most significant digit is the one with the greatest exponent value (the leftmost significant digit/figure), while the least significant digit
954-433: A device to serve wine, and five devices to lift water from rivers or pools, where three of them are animal-powered and one can be powered by animal or water. Moreover, they included an endless belt with jugs attached, a cow-powered shadoof (a crane-like irrigation tool), and a reciprocating device with hinged valves. In the 19th century, French engineer Benoît Fourneyron developed the first hydropower turbine. This device
1060-435: A distance. A hydropower resource can be evaluated by its available power . Power is a function of the hydraulic head and volumetric flow rate . The head is the energy per unit weight (or unit mass) of water. The static head is proportional to the difference in height through which the water falls. Dynamic head is related to the velocity of moving water. Each unit of water can do an amount of work equal to its weight times
1166-536: A length measurement yields 114.8 mm, using a ruler with the smallest interval between marks at 1 mm, the first three digits (1, 1, and 4, representing 114 mm) are certain and constitute significant figures. Further, digits that are uncertain yet meaningful are also included in the significant figures. In this example, the last digit (8, contributing 0.8 mm) is likewise considered significant despite its uncertainty. Therefore, this measurement contains four significant figures. Another example involves
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#17328700073611272-427: A low-carbon means for economic development . Since ancient times, hydropower from watermills has been used as a renewable energy source for irrigation and the operation of mechanical devices, such as gristmills , sawmills , textile mills, trip hammers , dock cranes , domestic lifts , and ore mills . A trompe , which produces compressed air from falling water, is sometimes used to power other machinery at
1378-460: A microturbine in a cylindrical housing. Electricity generated by that turbine is used to charge 12-volt batteries." The term rain power has also been applied to hydropower systems which include the process of capturing the rain. Evidence suggests that the fundamentals of hydropower date to ancient Greek civilization . Other evidence indicates that the waterwheel independently emerged in China around
1484-462: A more dependable source of power by smoothing seasonal changes in water flow. However, reservoirs have a significant environmental impact , as does alteration of naturally occurring streamflow. Dam design must account for the worst-case, "probable maximum flood" that can be expected at the site; a spillway is often included to route flood flows around the dam. A computer model of the hydraulic basin and rainfall and snowfall records are used to predict
1590-490: A mutual need for hydropower could lead to cooperation between otherwise adversarial nations. Hydropower technology and attitude began to shift in the second half of the 20th century. While countries had largely abandoned their small hydropower systems by the 1930s, the smaller hydropower plants began to make a comeback in the 1970s, boosted by government subsidies and a push for more independent energy producers. Some politicians who once advocated for large hydropower projects in
1696-446: A normal good quality ruler, it should be possible to estimate tenths between the nearest two marks to achieve an extra decimal place of accuracy. Failing to do this adds the error in reading the ruler to any error in the calibration of the ruler. When estimating the proportion of individuals carrying some particular characteristic in a population, from a random sample of that population, the number of significant figures should not exceed
1802-410: A number not containing a decimal point can be ambiguous. For example, it may not always be clear if the number 1300 is precise to the nearest unit (just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundreds due to rounding or uncertainty. Many conventions exist to address this issue. However, these are not universally used and would only be effective if
1908-421: A number requires knowing which digits are meaningful, which requires knowing the resolution with which the number is measured, obtained, or processed. For example, if the measurable smallest mass is 0.001 g, then in a measurement given as 0.00234 g the "4" is not useful and should be discarded, while the "3" is useful and should often be retained. The significance of trailing zeros in
2014-421: A number written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcome of a measurement (such as length, pressure, volume, or mass), if the number of digits exceeds what the measurement instrument can resolve, only the number of digits within the resolution 's capability are dependable and therefore considered significant. For instance, if
2120-525: A remote sensor." Villazon suggested a better application would be to collect the water from fallen rain and use it to drive a turbine, with an estimated energy generation of 3 kWh of energy per year for a 185 m roof. A microturbine-based system created by three students from the Technological University of Mexico has been used to generate electricity. The Pluvia system "uses the stream of rainwater runoff from houses' rooftop rain gutters to spin
2226-419: A result, the final answer is 1.234 + 1.234 + … + 1.234 = 11.10 6 = 11.106 (one significant digit increase). For quantities created from measured quantities via addition and subtraction , the last significant figure position (e.g., hundreds, tens, ones, tenths, hundredths, and so forth) in the calculated result should be the same as the leftmost or largest digit position among the last significant figures of
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#17328700073612332-712: A tool to interfere in the economic development of African countries, such as the World Bank with the Kariba and Akosombo Dams , and the Soviet Union with the Aswan Dam . The Nile River especially has borne the consequences of countries both along the Nile and distant foreign actors using the river to expand their economic power or national force. After the British occupation of Egypt in 1882,
2438-479: A turbine with 90% efficiency. He applied scientific principles and testing methods to the problem of turbine design. His mathematical and graphical calculation methods allowed the confident design of high-efficiency turbines to exactly match a site's specific flow conditions. The Francis reaction turbine is still in use. In the 1870s, deriving from uses in the California mining industry, Lester Allan Pelton developed
2544-578: A volume measurement of 2.98 L with an uncertainty of ± 0.05 L. The actual volume falls between 2.93 L and 3.03 L. Even if certain digits are not completely known, they are still significant if they are meaningful, as they indicate the actual volume within an acceptable range of uncertainty. In this case, the actual volume might be 2.94 L or possibly 3.02 L, so all three digits are considered significant. Thus, there are three significant figures in this example. The following types of digits are not considered significant: A zero after
2650-535: Is a mill that uses hydropower. It is a structure that uses a water wheel or water turbine to drive a mechanical process such as milling (grinding) , rolling , or hammering . Such processes are needed in the production of many material goods, including flour , lumber , paper , textiles , and many metal products. These watermills may comprise gristmills , sawmills , paper mills , textile mills , hammermills , trip hammering mills, rolling mills , and wire drawing mills. One major way to classify watermills
2756-419: Is a recent standard, ISO 5725, which keeps the same definition of precision but defines the term "trueness" as the closeness of a given measurement to its true value and uses the term "accuracy" as the combination of trueness and precision. (See the accuracy and precision article for a full discussion.) In either case, the number of significant figures roughly corresponds to precision , not to accuracy or
2862-423: Is an attractive alternative to fossil fuels as it does not directly produce carbon dioxide or other atmospheric pollutants and it provides a relatively consistent source of power. Nonetheless, it has economic, sociological, and environmental downsides and requires a sufficiently energetic source of water, such as a river or elevated lake . International institutions such as the World Bank view hydropower as
2968-501: Is available on demand to be used to generate electricity by passing through channels that connect the dam to the reservoir. The water spins a turbine, which is connected to the generator that produces electricity. The other type is called a run-of-river plant. In this case, a barrage is built to control the flow of water, absent a reservoir . The run-of river power plant needs continuous water flow and therefore has less ability to provide power on demand. The kinetic energy of flowing water
3074-400: Is by an essential trait about their location: tide mills use the movement of the tide; ship mills are water mills onboard (and constituting) a ship. A plentiful head of water can be made to generate compressed air directly without moving parts. In these designs, a falling column of water is deliberately mixed with air bubbles generated through turbulence or a venturi pressure reducer at
3180-445: Is by using hybrid solar panels called "all-weather solar panels" that can generate electricity from both the sun and the rain. According to zoologist and science and technology educator, Luis Villazon, "A 2008 French study estimated that you could use piezoelectric devices, which generate power when they move, to extract 12 milliwatts from a raindrop. Over a year, this would amount to less than 0.001kWh per square metre – enough to power
3286-420: Is by wheel orientation (vertical or horizontal), one powered by a vertical waterwheel through a gear mechanism, and the other equipped with a horizontal waterwheel without such a mechanism. The former type can be further subdivided, depending on where the water hits the wheel paddles, into undershot, overshot, breastshot and pitchback (backshot or reverse shot) waterwheel mills. Another way to classify water mills
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3392-439: Is lost from erosion. Furthermore, studies found that the construction of dams and reservoirs can result in habitat loss for some aquatic species. Large and deep dam and reservoir plants cover large areas of land which causes greenhouse gas emissions from underwater rotting vegetation. Furthermore, although at lower levels than other renewable energy sources, it was found that hydropower produces methane equivalent to almost
3498-399: Is not explicitly expressed. The implied uncertainty is ± the half of the minimum scale at the last significant figure position. For example, if the mass of an object is reported as 3.78 kg without mentioning uncertainty, then ± 0.005 kg measurement uncertainty may be implied. If the mass of an object is estimated as 3.78 ± 0.07 kg, so the actual mass is probably somewhere in
3604-507: Is rounded down to the nearest pound, whilst tax paid is calculated to the nearest penny. As an illustration, the decimal quantity 12.345 can be expressed with various numbers of significant figures or decimal places. If insufficient precision is available then the number is rounded in some manner to fit the available precision. The following table shows the results for various total precision at two rounding ways (N/A stands for Not Applicable). Another example for 0.012345 . (Remember that
3710-429: Is the condition number . When performing multiple stage calculations, do not round intermediate stage calculation results; keep as many digits as is practical (at least one more digit than the rounding rule allows per stage) until the end of all the calculations to avoid cumulative rounding errors while tracking or recording the significant figures in each intermediate result. Then, round the final result, for example, to
3816-403: Is the decreased efficiency of electricity generation because the process depends on the speed of the seasonal river flow. This means that the rainy season increases electricity generation compared to the dry season. The size of hydroelectric plants can vary from small plants called micro hydro , to large plants that supply power to a whole country. As of 2019, the five largest power stations in
3922-423: Is the main source of energy. Both designs have limitations. For example, dam construction can result in discomfort to nearby residents. The dam and reservoirs occupy a relatively large amount of space that may be opposed by nearby communities. Moreover, reservoirs can potentially have major environmental consequences such as harming downstream habitats. On the other hand, the limitation of the run-of-river project
4028-436: Is the one with the lowest exponent value (the rightmost significant digit/figure). For example, in the number "123" the "1" is the most significant digit, representing hundreds (10 ), while the "3" is the least significant digit, representing ones (10 ). To avoid conveying a misleading level of precision, numbers are often rounded . For instance, it would create false precision to present a measurement as 12.34525 kg when
4134-414: Is the second one with only one, so the final calculated result should also have one significant figure. For unit conversion, the implied uncertainty of the result can be unsatisfactorily higher than that in the previous unit if this rounding guideline is followed; For example, 8 inch has the implied uncertainty of ± 0.5 inch = ± 1.27 cm. If it is converted to the centimeter scale and
4240-461: Is the use of falling or fast-running water to produce electricity or to power machines. This is achieved by converting the gravitational potential or kinetic energy of a water source to produce power. Hydropower is a method of sustainable energy production. Hydropower is now used principally for hydroelectric power generation , and is also applied as one half of an energy storage system known as pumped-storage hydroelectricity . Hydropower
4346-891: The Columbia River and its tributaries. The Bureau of Reclamation built the Hoover Dam in 1931, symbolically linking the job creation and economic growth priorities of the New Deal . The federal government quickly followed Hoover with the Shasta Dam and Grand Coulee Dam . Power demand in Oregon did not justify damming the Columbia until WWI revealed the weaknesses of a coal-based energy economy. The federal government then began prioritizing interconnected power—and lots of it. Electricity from all three dams poured into war production during WWII . After
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4452-639: The Democratic Republic of the Congo and Ghana , frequently sell excess power to neighboring countries. Foreign actors such as Chinese hydropower companies have proposed a significant amount of new hydropower projects in Africa, and already funded and consulted on many others in countries like Mozambique and Ghana. Small hydropower also played an important role in early 20th century electrification across Africa. In South Africa, small turbines powered gold mines and
4558-579: The Industrial Revolution would drive development as well. At the beginning of the Industrial Revolution in Britain, water was the main power source for new inventions such as Richard Arkwright 's water frame . Although water power gave way to steam power in many of the larger mills and factories, it was still used during the 18th and 19th centuries for many smaller operations, such as driving
4664-670: The Mauryan , Gupta and Chola empires. Another example of the early use of hydropower is seen in hushing , a historic method of mining that uses flood or torrent of water to reveal mineral veins. The method was first used at the Dolaucothi Gold Mines in Wales from 75 AD onwards. This method was further developed in Spain in mines such as Las Médulas . Hushing was also widely used in Britain in
4770-853: The Medieval and later periods to extract lead and tin ores. It later evolved into hydraulic mining when used during the California Gold Rush in the 19th century. The Islamic Empire spanned a large region, mainly in Asia and Africa, along with other surrounding areas. During the Islamic Golden Age and the Arab Agricultural Revolution (8th–13th centuries), hydropower was widely used and developed. Early uses of tidal power emerged along with large hydraulic factory complexes. A wide range of water-powered industrial mills were used in
4876-400: The least number of significant figures among the measured quantities used in the calculation. For example, with one , two , and one significant figures respectively. (2 here is assumed not an exact number.) For the first example, the first multiplication factor has four significant figures and the second has one significant figure. The factor with the fewest or least significant figures
4982-436: The measured quantities in the calculation. For example, with the last significant figures in the ones place, tenths place, ones place, and thousands place respectively. (2 here is assumed not an exact number.) For the first example, the first term has its last significant figure in the thousandths place and the second term has its last significant figure in the ones place. The leftmost or largest digit position among
5088-707: The radix , also known as the base, of the number system used). Electronic calculators supporting a dedicated significant figures display mode are relatively rare. Among the calculators to support related features are the Commodore M55 Mathematician (1976) and the S61 Statistician (1976), which support two display modes, where DISP + n will give n significant digits in total, while DISP + . + n will give n decimal places. The Texas Instruments TI-83 Plus (1999) and TI-84 Plus (2004) families of graphical calculators support
5194-481: The 4th century BC refer to the term cakkavattaka (turning wheel), which commentaries explain as arahatta-ghati-yanta (machine with wheel-pots attached), however whether this is water or hand powered is disputed by scholars India received Roman water mills and baths in the early 4th century AD when a certain according to Greek sources. Dams, spillways, reservoirs, channels, and water balance would develop in India during
5300-807: The American West, organized opposition to hydroelectric dams sparked up in the 1950s and 60s based on environmental concerns. Environmental movements successfully shut down proposed hydropower dams in Dinosaur National Monument and the Grand Canyon , and gained more hydropower-fighting tools with 1970s environmental legislation. As nuclear and fossil fuels grew in the 70s and 80s and environmental activists push for river restoration, hydropower gradually faded in American importance. Foreign powers and IGOs have frequently used hydropower projects in Africa as
5406-656: The British worked with Egypt to construct the first Aswan Dam, which they heightened in 1912 and 1934 to try to hold back the Nile floods. Egyptian engineer Adriano Daninos developed a plan for the Aswan High Dam, inspired by the Tennessee Valley Authority's multipurpose dam. When Gamal Abdel Nasser took power in the 1950s, his government decided to undertake the High Dam project, publicizing it as an economic development project. After American refusal to help fund
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#17328700073615512-672: The Grand Coulee to build a nuclear site placed on the banks of the Columbia. The nuclear site leaked radioactive matter into the river, contaminating the entire area. Post-WWII Americans, especially engineers from the Tennessee Valley Authority , refocused from simply building domestic dams to promoting hydropower abroad. While domestic dam building continued well into the 1970s, with the Reclamation Bureau and Army Corps of Engineers building more than 150 new dams across
5618-596: The Hun waterwheel; some of the earliest ones are the Jijiupian dictionary of 40 BC, Yang Xiong 's text known as the Fangyan of 15 BC, as well as Xin Lun, written by Huan Tan about 20 AD. It was also during this time that the engineer Du Shi (c. AD 31) applied the power of waterwheels to piston - bellows in forging cast iron. Ancient Indian texts dating back to
5724-622: The Nile, hydroelectric projects cover the rivers and lakes of Africa. The Inga powerplant on the Congo River had been discussed since Belgian colonization in the late 19th century, and was successfully built after independence. Mobutu's government failed to regularly maintain the plants and their capacity declined until the 1995 formation of the Southern African Power Pool created a multi-national power grid and plant maintenance program. States with an abundance of hydropower, such as
5830-1235: The United States' hydroelectric plants in Niagara Falls and the Sierra Nevada inspired bigger and bolder creations across the globe. American and USSR financers and hydropower experts also spread the gospel of dams and hydroelectricity across the globe during the Cold War , contributing to projects such as the Three Gorges Dam and the Aswan High Dam . Feeding desire for large scale electrification with water inherently required large dams across powerful rivers, which impacted public and private interests downstream and in flood zones. Inevitably smaller communities and marginalized groups suffered. They were unable to successfully resist companies flooding them out of their homes or blocking traditional salmon passages. The stagnant water created by hydroelectric dams provides breeding ground for pests and pathogens , leading to local epidemics . However, in some cases,
5936-413: The above rounding guideline is to multiply a number by an integer, such as 1.234 × 9. If the above guideline is followed, then the result is rounded as 1.234 × 9.000.... = 11.1 0 6 ≈ 11.11. However, this multiplication is essentially adding 1.234 to itself 9 times such as 1.234 + 1.234 + … + 1.234 so the rounding guideline for addition and subtraction described below is more proper rounding approach. As
6042-613: The bellows in small blast furnaces (e.g. the Dyfi Furnace ) and gristmills , such as those built at Saint Anthony Falls , which uses the 50-foot (15 m) drop in the Mississippi River . Technological advances moved the open water wheel into an enclosed turbine or water motor . In 1848, the British-American engineer James B. Francis , head engineer of Lowell's Locks and Canals company, improved on these designs to create
6148-429: The best estimate and uncertainty in the measurement respectively. x best can be the average of measured values and σ x can be the standard deviation or a multiple of the measurement deviation. The rules to write x b e s t ± σ x {\displaystyle x_{best}\pm \sigma _{x}} are: Uncertainty may be implied by the last significant figure if it
6254-416: The calculation. An exact number such as ½ in the formula for the kinetic energy of a mass m with velocity v as ½ mv has no bearing on the significant figures in the calculated kinetic energy since its number of significant figures is infinite (0.500000...). The guidelines described below are intended to avoid a calculation result more precise than the measured quantities, but it does not ensure
6360-440: The cost of building new hydroelectric dams increased 4% annually between 1965 and 1990, due both to the increasing costs of construction and to the decrease in high quality building sites. In the 1990s, only 18% of the world's electricity came from hydropower. Tidal power production also emerged in the 1960s as a burgeoning alternative hydropower system, though still has not taken hold as a strong energy contender. Especially at
6466-540: The country. Its mission is to protect and promote the nation's largest renewable resource through its legislative, regulatory, technical and public communications activities. The current president and CEO is Malcolm Woolf. Woolf previously worked for Maryland Governor Martin O'Malley and worked on energy policy for the National Governor's Association. www.enerset.eu Hydropower Hydropower (from Ancient Greek ὑδρο -, "water"), also known as water power ,
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#17328700073616572-651: The dam, and anti-British sentiment in Egypt and British interests in neighboring Sudan combined to make the United Kingdom pull out as well, the Soviet Union funded the Aswan High Dam. Between 1977 and 1990 the dam's turbines generated one third of Egypt's electricity. The building of the Aswan Dam triggered a dispute between Sudan and Egypt over the sharing of the Nile, especially since the dam flooded part of Sudan and decreased
6678-403: The determination of significant figures in calculated quantities with them. A mathematical or physical constant (e.g., π in the formula for the area of a circle with radius r as π r ) has no effect on the determination of the significant figures in the result of a calculation with it if its known digits are equal to or more than the significant figures in the measured quantities used in
6784-477: The digit position of the last significant figure in each factor is irrelevant. For addition and subtraction, only the digit position of the last significant figure in each of the terms in the calculation matters; the total number of significant figures in each term is irrelevant. However, greater accuracy will often be obtained if some non-significant digits are maintained in intermediate results which are used in subsequent calculations. The base -10 logarithm of
6890-605: The early 20th century, two major factors motivated the expansion of hydropower in Europe: in the northern countries of Norway and Sweden high rainfall and mountains proved exceptional resources for abundant hydropower, and in the south coal shortages pushed governments and utility companies to seek alternative power sources. Early on, Switzerland dammed the Alpine rivers and the Swiss Rhine , creating, along with Italy and Scandinavia ,
6996-555: The falls far enough away to actually reach enough people and justify installation. The project succeeded in large part due to Nikola Tesla's invention of the alternating current motor . On the other side of the country, San Francisco engineers, the Sierra Club , and the federal government fought over acceptable use of the Hetch Hetchy Valley . Despite ostensible protection within a national park, city engineers successfully won
7102-422: The fewest number of significant figures (for multiplication or division) or leftmost last significant digit position (for addition or subtraction) among the inputs in the final calculation. When using a ruler, initially use the smallest mark as the first estimated digit. For example, if a ruler's smallest mark is 0.1 cm, and 4.5 cm is read, then it is 4.5 (±0.1 cm) or 4.4 cm to 4.6 cm as to
7208-584: The first century BC. The Barbegal mill , located in modern-day France, had 16 water wheels processing up to 28 tons of grain per day. Roman waterwheels were also used for sawing marble such as the Hierapolis sawmill of the late 3rd century AD. Such sawmills had a waterwheel that drove two crank-and-connecting rods to power two saws. It also appears in two 6th century Eastern Roman sawmills excavated at Ephesus and Gerasa respectively. The crank and connecting rod mechanism of these Roman watermills converted
7314-446: The first electric railway in the 1890s, and Zimbabwean farmers installed small hydropower stations in the 1930s. While interest faded as national grids improved in the second half of the century, 21st century national governments in countries including South Africa and Mozambique, as well as NGOs serving countries like Zimbabwe, have begun re-exploring small-scale hydropower to diversify power sources and improve rural electrification. In
7420-403: The first half of the 20th century began to speak out against them, and citizen groups organizing against dam projects increased. In the 1980s and 90s the international anti-dam movement had made finding government or private investors for new large hydropower projects incredibly difficult, and given rise to NGOs devoted to fighting dams. Additionally, while the cost of other energy sources fell,
7526-453: The flow of a body of water without necessarily changing its height. In this case, the available power is the kinetic energy of the flowing water. Over-shot water wheels can efficiently capture both types of energy. The flow in a stream can vary widely from season to season. The development of a hydropower site requires analysis of flow records , sometimes spanning decades, to assess the reliable annual energy supply. Dams and reservoirs provide
7632-926: The formula ( s i g n i f i c a n t f i g u r e s o f f ( x ) ) ≈ ( s i g n i f i c a n t f i g u r e s o f x ) − log 10 ( | d f ( x ) d x x f ( x ) | ) {\displaystyle {\rm {(significant~figures~of~f(x))}}\approx {\rm {(significant~figures~of~x)}}-\log _{10}\left(\left\vert {{\frac {df(x)}{dx}}{\frac {x}{f(x)}}}\right\vert \right)} , where | d f ( x ) d x x f ( x ) | {\displaystyle \left\vert {{\frac {df(x)}{dx}}{\frac {x}{f(x)}}}\right\vert }
7738-502: The head lost due to flow friction in the power canal or penstock, rise in tailwater level due to flow, the location of the station and effect of varying gravity, the air temperature and barometric pressure, the density of the water at ambient temperature, and the relative altitudes of the forebay and tailbay. For precise calculations, errors due to rounding and the number of significant digits of constants must be considered. Some hydropower systems such as water wheels can draw power from
7844-419: The head. The power available from falling water can be calculated from the flow rate and density of water, the height of fall, and the local acceleration due to gravity: To illustrate, the power output of a turbine that is 85% efficient, with a flow rate of 80 cubic metres per second (2800 cubic feet per second) and a head of 145 metres (476 feet), is 97 megawatts: Operators of hydroelectric stations compare
7950-460: The high-efficiency Pelton wheel impulse turbine , which used hydropower from the high head streams characteristic of the Sierra Nevada . The modern history of hydropower begins in the 1900s, with large dams built not simply to power neighboring mills or factories but provide extensive electricity for increasingly distant groups of people. Competition drove much of the global hydroelectric craze: Europe competed amongst itself to electrify first, and
8056-400: The high-level intake. This allows it to fall down a shaft into a subterranean, high-roofed chamber where the now-compressed air separates from the water and becomes trapped. The height of the falling water column maintains compression of the air in the top of the chamber, while an outlet, submerged below the water level in the chamber allows water to flow back to the surface at a lower level than
8162-401: The highest among all renewable energy technologies. Hydroelectricity generation starts with converting either the potential energy of water that is present due to the site's elevation or the kinetic energy of moving water into electrical energy. Hydroelectric power plants vary in terms of the way they harvest energy. One type involves a dam and a reservoir . The water in the reservoir
8268-591: The intake. A separate outlet in the roof of the chamber supplies the compressed air. A facility on this principle was built on the Montreal River at Ragged Shutes near Cobalt, Ontario , in 1910 and supplied 5,000 horsepower to nearby mines. Hydroelectricity is the biggest hydropower application. Hydroelectricity generates about 15% of global electricity and provides at least 50% of the total electricity supply for more than 35 countries. In 2021, global installed hydropower electrical capacity reached almost 1400 GW,
8374-415: The last significant figures of these terms is the ones place, so the calculated result should also have its last significant figure in the ones place. The rule to calculate significant figures for multiplication and division are not the same as the rule for addition and subtraction. For multiplication and division, only the total number of significant figures in each of the factors in the calculation matters;
8480-497: The last unexploited energy sources in nature. When it rains, billions of litres of water can fall, which have an enormous electric potential if used in the right way." Research is being done into the different methods of generating power from rain, such as by using the energy in the impact of raindrops. This is in its very early stages with new and emerging technologies being tested, prototyped and created. Such power has been called rain power. One method in which this has been attempted
8586-570: The leading zeros are not significant.) The representation of a non-zero number x to a precision of p significant digits has a numerical value that is given by the formula: which may need to be written with a specific marking as detailed above to specify the number of significant trailing zeros. It is recommended for a measurement result to include the measurement uncertainty such as x b e s t ± σ x {\displaystyle x_{best}\pm \sigma _{x}} , where x best and σ x are
8692-408: The lower plain. Italy prioritized early near-nationwide electrification, almost entirely from hydropower, which powered their rise as a dominant European and imperial force. However, they failed to reach any conclusive standard for determining water rights before WWI. Significant digit Significant figures , also referred to as significant digits or sig figs , are specific digits within
8798-500: The maximum flood. Some disadvantages of hydropower have been identified. Dam failures can have catastrophic effects, including loss of life, property and pollution of land. Dams and reservoirs can have major negative impacts on river ecosystems such as preventing some animals traveling upstream, cooling and de-oxygenating of water released downstream, and loss of nutrients due to settling of particulates. River sediment builds river deltas and dams prevent them from restoring what
8904-409: The maximum precision allowed by that sample size. Traditionally, in various technical fields, "accuracy" refers to the closeness of a given measurement to its true value; "precision" refers to the stability of that measurement when repeated many times. Thus, it is possible to be "precisely wrong". Hoping to reflect the way in which the term "accuracy" is actually used in the scientific community, there
9010-541: The measuring instrument only provides accuracy to the nearest gram (0.001 kg). In this case, the significant figures are the first five digits (1, 2, 3, 4, and 5) from the leftmost digit, and the number should be rounded to these significant figures, resulting in 12.345 kg as the accurate value. The rounding error (in this example, 0.00025 kg = 0.25 g) approximates the numerical resolution or precision. Numbers can also be rounded for simplicity, not necessarily to indicate measurement precision, such as for
9116-400: The newer concept of trueness. Computer representations of floating-point numbers use a form of rounding to significant figures (while usually not keeping track of how many), in general with binary numbers . The number of correct significant figures is closely related to the notion of relative error (which has the advantage of being a more accurate measure of precision, and is independent of
9222-417: The range 3.71 to 3.85 kg, and it is desired to report it with a single number, then 3.8 kg is the best number to report since its implied uncertainty ± 0.05 kg gives a mass range of 3.75 to 3.85 kg, which is close to the measurement range. If the uncertainty is a bit larger, i.e. 3.78 ± 0.09 kg, then 3.8 kg is still the best single number to quote, since if "4 kg"
9328-411: The reader is familiar with the convention: As the conventions above are not in general use, the following more widely recognized options are available for indicating the significance of number with trailing zeros: Rounding to significant figures is a more general-purpose technique than rounding to n digits, since it handles numbers of different scales in a uniform way. For example, the population of
9434-593: The region including fulling mills, gristmills , paper mills , hullers , sawmills , ship mills , stamp mills , steel mills , sugar mills , and tide mills . By the 11th century, every province throughout the Islamic Empire had these industrial mills in operation, from Al-Andalus and North Africa to the Middle East and Central Asia . Muslim engineers also used water turbines while employing gears in watermills and water-raising machines. They also pioneered
9540-437: The resulted implied uncertainty close enough to the measured uncertainties. This problem can be seen in unit conversion. If the guidelines give the implied uncertainty too far from the measured ones, then it may be needed to decide significant digits that give comparable uncertainty. For quantities created from measured quantities via multiplication and division , the calculated result should have as many significant figures as
9646-468: The rights to both water and power in the Hetch Hetchy Valley in 1913. After their victory they delivered Hetch Hetchy hydropower and water to San Francisco a decade later and at twice the promised cost, selling power to PG&E which resold to San Francisco residents at a profit. The American West, with its mountain rivers and lack of coal, turned to hydropower early and often, especially along
9752-511: The rotary motion of the waterwheel into the linear movement of the saw blades. Water-powered trip hammers and bellows in China, during the Han dynasty (202 BC – 220 AD), were initially thought to be powered by water scoops . However, some historians suggested that they were powered by waterwheels. This is since it was theorized that water scoops would not have had the motive force to operate their blast furnace bellows. Many texts describe
9858-402: The rounding guideline for multiplication and division is followed, then 2 0.32 cm ≈ 20 cm with the implied uncertainty of ± 5 cm. If this implied uncertainty is considered as too overestimated, then more proper significant digits in the unit conversion result may be 2 0 .32 cm ≈ 20. cm with the implied uncertainty of ± 0.5 cm. Another exception of applying
9964-500: The rules to write uncertainty above) and the implied uncertainty of it respectively. For example, 6 kg with the implied uncertainty ± 0.5 kg can be stated as 6.0 ± 0.5 kg. As there are rules to determine the significant figures in directly measured quantities, there are also guidelines (not rules) to determine the significant figures in quantities calculated from these measured quantities. Significant figures in measured quantities are most important in
10070-421: The sake of expediency in news broadcasts. Significance arithmetic encompasses a set of approximate rules for preserving significance through calculations. More advanced scientific rules are known as the propagation of uncertainty . Radix 10 (base-10, decimal numbers) is assumed in the following. (See unit in the last place for extending these concepts to other bases.) Identifying the significant figures in
10176-507: The same period. Evidence of water wheels and watermills date to the ancient Near East in the 4th century BC. Moreover, evidence indicates the use of hydropower using irrigation machines to ancient civilizations such as Sumer and Babylonia . Studies suggest that the water wheel was the initial form of water power and it was driven by either humans or animals. In the Roman Empire , water-powered mills were described by Vitruvius by
10282-438: The size of the quantity being measured. To round a number to n significant figures: In financial calculations, a number is often rounded to a given number of places. For example, to two places after the decimal separator for many world currencies. This is done because greater precision is immaterial, and usually it is not possible to settle a debt of less than the smallest currency unit. In UK personal tax returns, income
10388-433: The smallest mark interval. However, in practice a measurement can usually be estimated by eye to closer than the interval between the ruler's smallest mark, e.g. in the above case it might be estimated as between 4.51 cm and 4.53 cm. It is also possible that the overall length of a ruler may not be accurate to the degree of the smallest mark, and the marks may be imperfectly spaced within each unit. However assuming
10494-478: The start of the American hydropower experiment, engineers and politicians began major hydroelectricity projects to solve a problem of 'wasted potential' rather than to power a population that needed the electricity. When the Niagara Falls Power Company began looking into damming Niagara, the first major hydroelectric project in the United States, in the 1890s they struggled to transport electricity from
10600-423: The total electrical energy produced with the theoretical potential energy of the water passing through the turbine to calculate efficiency. Procedures and definitions for calculation of efficiency are given in test codes such as ASME PTC 18 and IEC 60041. Field testing of turbines is used to validate the manufacturer's efficiency guarantee. Detailed calculation of the efficiency of a hydropower turbine accounts for
10706-703: The use of dams as a source of water power, used to provide additional power to watermills and water-raising machines. Islamic irriguation techniques including Persian Wheels would be introduced to India, and would be combined with local methods, during the Delhi Sultanate and the Mughal Empire . Furthermore, in his book, The Book of Knowledge of Ingenious Mechanical Devices , the Muslim mechanical engineer, Al-Jazari (1136–1206) described designs for 50 devices. Many of these devices were water-powered, including clocks,
10812-545: The volume of water available to them. Ethiopia , also located on the Nile, took advantage of the Cold War tensions to request assistance from the United States for their own irrigation and hydropower investments in the 1960s. While progress stalled due to the coup d'état of 1974 and following 17-year-long Ethiopian Civil War Ethiopia began construction on the Grand Ethiopian Renaissance Dam in 2011. Beyond
10918-473: The war, the Grand Coulee Dam and accompanying hydroelectric projects electrified almost all of the rural Columbia Basin , but failed to improve the lives of those living and farming there the way its boosters had promised and also damaged the river ecosystem and migrating salmon populations. In the 1940s as well, the federal government took advantage of the sheer amount of unused power and flowing water from
11024-618: The world are conventional hydroelectric power stations with dams. Hydroelectricity can also be used to store energy in the form of potential energy between two reservoirs at different heights with pumped-storage . Water is pumped uphill into reservoirs during periods of low demand to be released for generation when demand is high or system generation is low. Other forms of electricity generation with hydropower include tidal stream generators using energy from tidal power generated from oceans, rivers, and human-made canal systems to generating electricity. Rain has been referred to as "one of
11130-652: Was implemented in the commercial plant of Niagara Falls in 1895 and it is still operating. In the early 20th century, English engineer William Armstrong built and operated the first private electrical power station which was located in his house in Cragside in Northumberland , England. In 1753, the French engineer Bernard Forest de Bélidor published his book, Architecture Hydraulique , which described vertical-axis and horizontal-axis hydraulic machines. The growing demand for
11236-435: Was reported then a lot of information would be lost. If there is a need to write the implied uncertainty of a number, then it can be written as x ± σ x {\displaystyle x\pm \sigma _{x}} with stating it as the implied uncertainty (to prevent readers from recognizing it as the measurement uncertainty), where x and σ x are the number with an extra zero digit (to follow
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