1313:
992:
1308:{\displaystyle S={4^{1.167}\,4^{1.852}\,Q^{1.852} \over \pi ^{1.852}\,k^{1.852}\,C^{1.852}\,d^{1.167}\,d^{3.7034}}={4^{3.019}\,Q^{1.852} \over \pi ^{1.852}\,k^{1.852}\,C^{1.852}\,d^{4.8704}}={4^{3.019} \over \pi ^{1.852}\,k^{1.852}}{Q^{1.852} \over C^{1.852}\,d^{4.8704}}={7.8828 \over k^{1.852}}{Q^{1.852} \over C^{1.852}\,d^{4.8704}}}
1537:
Caution with U S Customary Units is advised. The equation for head loss in pipes, also referred to as slope, S, expressed in "feet per foot of length" vs. in 'psi per foot of length' as described above, with the inside pipe diameter, d, being entered in feet vs. inches, and the flow rate, Q, being
2139:
Hydraulic tables: the elements of gagings and the friction of water flowing in pipes, aqueducts, sewers, etc., as determined by the Hazen and
Williams formula and the flow of water over sharp-edged and irregular weirs, and the quantity discharged as determined by Bazin's formula and experimental
2128:
Hydraulic tables: the elements of gagings and the friction of water flowing in pipes, aqueducts, sewers, etc., as determined by the Hazen and
Williams formula and the flow of water over sharp-edged and irregular weirs, and the quantity discharged as determined by Bazin's formula and experimental
947:
1538:
entered in cubic feet per second, cfs, vs. gallons per minute, gpm, appears very similar. However, the constant is 4.73 vs. the 4.52 constant as shown above in the formula as arranged by NFPA for sprinkler system design. The exponents and the Hazen-Williams "C" values are unchanged.
1460:
1647:
1798:
796:
772:
695:
322:
The equation is similar to the Chézy formula but the exponents have been adjusted to better fit data from typical engineering situations. A result of adjusting the exponents is that the value of
169:
619:
270:
1333:
1802:
2047:
217:
that was easy to use. The general form of the equation relates the mean velocity of water in a pipe with the geometric properties of the pipe and slope of the energy line.
77:
discovered that the velocity of a fluid was proportional to the square root of its head in the early 18th century. It takes energy to push a fluid through a pipe, and
1562:
2188:
States pocket calculators and computers make calculations easier. H-W is good for smooth pipes, but
Manning better for rough pipes (compared to D-W model).
27:
which relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of
942:{\displaystyle S={V^{1.852}A^{1.852} \over k^{1.852}\,C^{1.852}\,R^{1.167}\,A^{1.852}}={Q^{1.852} \over k^{1.852}\,C^{1.852}\,R^{1.167}\,A^{1.852}}}
213:
The Darcy-Weisbach equation was difficult to use because the friction factor was difficult to estimate. In 1906, Hazen and
Williams provided an
1772:
2112:
Hydraulic tables: showing the loss of head due to the friction of water flowing in pipes, aqueducts, sewers, etc. and the discharge over weirs
706:
2054:
634:
2430:
1859:
436:
1958:, p. 1, stating "Exponents can be selected, however, representing approximate average conditions, so that the value of
2435:
2213:
110:
2399:
1833:
187:
1455:{\displaystyle S_{\mathrm {psi\ per\ foot} }={\frac {P_{d}}{L}}={\frac {4.52\ Q^{1.852}}{C^{1.852}\ d^{4.8704}}}}
572:
223:
2404:
1549:
195:
2165:
2015:
2272:
1718:
1496:
1476:
207:
352:
factors used in design, which take into account some increase in roughness as pipe ages are as follows:
2409:
1883:
2037:
2007 version of NFPA 13: Standard for the
Installation of Sprinkler Systems, page 13-213, eqn 22.4.2.1
288:
is a conversion factor for the unit system (k = 1.318 for US customary units, k = 0.849 for SI units)
2287:
2277:
1738:
2160:
1776:
2267:
2206:
544:
2358:
2455:
2378:
2343:
214:
24:
2185:
2180:
2323:
2302:
2251:
32:
2126:
1854:. Jones, Garr M. (3rd ed.). Burlington, MA: Butterworth-Heinemann. 2006. p. 3.4.
1753:
66:
of the water, and therefore is only valid at room temperature and conventional velocities.
36:
2175:
2170:
8:
2460:
2450:
2318:
2199:
1667:
78:
2348:
2338:
1914:
1910:
1877:
1513:
1324:
528:
1642:{\displaystyle S={\frac {h_{f}}{L}}={\frac {10.67\ Q^{1.852}}{C^{1.852}\ d^{4.8704}}}}
2445:
2333:
2292:
2143:
1918:
1865:
1855:
1829:
1962:
for a given condition of surface will vary so little as to be practically constant."
1906:
953:
301:
98:
86:
2440:
2363:
2353:
2328:
2296:
2241:
2119:
2110:
566:
The general form can be specialized for full pipe flows. Taking the general form
498:
199:
55:
2383:
2368:
1824:
Brater, Ernest F.; King, Horace W.; Lindell, James E.; Wei, C. Y. (1996). "6".
1728:
1722:
183:
82:
2424:
2373:
1869:
2147:
513:
191:
1849:
2246:
337:
were the same as in the Chézy formula for the typical hydraulic slope of
203:
74:
44:
326:
appears more like a constant over a wide range of the other parameters.
2236:
2222:
40:
28:
1475:= frictional resistance (pressure drop per foot of pipe) in psig/ft (
420:
404:
388:
311:
63:
1897:
Walski, Thomas M. (March 2006), "A history of water distribution",
1748:
1743:
1733:
767:{\displaystyle S={V^{1.852} \over k^{1.852}\,C^{1.852}\,R^{1.167}}}
452:
50:
The Hazen–Williams equation has the advantage that the coefficient
2132:(2nd revised and enlarged ed.), New York: John Wiley and Sons
85:
loss was proportional to the velocity squared. Consequently, the
372:
282:
is velocity (in ft/s for US customary units, in m/s for SI units)
2048:"Comparison of Pipe Flow Equations and Head Losses in Fittings"
467:
2191:
482:
59:
690:{\displaystyle V^{1.852}=k^{1.852}\,C^{1.852}\,R^{1.167}\,S}
2186:
https://books.google.com/books?id=RAMX5xuXSrUC&pg=PA145
2181:
https://books.google.com/books?id=DxoMAQAAIAAJ&pg=PA736
1707:× the unit weight of water (e.g., 9810 N/m at 4 deg C)
1828:(Seventh ed.). New York: McGraw Hill. p. 6.29.
58:, but it has the disadvantage that it is only valid for
2176:
Online Hazen–Williams calculator for pressurized pipes.
2171:
Online Hazen–Williams calculator for gravity-fed pipes.
1700:
Note: pressure drop can be computed from head loss as
1682:= volumetric flow rate, m/s (cubic meters per second)
1565:
1336:
995:
799:
709:
637:
575:
226:
113:
1823:
1799:"Hazen–Williams equation in fire protection systems"
62:. Also, it does not account for the temperature or
2040:
1323:When used to calculate the pressure drop using the
164:{\displaystyle V=C{\sqrt {RS}}=C\,R^{0.5}\,S^{0.5}}
1641:
1454:
1318:
1307:
941:
766:
689:
613:
264:
190:independently determined a head loss equation for
163:
93:(head loss per unit length) to the fluid velocity
2081:
1495:= pressure drop over the length of pipe in psig (
304:(in ft for US customary units, in m for SI units)
2422:
2137:Williams, Gardner Stewart; Hazen, Allen (1920),
2125:Williams, Gardner Stewart; Hazen, Allen (1914),
2109:Williams, Gardner Stewart; Hazen, Allen (1905),
2082:Finnemore, E. John; Franzini, Joseph B. (2002),
1905:(3), American Water Works Association: 110–121,
178:expresses the proportionality, but the value of
2166:Engineering toolbox Hazen–Williams coefficients
2142:(3rd ed.), New York: John Wiley and Sons,
2115:(first ed.), New York: John Wiley and Sons
1899:Journal of the American Water Works Association
1548:When used to calculate the head loss with the
959:(which is different from the geometric radius
2207:
2136:
2124:
2108:
1983:
1971:
1955:
1801:. Canute LLP. 27 January 2009. Archived from
628:gives (rounding exponents to 3–4 decimals)
2214:
2200:
614:{\displaystyle V=k\,C\,R^{0.63}\,S^{0.54}}
265:{\displaystyle V=k\,C\,R^{0.63}\,S^{0.54}}
1670:in meters (water) over the length of pipe
1291:
1234:
1197:
1157:
1146:
1135:
1112:
1082:
1071:
1060:
1049:
1026:
1015:
925:
914:
903:
863:
852:
841:
750:
739:
683:
672:
661:
600:
589:
585:
251:
240:
236:
150:
139:
2120:Williams and Hazen, Second edition, 1909
963:) for a full pipe of geometric diameter
2099:
2423:
1943:
1931:
1896:
2195:
2010:
2008:
2006:
2004:
2002:
2000:
1998:
1996:
1994:
1992:
1497:pounds per square inch gauge pressure
1477:pounds per square inch gauge pressure
437:Cement-Mortar Lined Ductile Iron Pipe
182:is not a constant. In 1838 and 1839,
2090:
1528:= inside pipe diameter, in (inches)
13:
2075:
1989:
1911:10.1002/j.1551-8833.2006.tb07611.x
1694:= inside pipe diameter, m (meters)
1376:
1373:
1370:
1367:
1361:
1358:
1355:
1349:
1346:
1343:
974:; the pipe's cross sectional area
333:was chosen so that the values for
14:
2472:
2154:
2140:investigations upon large models.
2129:investigations upon large models.
310:is the slope of the energy line (
1552:, the equation will then become
624:and exponentiating each side by
561:
2031:
1977:
1319:U.S. customary units (Imperial)
69:
16:Equation on water flow in pipes
2431:Eponymous equations of physics
2221:
1965:
1949:
1937:
1925:
1890:
1842:
1817:
1791:
1765:
1486:foot of water per foot of pipe
47:and Gardner Stewart Williams.
1:
2161:Engineering Toolbox reference
1759:
1550:International System of Units
188:Jean Léonard Marie Poiseuille
2086:(10th ed.), McGraw Hill
1688:= pipe roughness coefficient
1522:= pipe roughness coefficient
7:
2436:Equations of fluid dynamics
2017:Hazen-Williams Coefficients
1712:
1543:
43:systems. It is named after
10:
2477:
2100:Watkins, James A. (1987),
1676:= length of pipe in meters
294:is a roughness coefficient
2392:
2311:
2288:Hydrological optimization
2278:Groundwater flow equation
2260:
2229:
2093:Hydraulic Design Handbook
1984:Williams & Hazen 1914
1972:Williams & Hazen 1914
1956:Williams & Hazen 1914
1739:Minor losses in pipe flow
1327:system, the equation is:
196:Hagen–Poiseuille equation
54:is not a function of the
1773:"Hazen–Williams Formula"
1506:= length of pipe in feet
545:Fibre-reinforced plastic
89:relates hydraulic slope
2283:Hazen–Williams equation
2273:Darcy–Weisbach equation
2091:Mays, Larry W. (1999),
1719:Darcy–Weisbach equation
314:per length of pipe or h
208:Darcy–Weisbach equation
21:Hazen–Williams equation
2104:(5th ed.), Telsco
2102:Turf Irrigation Manual
1882:: CS1 maint: others (
1851:Pumping station design
1826:Handbook of Hydraulics
1643:
1456:
1309:
943:
768:
691:
615:
341:=0.001. The value of
329:The conversion factor
266:
165:
33:fire sprinkler systems
25:empirical relationship
2303:Pipe network analysis
2268:Bernoulli's principle
2252:Hydraulic engineering
2020:, Engineering ToolBox
1644:
1457:
1310:
944:
769:
692:
616:
267:
166:
37:water supply networks
1754:Volumetric flow rate
1563:
1334:
993:
797:
707:
635:
573:
224:
111:
81:discovered that the
2060:on 21 January 2022
1639:
1514:gallons per minute
1452:
1325:US customary units
1305:
939:
764:
700:Rearranging gives
687:
611:
529:Polyvinyl chloride
262:
161:
2418:
2417:
2293:Open-channel flow
1861:978-0-08-094106-6
1779:on 22 August 2008
1708:
1659:= Hydraulic slope
1637:
1625:
1600:
1587:
1539:
1450:
1438:
1413:
1400:
1366:
1354:
1303:
1266:
1246:
1209:
1169:
1094:
937:
875:
762:
559:
558:
215:empirical formula
131:
2468:
2216:
2209:
2202:
2193:
2192:
2150:
2133:
2116:
2105:
2096:
2087:
2070:
2069:
2067:
2065:
2059:
2053:. Archived from
2052:
2044:
2038:
2035:
2029:
2028:
2027:
2025:
2012:
1987:
1981:
1975:
1969:
1963:
1953:
1947:
1941:
1935:
1929:
1923:
1921:
1894:
1888:
1887:
1881:
1873:
1846:
1840:
1839:
1821:
1815:
1814:
1812:
1810:
1795:
1789:
1788:
1786:
1784:
1775:. Archived from
1769:
1725:for alternatives
1699:
1648:
1646:
1645:
1640:
1638:
1636:
1635:
1634:
1623:
1622:
1621:
1611:
1610:
1609:
1598:
1593:
1588:
1583:
1582:
1573:
1533:
1461:
1459:
1458:
1453:
1451:
1449:
1448:
1447:
1436:
1435:
1434:
1424:
1423:
1422:
1411:
1406:
1401:
1396:
1395:
1386:
1381:
1380:
1379:
1364:
1352:
1314:
1312:
1311:
1306:
1304:
1302:
1301:
1300:
1290:
1289:
1279:
1278:
1269:
1267:
1265:
1264:
1252:
1247:
1245:
1244:
1243:
1233:
1232:
1222:
1221:
1212:
1210:
1208:
1207:
1206:
1196:
1195:
1185:
1184:
1175:
1170:
1168:
1167:
1166:
1156:
1155:
1145:
1144:
1134:
1133:
1123:
1122:
1121:
1111:
1110:
1100:
1095:
1093:
1092:
1091:
1081:
1080:
1070:
1069:
1059:
1058:
1048:
1047:
1037:
1036:
1035:
1025:
1024:
1014:
1013:
1003:
985:
977:
973:
966:
962:
958:
954:hydraulic radius
948:
946:
945:
940:
938:
936:
935:
934:
924:
923:
913:
912:
902:
901:
891:
890:
881:
876:
874:
873:
872:
862:
861:
851:
850:
840:
839:
829:
828:
827:
818:
817:
807:
789:
773:
771:
770:
765:
763:
761:
760:
759:
749:
748:
738:
737:
727:
726:
717:
696:
694:
693:
688:
682:
681:
671:
670:
660:
659:
647:
646:
627:
620:
618:
617:
612:
610:
609:
599:
598:
355:
354:
302:hydraulic radius
271:
269:
268:
263:
261:
260:
250:
249:
170:
168:
167:
162:
160:
159:
149:
148:
132:
124:
99:hydraulic radius
79:Antoine de Chézy
31:systems such as
2476:
2475:
2471:
2470:
2469:
2467:
2466:
2465:
2421:
2420:
2419:
2414:
2393:Public networks
2388:
2307:
2297:Manning formula
2256:
2242:Hydraulic fluid
2225:
2220:
2157:
2084:Fluid Mechanics
2078:
2076:Further reading
2073:
2063:
2061:
2057:
2050:
2046:
2045:
2041:
2036:
2032:
2023:
2021:
2014:
2013:
1990:
1982:
1978:
1970:
1966:
1954:
1950:
1942:
1938:
1930:
1926:
1895:
1891:
1875:
1874:
1862:
1848:
1847:
1843:
1836:
1822:
1818:
1808:
1806:
1805:on 6 April 2013
1797:
1796:
1792:
1782:
1780:
1771:
1770:
1766:
1762:
1715:
1705:
1665:
1630:
1626:
1617:
1613:
1612:
1605:
1601:
1594:
1592:
1578:
1574:
1572:
1564:
1561:
1560:
1546:
1494:
1487:
1474:
1443:
1439:
1430:
1426:
1425:
1418:
1414:
1407:
1405:
1391:
1387:
1385:
1342:
1341:
1337:
1335:
1332:
1331:
1321:
1296:
1292:
1285:
1281:
1280:
1274:
1270:
1268:
1260:
1256:
1251:
1239:
1235:
1228:
1224:
1223:
1217:
1213:
1211:
1202:
1198:
1191:
1187:
1186:
1180:
1176:
1174:
1162:
1158:
1151:
1147:
1140:
1136:
1129:
1125:
1124:
1117:
1113:
1106:
1102:
1101:
1099:
1087:
1083:
1076:
1072:
1065:
1061:
1054:
1050:
1043:
1039:
1038:
1031:
1027:
1020:
1016:
1009:
1005:
1004:
1002:
994:
991:
990:
979:
975:
968:
964:
960:
956:
930:
926:
919:
915:
908:
904:
897:
893:
892:
886:
882:
880:
868:
864:
857:
853:
846:
842:
835:
831:
830:
823:
819:
813:
809:
808:
806:
798:
795:
794:
778:
755:
751:
744:
740:
733:
729:
728:
722:
718:
716:
708:
705:
704:
677:
673:
666:
662:
655:
651:
642:
638:
636:
633:
632:
625:
605:
601:
594:
590:
574:
571:
570:
564:
499:Galvanized iron
373:Asbestos-cement
317:
256:
252:
245:
241:
225:
222:
221:
200:Julius Weisbach
198:. Around 1845,
155:
151:
144:
140:
123:
112:
109:
108:
72:
56:Reynolds number
17:
12:
11:
5:
2474:
2464:
2463:
2458:
2453:
2448:
2443:
2438:
2433:
2416:
2415:
2413:
2412:
2407:
2402:
2396:
2394:
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2389:
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2376:
2371:
2366:
2361:
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2341:
2336:
2331:
2326:
2321:
2315:
2313:
2309:
2308:
2306:
2305:
2300:
2290:
2285:
2280:
2275:
2270:
2264:
2262:
2258:
2257:
2255:
2254:
2249:
2244:
2239:
2233:
2231:
2227:
2226:
2219:
2218:
2211:
2204:
2196:
2190:
2189:
2183:
2178:
2173:
2168:
2163:
2156:
2155:External links
2153:
2152:
2151:
2134:
2122:
2117:
2106:
2097:
2088:
2077:
2074:
2072:
2071:
2039:
2030:
1988:
1986:, pp. 1–2
1976:
1964:
1948:
1936:
1924:
1922:, p. 112.
1889:
1860:
1841:
1834:
1816:
1790:
1763:
1761:
1758:
1757:
1756:
1751:
1746:
1741:
1736:
1731:
1729:Fluid dynamics
1726:
1723:Prony equation
1714:
1711:
1710:
1709:
1703:
1696:
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1143:
1139:
1132:
1128:
1120:
1116:
1109:
1105:
1098:
1090:
1086:
1079:
1075:
1068:
1064:
1057:
1053:
1046:
1042:
1034:
1030:
1023:
1019:
1012:
1008:
1001:
998:
950:
949:
933:
929:
922:
918:
911:
907:
900:
896:
889:
885:
879:
871:
867:
860:
856:
849:
845:
838:
834:
826:
822:
816:
812:
805:
802:
777:The flow rate
775:
774:
758:
754:
747:
743:
736:
732:
725:
721:
715:
712:
698:
697:
686:
680:
676:
669:
665:
658:
654:
650:
645:
641:
622:
621:
608:
604:
597:
593:
588:
584:
581:
578:
563:
560:
557:
556:
554:
551:
548:
541:
540:
538:
535:
532:
525:
524:
522:
519:
516:
510:
509:
507:
504:
501:
495:
494:
491:
488:
485:
479:
478:
476:
473:
470:
464:
463:
461:
458:
455:
449:
448:
445:
442:
439:
433:
432:
430:
427:
424:
417:
416:
414:
411:
408:
401:
400:
398:
395:
392:
385:
384:
381:
378:
375:
369:
368:
365:
362:
359:
320:
319:
315:
305:
295:
289:
283:
273:
272:
259:
255:
248:
244:
239:
235:
232:
229:
206:developed the
184:Gotthilf Hagen
172:
171:
158:
154:
147:
143:
138:
135:
130:
127:
122:
119:
116:
83:hydraulic head
71:
68:
15:
9:
6:
4:
3:
2:
2473:
2462:
2459:
2457:
2456:Hydrodynamics
2454:
2452:
2449:
2447:
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2428:
2426:
2411:
2408:
2406:
2403:
2401:
2398:
2397:
2395:
2391:
2385:
2382:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2359:Power network
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2330:
2327:
2325:
2322:
2320:
2317:
2316:
2314:
2310:
2304:
2301:
2298:
2294:
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2265:
2263:
2259:
2253:
2250:
2248:
2245:
2243:
2240:
2238:
2235:
2234:
2232:
2228:
2224:
2217:
2212:
2210:
2205:
2203:
2198:
2197:
2194:
2187:
2184:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2158:
2149:
2145:
2141:
2135:
2131:
2130:
2123:
2121:
2118:
2114:
2113:
2107:
2103:
2098:
2095:, McGraw Hill
2094:
2089:
2085:
2080:
2079:
2056:
2049:
2043:
2034:
2019:
2018:
2011:
2009:
2007:
2005:
2003:
2001:
1999:
1997:
1995:
1993:
1985:
1980:
1973:
1968:
1961:
1957:
1952:
1946:, p. 113
1945:
1940:
1934:, p. 112
1933:
1928:
1920:
1916:
1912:
1908:
1904:
1900:
1893:
1885:
1879:
1871:
1867:
1863:
1857:
1853:
1852:
1845:
1837:
1835:0-07-007247-7
1831:
1827:
1820:
1804:
1800:
1794:
1778:
1774:
1768:
1764:
1755:
1752:
1750:
1747:
1745:
1742:
1740:
1737:
1735:
1732:
1730:
1727:
1724:
1720:
1717:
1716:
1706:
1698:
1697:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1669:
1661:
1658:
1655:
1654:
1653:
1631:
1627:
1618:
1614:
1606:
1602:
1595:
1589:
1584:
1579:
1575:
1569:
1566:
1559:
1558:
1555:
1554:
1553:
1551:
1536:
1532:
1531:
1527:
1524:
1521:
1518:
1515:
1512:= flow, gpm (
1511:
1508:
1505:
1502:
1500:
1498:
1489:
1484:
1481:
1478:
1471:
1468:
1467:
1466:
1444:
1440:
1431:
1427:
1419:
1415:
1408:
1402:
1397:
1392:
1388:
1382:
1338:
1330:
1329:
1328:
1326:
1297:
1293:
1286:
1282:
1275:
1271:
1261:
1257:
1253:
1248:
1240:
1236:
1229:
1225:
1218:
1214:
1203:
1199:
1192:
1188:
1181:
1177:
1171:
1163:
1159:
1152:
1148:
1141:
1137:
1130:
1126:
1118:
1114:
1107:
1103:
1096:
1088:
1084:
1077:
1073:
1066:
1062:
1055:
1051:
1044:
1040:
1032:
1028:
1021:
1017:
1010:
1006:
999:
996:
989:
988:
987:
983:
971:
955:
931:
927:
920:
916:
909:
905:
898:
894:
887:
883:
877:
869:
865:
858:
854:
847:
843:
836:
832:
824:
820:
814:
810:
803:
800:
793:
792:
791:
788:
785:
781:
756:
752:
745:
741:
734:
730:
723:
719:
713:
710:
703:
702:
701:
684:
678:
674:
667:
663:
656:
652:
648:
643:
639:
631:
630:
629:
606:
602:
595:
591:
586:
582:
579:
576:
569:
568:
567:
562:Pipe equation
555:
552:
549:
546:
543:
542:
539:
536:
533:
530:
527:
526:
523:
520:
517:
515:
512:
511:
508:
505:
502:
500:
497:
496:
492:
489:
486:
484:
481:
480:
477:
474:
471:
469:
466:
465:
462:
459:
456:
454:
451:
450:
446:
443:
440:
438:
435:
434:
431:
428:
425:
422:
419:
418:
415:
412:
409:
406:
403:
402:
399:
396:
393:
390:
387:
386:
382:
379:
376:
374:
371:
370:
366:
364:C Factor high
363:
360:
357:
356:
353:
351:
346:
344:
340:
336:
332:
327:
325:
313:
309:
306:
303:
299:
296:
293:
290:
287:
284:
281:
278:
277:
276:
257:
253:
246:
242:
237:
233:
230:
227:
220:
219:
218:
216:
211:
209:
205:
201:
197:
193:
189:
185:
181:
177:
174:The variable
156:
152:
145:
141:
136:
133:
128:
125:
120:
117:
114:
107:
106:
105:
103:
100:
96:
92:
88:
87:Chézy formula
84:
80:
76:
67:
65:
61:
57:
53:
48:
46:
42:
38:
34:
30:
26:
22:
2379:Rescue tools
2344:Drive system
2312:Technologies
2282:
2138:
2127:
2111:
2101:
2092:
2083:
2062:. Retrieved
2055:the original
2042:
2033:
2022:, retrieved
2016:
1979:
1967:
1959:
1951:
1939:
1927:
1902:
1898:
1892:
1850:
1844:
1825:
1819:
1807:. Retrieved
1803:the original
1793:
1781:. Retrieved
1777:the original
1767:
1701:
1691:
1685:
1679:
1673:
1656:
1651:
1547:
1534:
1525:
1519:
1509:
1503:
1490:
1482:
1473:psi per foot
1469:
1464:
1322:
981:
969:
951:
786:
783:
779:
776:
699:
623:
565:
514:Polyethylene
361:C Factor low
349:
347:
342:
338:
334:
330:
328:
323:
321:
307:
297:
291:
285:
279:
274:
212:
192:laminar flow
179:
175:
173:
101:
94:
90:
73:
70:General form
51:
49:
20:
18:
2324:Accumulator
2247:Fluid power
1974:, p. 1
1944:Walski 2006
1932:Walski 2006
204:Henry Darcy
75:Henri Pitot
45:Allen Hazen
2461:Irrigation
2451:Hydraulics
2425:Categories
2410:Manchester
2237:Hydraulics
2223:Hydraulics
2064:6 December
1809:27 January
1783:6 December
1760:References
367:Reference
345:is 0.001.
41:irrigation
29:water pipe
2400:Liverpool
2319:Machinery
2024:7 October
1919:108604497
1878:cite book
1870:144609617
1668:head loss
1479:per foot)
1189:π
1127:π
1041:π
421:Cast iron
405:Cast iron
389:Cast iron
312:head loss
64:viscosity
2446:Plumbing
2349:Manifold
2339:Cylinder
2261:Modeling
2230:Concepts
1749:Pressure
1744:Plumbing
1734:Friction
1713:See also
1544:SI units
453:Concrete
423:20 years
407:10 years
358:Material
348:Typical
2334:Circuit
2148:1981183
1652:where:
1465:where:
980:π
300:is the
275:where:
2441:Piping
2405:London
2146:
1917:
1868:
1858:
1832:
1632:4.8704
1624:
1599:
1445:4.8704
1437:
1412:
1365:
1353:
1298:4.8704
1254:7.8828
1241:4.8704
1164:4.8704
1089:3.7034
626:1/0.54
468:Copper
194:, the
39:, and
23:is an
2364:Press
2354:Motor
2329:Brake
2058:(PDF)
2051:(PDF)
1915:S2CID
1619:1.852
1607:1.852
1596:10.67
1535:Note:
1432:1.852
1420:1.852
1287:1.852
1276:1.852
1262:1.852
1230:1.852
1219:1.852
1204:1.852
1193:1.852
1182:3.019
1153:1.852
1142:1.852
1131:1.852
1119:1.852
1108:3.019
1078:1.167
1067:1.852
1056:1.852
1045:1.852
1033:1.852
1022:1.852
1011:1.167
986:, so
932:1.852
921:1.167
910:1.852
899:1.852
888:1.852
870:1.852
859:1.167
848:1.852
837:1.852
825:1.852
815:1.852
790:, so
757:1.167
746:1.852
735:1.852
724:1.852
679:1.167
668:1.852
657:1.852
644:1.852
547:(FRP)
531:(PVC)
483:Steel
60:water
2384:Seal
2369:Pump
2144:OCLC
2066:2008
2026:2012
1884:link
1866:OCLC
1856:ISBN
1830:ISBN
1811:2009
1785:2008
1721:and
1409:4.52
952:The
607:0.54
596:0.63
258:0.54
247:0.63
202:and
186:and
97:and
19:The
2374:Ram
1907:doi
984:/ 4
978:is
967:is
553:150
550:150
537:150
534:150
521:140
518:140
506:120
503:120
490:110
475:140
472:130
460:140
457:100
444:140
441:140
429:100
413:113
410:107
397:130
394:130
391:new
380:140
377:140
318:/L)
157:0.5
146:0.5
2427::
1991:^
1913:,
1903:98
1901:,
1880:}}
1876:{{
1864:.
1666:=
972:/4
782:=
493:–
487:90
447:–
426:89
383:-
210:.
104::
35:,
2299:)
2295:(
2215:e
2208:t
2201:v
2068:.
1960:c
1909::
1886:)
1872:.
1838:.
1813:.
1787:.
1704:f
1702:h
1692:d
1686:C
1680:Q
1674:L
1664:f
1662:h
1657:S
1628:d
1615:C
1603:Q
1590:=
1585:L
1580:f
1576:h
1570:=
1567:S
1526:d
1520:C
1516:)
1510:Q
1504:L
1499:)
1493:d
1491:P
1483:S
1470:S
1441:d
1428:C
1416:Q
1403:=
1398:L
1393:d
1389:P
1383:=
1377:t
1374:o
1371:o
1368:f
1362:r
1359:e
1356:p
1350:i
1347:s
1344:p
1339:S
1294:d
1283:C
1272:Q
1258:k
1249:=
1237:d
1226:C
1215:Q
1200:k
1178:4
1172:=
1160:d
1149:C
1138:k
1115:Q
1104:4
1097:=
1085:d
1074:d
1063:C
1052:k
1029:Q
1018:4
1007:4
1000:=
997:S
982:d
976:A
970:d
965:d
961:r
957:R
928:A
917:R
906:C
895:k
884:Q
878:=
866:A
855:R
844:C
833:k
821:A
811:V
804:=
801:S
787:A
784:V
780:Q
753:R
742:C
731:k
720:V
714:=
711:S
685:S
675:R
664:C
653:k
649:=
640:V
603:S
592:R
587:C
583:k
580:=
577:V
350:C
343:k
339:S
335:C
331:k
324:C
316:f
308:S
298:R
292:C
286:k
280:V
254:S
243:R
238:C
234:k
231:=
228:V
180:C
176:C
153:S
142:R
137:C
134:=
129:S
126:R
121:C
118:=
115:V
102:R
95:V
91:S
52:C
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