113:
22:
1719:
1728:
2179:
1680:
105:
89:
1499:
1839:
For relatively short pipe systems, with a relatively large number of bends and fittings, minor losses can easily exceed major losses. In design, minor losses are usually estimated from tables using coefficients or a simpler and less accurate reduction of minor losses to equivalent length of pipe, a
1682:
This vector describes the direction of the groundwater flow, where negative values indicate flow along the dimension, and zero indicates 'no flow'. As with any other example in physics, energy must flow from high to low, which is why the flow is in the negative gradient. This vector can be used in
154:), and given information of the piezometer's elevation and screen depth. Hydraulic head can similarly be measured in a column of water using a standpipe piezometer by measuring the height of the water surface in the tube relative to a common datum. The hydraulic head can be used to determine a
1744:
example (first figure), where the hydraulic head is constant, there is no flow. However, if there is a difference in hydraulic head from the top to bottom due to draining from the bottom (second figure), the water will flow downward, due to the difference in head, also called the
1675:{\displaystyle \nabla h=\left({\frac {\partial h}{\partial x}},{\frac {\partial h}{\partial y}},{\frac {\partial h}{\partial z}}\right)={\frac {\partial h}{\partial x}}\mathbf {i} +{\frac {\partial h}{\partial y}}\mathbf {j} +{\frac {\partial h}{\partial z}}\mathbf {k} }
1784:
upon water levels observed in wells has been known for many years. The effect is a direct one, an increase in atmospheric pressure is an increase in load on the water in the aquifer, which increases the depth to water (lowers the water level elevation).
1105:, in particular). This means that the hydraulic head calculation is dependent on the density of the water within the piezometer. If one or more hydraulic head measurements are to be compared, they need to be standardized, usually to their
1824:, is divided into two main categories, "major losses" associated with energy loss per length of pipe, and "minor losses" associated with bends, fittings, valves, etc. The most common equation used to calculate major head losses is the
338:
1176:
1390:
983:
563:
723:
1248:
443:
764:
651:
1214:
456:, the internal molecular motion of a fluid that exerts a force on its container. It is equal to the pressure divided by the force/volume of the fluid in a gravitational field:
498:
247:
371:
830:
1026:
1115:
1056:
879:
1463:
1438:
1300:
1413:
1082:
1003:
909:
853:
671:
604:
1777:
through time, so this is often disregarded (contributing to large errors at locations where hydraulic gradients are low or the angle between wells is acute.)
214:. On Earth, additional height of fresh water adds a static pressure of about 9.8 kPa per meter (0.098 bar/m) or 0.433 psi per foot of water column height.
221:
of a pump is the maximum height (pressure) it can deliver. The capability of the pump at a certain RPM can be read from its Q-H curve (flow vs. height).
2143:
937:
2029:
186:, the total energy at a given point in a fluid is the kinetic energy associated with the speed of flow of the fluid, plus energy from
513:) is due to the frictional forces acting against a fluid's motion by the container. For a continuous medium, this is described by
1797:
531:
680:
2112:
398:
616:
1941:
1910:
770:, expressed as a length measurement. In a flowing fluid, it represents the energy of the fluid due to its bulk motion.
2168:
1995:
142:
It is usually measured as a liquid surface elevation, expressed in units of length, at the entrance (or bottom) of a
65:
43:
459:
36:
2148:
2022:
1789:
first qualitatively observed these effects in the 17th century, and they were more rigorously described by the
803:
2069:
566:
1970:
1221:
194:. Head is expressed in units of distance such as meters or feet. The force per unit volume on a fluid in a
1829:
1825:
730:
108:
Fluid flows from the tank at the top to the basin at the bottom under the pressure of the hydraulic head.
919:
In an example with a 400 m deep piezometer, with an elevation of 1000 m, and a depth to water of 100 m:
2015:
1187:
1085:
211:
1859:
1849:
132:
2105:
2007:
797:
570:
183:
30:
2001:
for other references which discuss hydraulic head in the context of hydrogeology, see that page's
2267:
343:
112:
2211:
2059:
1692:
522:
47:
885:, in terms of the elevation difference of the water column relative to the piezometer bottom (
1879:
1493:
1473:
1011:
2272:
2002:
1781:
1766:
1485:
1041:
864:
788:
of a column of water at the base of the piezometer, and the elevation head is the relative
785:
8:
2098:
1770:
782:
388:
195:
179:
1840:
method often used for shortcut calculations of pneumatic conveying lines pressure drop.
1445:
1420:
2262:
2226:
1864:
1398:
1067:
988:
894:
838:
656:
589:
333:{\displaystyle h_{v}={\tfrac {1}{2}}\rho v^{2}/\rho g={\frac {1}{2}}{\frac {v^{2}}{g}}}
1271:
between two or more hydraulic head measurements over the length of the flow path. For
2277:
2252:
1991:
1937:
1906:
1869:
1762:
1718:
1284:
1101:
of water, which can vary depending on both the temperature and chemical composition (
378:
228:
because their pumping characteristics tend to be independent of the fluid's density.
93:
1769:), since this is truly what drives groundwater flow. Often detailed observations of
150:, it can be calculated from the depth to water in a piezometric well (a specialized
2187:
2129:
2064:
1874:
1854:
1793:
1297:
hydraulic gradient can be calculated between two points with known head values as:
789:
374:
225:
117:
82:
2196:
1817:
1727:
1289:
453:
191:
187:
1465:
is the flow path length between the two piezometers (length, usually in m or ft)
190:
in the fluid, plus energy from the height of the fluid relative to an arbitrary
2257:
2201:
1929:
1833:
1758:
1741:
1684:
1440:
is the difference between two hydraulic heads (length, usually in m or ft), and
1171:{\displaystyle h_{\mathrm {fw} }=\psi {\frac {\rho }{\rho _{\mathrm {fw} }}}+z}
514:
241:
167:
136:
2246:
2221:
2206:
2079:
1786:
1294:
882:
448:
236:
1293:
and can be used to determine whether a reach is gaining or losing energy. A
2216:
2178:
2043:
1790:
1477:
1385:{\displaystyle i={\frac {dh}{dl}}={\frac {h_{2}-h_{1}}{\mathrm {length} }}}
2231:
2158:
2153:
1272:
1033:
1029:
391:
acting on a column of fluid. The elevation head is simply the elevation (
1480:, which can be practically obtained only from numerical models, such as
2163:
2121:
1813:
1774:
1280:
182:
fluid to the height of an equivalent static column of that fluid. From
151:
143:
1469:
The hydraulic gradient can be expressed in vector notation, using the
583:
2037:
2074:
1809:
1268:
1102:
2039:
1737:
1489:
1481:
1251:
1098:
1059:
147:
88:
1761:
in the calculation of hydraulic head, it is more correct to use
1688:
912:
886:
856:
607:
175:
104:
1005:
is the gauge pressure (Force per unit area, often Pa or psi),
978:{\displaystyle \psi ={\frac {P}{\gamma }}={\frac {P}{\rho g}}}
78:
Specific measurement of liquid pressure above a vertical datum
2090:
611:
395:) of the fluid above an arbitrarily designated zero point:
1216:
is the fresh water head (Length, measured in m or ft), and
1062:
of the liquid (Mass per unit volume, frequently kg¡m), and
610:
from an initial velocity of 0, a mass will have reached a
2138:
1470:
565:
while in a piped system head losses are described by the
1254:
of fresh water (Mass per unit volume, typically in kg¡m)
1032:
of the liquid (Force per unit volume, typically N¡m or
1808:
In any real moving fluid, energy is dissipated due to
265:
1502:
1448:
1423:
1401:
1303:
1224:
1190:
1118:
1070:
1044:
1014:
991:
940:
897:
867:
841:
806:
733:
683:
659:
619:
592:
534:
462:
401:
346:
250:
1695:
to determine the flux of water in three dimensions.
673:
is the acceleration due to gravity. Rearranged as a
521:) to the gradient of the hydraulic head through the
773:The total hydraulic head of a fluid is composed of
120:, where the water level is above the ground surface
1674:
1457:
1432:
1407:
1384:
1242:
1208:
1170:
1076:
1050:
1020:
997:
977:
903:
873:
847:
824:
758:
717:
665:
645:
598:
557:
492:
437:
365:
332:
2144:List of conventional hydroelectric power stations
2244:
1934:Hydraulics of Open Channel Flow: An Introduction
859:in m or ft), also known as the piezometric head.
800:for incompressible fluids, can be expressed as:
92:Available difference in hydraulic head across a
1903:Flow of Industrial Fluids: Theory and Equations
1971:"Pipe equivalent length (Pneumatic conveying)"
1896:
1894:
1736:The distribution of hydraulic head through an
2106:
2023:
1740:determines where groundwater will flow. In a
100:due to turbines, wall friction and turbulence
1924:
1922:
1960:, Section 3.7 (Fourth edition) McGraw-Hill
1891:
1828:. Older, more empirical approaches are the
911:is the elevation at the piezometer bottom (
2113:
2099:
2030:
2016:
1415:is the hydraulic gradient (dimensionless),
1283:or discharge. It also has applications in
1088:(velocity change per unit time, often m¡s)
1919:
66:Learn how and when to remove this message
1279:, since it determines the quantity of a
231:There are generally four types of head:
111:
103:
87:
29:This article includes a list of general
1928:
1800:(USDA)) using air flow models in 1907.
1798:United States Department of Agriculture
1752:
934:The pressure head can be expressed as:
558:{\displaystyle \mathbf {q} =-K\nabla h}
2245:
1900:
1097:The pressure head is dependent on the
781:. The pressure head is the equivalent
718:{\displaystyle h={\frac {v^{2}}{2g}}.}
2094:
2011:
1816:dissipates even more energy for high
1258:
1243:{\displaystyle \rho _{\mathrm {fw} }}
1757:Even though it is convention to use
438:{\displaystyle h_{e}=\rho gh/\rho g}
15:
1092:
759:{\displaystyle {\frac {v^{2}}{2g}}}
646:{\displaystyle v={\sqrt {{2g}{h}}}}
13:
1988:Dynamics of Fluids in Porous Media
1658:
1650:
1630:
1622:
1602:
1594:
1574:
1566:
1551:
1543:
1528:
1520:
1503:
1376:
1373:
1370:
1367:
1364:
1361:
1234:
1231:
1200:
1197:
1154:
1151:
1128:
1125:
549:
387:is due to the fluid's weight, the
35:it lacks sufficient corresponding
14:
2289:
2169:Run-of-the-river hydroelectricity
1698:
1476:. This requires a hydraulic head
1209:{\displaystyle h_{\mathrm {fw} }}
206:is the density of the fluid, and
2177:
1820:flows. This dissipation, called
1726:
1717:
1668:
1640:
1612:
536:
517:which relates volume flow rate (
20:
2149:Pumped-storage hydroelectricity
116:Measuring hydraulic head in an
2120:
1963:
1950:
1702:
1109:, which can be calculated as:
792:in terms of an elevation. The
510:
493:{\displaystyle h_{p}=p/\rho g}
174:is a concept that relates the
97:
1:
1980:
1704:Relation between heads for a
577:
224:Head is useful in specifying
161:
131:is a specific measurement of
1803:
1496:, this can be expressed as:
158:between two or more points.
7:
1956:Streeter, Victor L. (1958)
1916:, 410 pages. See pp. 43â44.
1843:
796:, a simplified form of the
366:{\displaystyle \rho gh_{v}}
240:is due to the bulk motion (
10:
2294:
1780:The effects of changes in
1773:are not available at each
1287:where it is also known as
1086:gravitational acceleration
212:gravitational acceleration
80:
2186:
2175:
2128:
2050:
1936:, ButterworthâHeinemann,
1860:Minor losses in pipe flow
825:{\displaystyle h=\psi +z}
567:HagenâPoiseuille equation
1901:Mulley, Raymond (2004),
1885:
1275:, it is also called the
81:Not to be confused with
2003:further reading section
1947:, 650 pages. See p. 22.
1830:HazenâWilliams equation
1826:DarcyâWeisbach equation
1021:{\displaystyle \gamma }
855:is the hydraulic head (
50:more precise citations.
2212:Gorlov helical turbine
2060:hydraulic conductivity
1693:hydraulic conductivity
1676:
1492:for open channels. In
1459:
1434:
1409:
1386:
1244:
1210:
1172:
1078:
1052:
1022:
999:
979:
905:
875:
849:
826:
760:
719:
667:
647:
600:
559:
523:hydraulic conductivity
494:
439:
367:
334:
121:
109:
101:
1880:Hydraulic accumulator
1850:BordaâCarnot equation
1677:
1494:Cartesian coordinates
1460:
1435:
1410:
1387:
1245:
1211:
1173:
1079:
1053:
1051:{\displaystyle \rho }
1023:
1000:
980:
906:
876:
874:{\displaystyle \psi }
850:
827:
761:
720:
668:
648:
601:
560:
495:
440:
368:
335:
184:Bernoulli's principle
115:
107:
91:
1782:atmospheric pressure
1767:atmospheric pressure
1753:Atmospheric pressure
1500:
1446:
1421:
1399:
1301:
1222:
1188:
1116:
1068:
1042:
1012:
989:
938:
895:
865:
839:
804:
731:
681:
657:
617:
590:
571:Bernoulliâs equation
532:
460:
399:
344:
248:
2042:properties used in
1771:barometric pressure
1713:
1484:for groundwater or
798:Bernoulli principle
389:gravitational force
196:gravitational field
2227:Cross-flow turbine
1865:Total dynamic head
1765:(gauge pressure +
1747:hydraulic gradient
1703:
1672:
1458:{\displaystyle dl}
1455:
1433:{\displaystyle dh}
1430:
1405:
1382:
1265:hydraulic gradient
1259:Hydraulic gradient
1240:
1206:
1168:
1074:
1048:
1018:
995:
975:
901:
871:
845:
822:
756:
715:
663:
643:
596:
555:
490:
435:
363:
330:
274:
156:hydraulic gradient
122:
110:
102:
2240:
2239:
2088:
2087:
1870:Stage (hydrology)
1796:(working for the
1763:absolute pressure
1734:
1733:
1683:conjunction with
1665:
1637:
1609:
1581:
1558:
1535:
1408:{\displaystyle i}
1380:
1328:
1285:open-channel flow
1160:
1077:{\displaystyle g}
998:{\displaystyle P}
973:
955:
904:{\displaystyle z}
848:{\displaystyle h}
754:
710:
666:{\displaystyle g}
641:
599:{\displaystyle h}
586:through a height
379:irrotational flow
328:
311:
273:
226:centrifugal pumps
94:hydroelectric dam
76:
75:
68:
2285:
2188:Hydroelectricity
2181:
2130:Hydroelectricity
2115:
2108:
2101:
2092:
2091:
2032:
2025:
2018:
2009:
2008:
1975:
1974:
1967:
1961:
1954:
1948:
1946:
1926:
1917:
1915:
1898:
1875:Head (hydrology)
1855:Dynamic pressure
1794:Edgar Buckingham
1730:
1721:
1714:
1681:
1679:
1678:
1673:
1671:
1666:
1664:
1656:
1648:
1643:
1638:
1636:
1628:
1620:
1615:
1610:
1608:
1600:
1592:
1587:
1583:
1582:
1580:
1572:
1564:
1559:
1557:
1549:
1541:
1536:
1534:
1526:
1518:
1464:
1462:
1461:
1456:
1439:
1437:
1436:
1431:
1414:
1412:
1411:
1406:
1391:
1389:
1388:
1383:
1381:
1379:
1359:
1358:
1357:
1345:
1344:
1334:
1329:
1327:
1319:
1311:
1249:
1247:
1246:
1241:
1239:
1238:
1237:
1215:
1213:
1212:
1207:
1205:
1204:
1203:
1177:
1175:
1174:
1169:
1161:
1159:
1158:
1157:
1141:
1133:
1132:
1131:
1107:fresh water head
1093:Fresh water head
1083:
1081:
1080:
1075:
1057:
1055:
1054:
1049:
1027:
1025:
1024:
1019:
1004:
1002:
1001:
996:
984:
982:
981:
976:
974:
972:
961:
956:
948:
910:
908:
907:
902:
889:in m or ft), and
880:
878:
877:
872:
854:
852:
851:
846:
831:
829:
828:
823:
790:potential energy
765:
763:
762:
757:
755:
753:
745:
744:
735:
724:
722:
721:
716:
711:
709:
701:
700:
691:
672:
670:
669:
664:
652:
650:
649:
644:
642:
640:
635:
627:
605:
603:
602:
597:
564:
562:
561:
556:
539:
499:
497:
496:
491:
483:
472:
471:
444:
442:
441:
436:
428:
411:
410:
375:dynamic pressure
373:is equal to the
372:
370:
369:
364:
362:
361:
339:
337:
336:
331:
329:
324:
323:
314:
312:
304:
293:
288:
287:
275:
266:
260:
259:
129:piezometric head
118:artesian aquifer
83:Head (hydrology)
71:
64:
60:
57:
51:
46:this article by
37:inline citations
24:
23:
16:
2293:
2292:
2288:
2287:
2286:
2284:
2283:
2282:
2243:
2242:
2241:
2236:
2197:Francis turbine
2182:
2173:
2124:
2119:
2089:
2084:
2046:
2036:
1986:Bear, J. 1972.
1983:
1978:
1969:
1968:
1964:
1958:Fluid Mechanics
1955:
1951:
1944:
1930:Chanson, Hubert
1927:
1920:
1913:
1899:
1892:
1888:
1846:
1818:Reynolds number
1806:
1755:
1701:
1667:
1657:
1649:
1647:
1639:
1629:
1621:
1619:
1611:
1601:
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1573:
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1527:
1519:
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1501:
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1349:
1340:
1336:
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1333:
1320:
1312:
1310:
1302:
1299:
1298:
1290:stream gradient
1269:vector gradient
1261:
1230:
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1225:
1223:
1220:
1219:
1196:
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1191:
1189:
1186:
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1140:
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1123:
1119:
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1113:
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1043:
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987:
986:
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947:
939:
936:
935:
896:
893:
892:
866:
863:
862:
840:
837:
836:
805:
802:
801:
746:
740:
736:
734:
732:
729:
728:
702:
696:
692:
690:
682:
679:
678:
658:
655:
654:
636:
628:
626:
618:
615:
614:
591:
588:
587:
580:
535:
533:
530:
529:
503:Resistance head
479:
467:
463:
461:
458:
457:
454:static pressure
424:
406:
402:
400:
397:
396:
357:
353:
345:
342:
341:
319:
315:
313:
303:
289:
283:
279:
264:
255:
251:
249:
246:
245:
188:static pressure
164:
133:liquid pressure
86:
79:
72:
61:
55:
52:
42:Please help to
41:
25:
21:
12:
11:
5:
2291:
2281:
2280:
2275:
2270:
2268:Fluid dynamics
2265:
2260:
2255:
2238:
2237:
2235:
2234:
2229:
2224:
2219:
2214:
2209:
2204:
2202:Kaplan turbine
2199:
2193:
2191:
2184:
2183:
2176:
2174:
2172:
2171:
2166:
2161:
2156:
2151:
2146:
2141:
2135:
2133:
2126:
2125:
2118:
2117:
2110:
2103:
2095:
2086:
2085:
2083:
2082:
2077:
2072:
2067:
2062:
2057:
2055:hydraulic head
2051:
2048:
2047:
2035:
2034:
2027:
2020:
2012:
2006:
2005:
1999:
1982:
1979:
1977:
1976:
1962:
1949:
1943:978-0750659789
1942:
1918:
1912:978-0849327674
1911:
1889:
1887:
1884:
1883:
1882:
1877:
1872:
1867:
1862:
1857:
1852:
1845:
1842:
1834:Prony equation
1805:
1802:
1791:soil physicist
1759:gauge pressure
1754:
1751:
1732:
1731:
1723:
1722:
1700:
1699:In groundwater
1697:
1670:
1663:
1660:
1655:
1652:
1646:
1642:
1635:
1632:
1627:
1624:
1618:
1614:
1607:
1604:
1599:
1596:
1590:
1586:
1579:
1576:
1571:
1568:
1562:
1556:
1553:
1548:
1545:
1539:
1533:
1530:
1525:
1522:
1515:
1511:
1508:
1505:
1467:
1466:
1454:
1451:
1441:
1429:
1426:
1416:
1404:
1378:
1375:
1372:
1369:
1366:
1363:
1356:
1352:
1348:
1343:
1339:
1332:
1326:
1323:
1318:
1315:
1309:
1306:
1260:
1257:
1256:
1255:
1236:
1233:
1228:
1217:
1202:
1199:
1194:
1179:
1178:
1167:
1164:
1156:
1153:
1148:
1144:
1139:
1136:
1130:
1127:
1122:
1094:
1091:
1090:
1089:
1073:
1063:
1047:
1037:
1017:
994:
971:
968:
964:
959:
954:
951:
946:
943:
917:
916:
900:
890:
870:
860:
844:
821:
818:
815:
812:
809:
779:elevation head
766:is called the
752:
749:
743:
739:
714:
708:
705:
699:
695:
689:
686:
662:
639:
634:
631:
625:
622:
595:
579:
576:
575:
574:
554:
551:
548:
545:
542:
538:
500:
489:
486:
482:
478:
475:
470:
466:
452:is due to the
445:
434:
431:
427:
423:
420:
417:
414:
409:
405:
385:Elevation head
382:
360:
356:
352:
349:
327:
322:
318:
310:
307:
302:
299:
296:
292:
286:
282:
278:
272:
269:
263:
258:
254:
242:kinetic energy
180:incompressible
168:fluid dynamics
163:
160:
137:vertical datum
125:Hydraulic head
77:
74:
73:
28:
26:
19:
9:
6:
4:
3:
2:
2290:
2279:
2276:
2274:
2271:
2269:
2266:
2264:
2261:
2259:
2256:
2254:
2251:
2250:
2248:
2233:
2230:
2228:
2225:
2223:
2222:Turgo turbine
2220:
2218:
2215:
2213:
2210:
2208:
2207:Tyson turbine
2205:
2203:
2200:
2198:
2195:
2194:
2192:
2189:
2185:
2180:
2170:
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2145:
2142:
2140:
2137:
2136:
2134:
2131:
2127:
2123:
2116:
2111:
2109:
2104:
2102:
2097:
2096:
2093:
2081:
2080:water content
2078:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2053:
2052:
2049:
2045:
2041:
2033:
2028:
2026:
2021:
2019:
2014:
2013:
2010:
2004:
2000:
1997:
1996:0-486-65675-6
1993:
1989:
1985:
1984:
1972:
1966:
1959:
1953:
1945:
1939:
1935:
1931:
1925:
1923:
1914:
1908:
1905:, CRC Press,
1904:
1897:
1895:
1890:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
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1858:
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1848:
1847:
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1837:
1835:
1831:
1827:
1823:
1819:
1815:
1811:
1801:
1799:
1795:
1792:
1788:
1783:
1778:
1776:
1772:
1768:
1764:
1760:
1750:
1748:
1743:
1739:
1729:
1725:
1724:
1720:
1716:
1715:
1711:
1710:downward flow
1707:
1696:
1694:
1690:
1686:
1661:
1653:
1644:
1633:
1625:
1616:
1605:
1597:
1588:
1584:
1577:
1569:
1560:
1554:
1546:
1537:
1531:
1523:
1513:
1509:
1506:
1495:
1491:
1487:
1486:standard step
1483:
1479:
1475:
1472:
1452:
1449:
1442:
1427:
1424:
1417:
1402:
1395:
1394:
1393:
1354:
1350:
1346:
1341:
1337:
1330:
1324:
1321:
1316:
1313:
1307:
1304:
1296:
1295:dimensionless
1292:
1291:
1286:
1282:
1278:
1274:
1270:
1266:
1253:
1226:
1218:
1192:
1184:
1183:
1182:
1165:
1162:
1146:
1142:
1137:
1134:
1120:
1112:
1111:
1110:
1108:
1104:
1100:
1087:
1071:
1064:
1061:
1045:
1038:
1035:
1031:
1015:
1008:
1007:
1006:
992:
969:
966:
962:
957:
952:
949:
944:
941:
932:
930:
927:= 300 m, and
926:
922:
914:
898:
891:
888:
884:
883:pressure head
868:
861:
858:
842:
835:
834:
833:
819:
816:
813:
810:
807:
799:
795:
794:head equation
791:
787:
784:
780:
776:
775:pressure head
771:
769:
768:velocity head
750:
747:
741:
737:
725:
712:
706:
703:
697:
693:
687:
684:
676:
660:
637:
632:
629:
623:
620:
613:
609:
593:
585:
572:
568:
552:
546:
543:
540:
527:
524:
520:
516:
512:
508:
507:friction head
504:
501:
487:
484:
480:
476:
473:
468:
464:
455:
451:
450:
449:Pressure head
446:
432:
429:
425:
421:
418:
415:
412:
407:
403:
394:
390:
386:
383:
380:
376:
358:
354:
350:
347:
325:
320:
316:
308:
305:
300:
297:
294:
290:
284:
280:
276:
270:
267:
261:
256:
252:
244:) of a fluid.
243:
239:
238:
237:Velocity head
234:
233:
232:
229:
227:
222:
220:
215:
213:
209:
205:
201:
197:
193:
189:
185:
181:
177:
173:
169:
159:
157:
153:
149:
145:
140:
138:
134:
130:
126:
119:
114:
106:
99:
95:
90:
84:
70:
67:
59:
49:
45:
39:
38:
32:
27:
18:
17:
2217:Pelton wheel
2070:permeability
2054:
2044:hydrogeology
1987:
1965:
1957:
1952:
1933:
1902:
1838:
1821:
1807:
1779:
1756:
1746:
1735:
1709:
1705:
1468:
1288:
1276:
1264:
1262:
1180:
1106:
1096:
933:
928:
924:
920:
918:
793:
778:
774:
772:
767:
726:
674:
584:free falling
581:
525:
518:
506:
502:
447:
392:
384:
235:
230:
223:
218:
216:
207:
203:
199:
198:is equal to
171:
165:
155:
141:
128:
124:
123:
62:
53:
34:
2273:Water wells
2232:Water wheel
2159:Micro hydro
2154:Small hydro
2065:storativity
1742:hydrostatic
1708:case and a
1706:hydrostatic
1685:Darcy's law
1277:Darcy slope
1273:groundwater
1030:unit weight
915:in m or ft)
515:Darcy's law
219:static head
98:head losses
48:introducing
2247:Categories
2164:Pico hydro
2132:generation
2122:Hydropower
1981:References
1814:turbulence
1281:Darcy flux
578:Components
340:Note that
162:Definition
152:water well
144:piezometer
56:April 2020
31:references
2263:Hydrology
2190:equipment
2038:Physical
1990:, Dover.
1822:head loss
1804:Head loss
1659:∂
1651:∂
1631:∂
1623:∂
1603:∂
1595:∂
1575:∂
1567:∂
1552:∂
1544:∂
1529:∂
1521:∂
1504:∇
1347:−
1227:ρ
1147:ρ
1143:ρ
1138:ψ
1046:ρ
1016:γ
967:ρ
953:γ
942:ψ
931:= 900 m.
923:= 600 m,
869:ψ
814:ψ
727:The term
550:∇
544:−
511:Head Loss
485:ρ
430:ρ
416:ρ
348:ρ
295:ρ
277:ρ
96:, before
2278:Pressure
2253:Aquifers
2075:porosity
1932:(2004),
1844:See also
1832:and the
1810:friction
1474:operator
1103:salinity
786:pressure
146:. In an
135:above a
2040:aquifer
1738:aquifer
1490:HEC-RAS
1482:MODFLOW
1252:density
1250:is the
1099:density
1084:is the
1060:density
1058:is the
1028:is the
881:is the
210:is the
200:ρg
148:aquifer
44:improve
1994:
1940:
1909:
1787:Pascal
1712:case.
1689:tensor
1687:and a
1392:where
1181:where
985:where
913:Length
887:Length
857:Length
832:where
653:where
608:vacuum
582:After
204:ρ
202:where
178:in an
176:energy
33:, but
2258:Water
1886:Notes
1478:field
1267:is a
1036:/ft),
783:gauge
612:speed
606:in a
192:datum
1992:ISBN
1938:ISBN
1907:ISBN
1775:well
1263:The
777:and
675:head
569:and
505:(or
377:for
217:The
172:head
2139:Dam
1691:of
1488:or
1471:del
1034:lbf
509:or
166:In
127:or
2249::
1921:^
1893:^
1836:.
1812:;
1749:.
677::
528::
170:,
139:.
2114:e
2107:t
2100:v
2031:e
2024:t
2017:v
1998:.
1973:.
1669:k
1662:z
1654:h
1645:+
1641:j
1634:y
1626:h
1617:+
1613:i
1606:x
1598:h
1589:=
1585:)
1578:z
1570:h
1561:,
1555:y
1547:h
1538:,
1532:x
1524:h
1514:(
1510:=
1507:h
1453:l
1450:d
1428:h
1425:d
1403:i
1377:h
1374:t
1371:g
1368:n
1365:e
1362:l
1355:1
1351:h
1342:2
1338:h
1331:=
1325:l
1322:d
1317:h
1314:d
1308:=
1305:i
1235:w
1232:f
1201:w
1198:f
1193:h
1166:z
1163:+
1155:w
1152:f
1135:=
1129:w
1126:f
1121:h
1072:g
993:P
970:g
963:P
958:=
950:P
945:=
929:h
925:Ď
921:z
899:z
843:h
820:z
817:+
811:=
808:h
751:g
748:2
742:2
738:v
713:.
707:g
704:2
698:2
694:v
688:=
685:h
661:g
638:h
633:g
630:2
624:=
621:v
594:h
573:.
553:h
547:K
541:=
537:q
526:K
519:q
488:g
481:/
477:p
474:=
469:p
465:h
433:g
426:/
422:h
419:g
413:=
408:e
404:h
393:h
381:.
359:v
355:h
351:g
326:g
321:2
317:v
309:2
306:1
301:=
298:g
291:/
285:2
281:v
271:2
268:1
262:=
257:v
253:h
208:g
85:.
69:)
63:(
58:)
54:(
40:.
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