1631:
1352:
1626:{\displaystyle \overbrace {\underbrace {\partial {\bf {v}} \over {\partial t}} _{\begin{smallmatrix}{\text{Local}}\\{\text{Change}}\end{smallmatrix}}+\underbrace {{\bf {v}}\cdot \nabla {\bf {v}}} _{\text{Advection}}} ^{\text{Inertial Acceleration}}=-\underbrace {{1 \over {\rho }}\nabla p} _{\begin{smallmatrix}{\text{Pressure}}\\{\text{Gradient}}\end{smallmatrix}}+\underbrace {\nu \Delta {\bf {v}}} _{\text{Diffusion}}-\underbrace {\nabla \Phi } _{\text{Gravity}}+\underbrace {\bf {F}} _{\begin{smallmatrix}{\text{External}}\\{\text{Forces}}\end{smallmatrix}}}
66:
2278:
3332:
1917:
2082:
3200:
3116:
1741:
217:
has a minor contribution, but does not play a significant enough role in most circumstances to be a governing factor. Due to the presence of a free surface, gravity is generally the most significant driver of open-channel flow; therefore, the ratio of inertial to gravity forces is the most important
191:
The discharge of a steady flow is non-uniform along a channel. This happens when water enters and/or leaves the channel along the course of flow. An example of flow entering a channel would be a road side gutter. An example of flow leaving a channel would be an irrigation channel. This flow can be
2929:
1085:
2606:
2962:
3657:
2746:
1266:
2273:{\displaystyle {\partial u \over {\partial t}}+u{\partial u \over {\partial x}}+g{\partial \zeta \over {\partial x}}=F_{x}\implies {\partial u \over {\partial t}}+u{\partial u \over {\partial x}}+g{\partial \eta \over {\partial x}}-gS=F_{x}}
2805:
3327:{\displaystyle E=\underbrace {{1 \over {2}}\rho \|{\bf {v}}\|^{2}} _{\begin{smallmatrix}{\text{Kinetic}}\\{\text{Energy}}\end{smallmatrix}}+\underbrace {\rho \Phi } _{\begin{smallmatrix}{\text{Potential}}\\{\text{Energy}}\end{smallmatrix}}}
4059:
795:
944:
1912:{\displaystyle {\begin{aligned}{\partial u \over {\partial t}}+u{\partial u \over {\partial x}}&=-{1 \over {\rho }}{\partial p \over {\partial x}}+F_{x}\\-{1 \over {\rho }}{\partial p \over {\partial z}}-g&=0\end{aligned}}}
559:
1335:
949:
3426:
457:
81:
Open-channel flow can be classified and described in various ways based on the change in flow depth with respect to time and space. The fundamental types of flow dealt with in open-channel hydraulics are:
3171:
123:
The depth of flow is the same at every section of the channel. Uniform flow can be steady or unsteady, depending on whether or not the depth changes with time, (although unsteady uniform flow is rare).
58:. These two types of flow are similar in many ways but differ in one important respect: open-channel flow has a free surface, whereas pipe flow does not, resulting in flow dominated by gravity but not
2488:
2385:
2660:
3558:
1746:
133:
The depth of flow changes along the length of the channel. Varied flow technically may be either steady or unsteady. Varied flow can be further classified as either rapidly or gradually-varied:
262:
3553:
2655:
2030:
1175:
675:
3111:{\displaystyle {\partial \over {\partial t}}\left({1 \over {2}}\|{\bf {v}}\|^{2}\right)+{\bf {v}}\cdot \nabla \left({1 \over {2}}\|{\bf {v}}\|^{2}+{p \over {\rho }}+\Phi \right)=0}
2480:
703:
800:
1170:
612:
3689:
1952:
1124:
2328:
3522:
2796:
496:
2957:
394:
1732:
2766:
1699:
2050:
3724:
3458:
3352:
2405:
2077:
579:
3357:
1675:
3545:
3478:
3191:
2429:
1651:
698:
639:
326:
302:
282:
192:
described using the continuity equation for continuous unsteady flow requires the consideration of the time effect and includes a time element as a variable.
2924:{\displaystyle {\partial {\bf {v}} \over {\partial t}}+\omega \times {\bf {v}}=-\nabla \left({1 \over {2}}\|{\bf {v}}\|^{2}+{p \over {\rho }}+\Phi \right)}
357:
177:
of the channel under consideration. This is often the case with a steady flow. This flow is considered continuous and therefore can be described using the
1274:
366:
for quantities that are useful in open-channel flow: mass, momentum, and energy. The governing equations result from considering the dynamics of the
2333:
1346:
399:
4107:
348:. However, it is generally acceptable to assume that the Reynolds number is sufficiently large so that viscous forces may be neglected.
225:
3918:
1080:{\displaystyle {d \over {dt}}\int _{x}\left(\int _{A}dA\right)dx=-\int _{x}{\partial \over {\partial x}}\left(\int _{A}u\;dA\right)dx}
4041:
3901:
141:
The depth changes abruptly over a comparatively short distance. Rapidly varied flow is known as a local phenomenon. Examples are the
4293:
4028:
4011:
3981:
3928:
3800:
345:
2601:{\displaystyle {\partial u \over {\partial t}}+u{\partial u \over {\partial x}}+g{\partial \eta \over {\partial x}}+g(S_{f}-S)=0}
96:
The depth of flow does not change over time, or if it can be assumed to be constant during the time interval under consideration.
3124:
4002:
4339:
4298:
3652:{\displaystyle {\begin{aligned}h&=e+{p \over {\rho g}}\\&={u^{2} \over {2g}}+z+{p \over {\gamma }}\end{aligned}}}
3763:
4176:
4166:
3844:
460:
2623:
1957:
4324:
4303:
329:
3888:
700:
can change with both time and space in the channel. If we start from the integral form of the continuity equation:
4181:
4171:
3428:
Assuming that the energy density is time-independent and the flow is one-dimensional leads to the simplification:
4100:
678:
4161:
3481:
644:
2741:{\displaystyle {\bf {v}}\cdot \nabla {\bf {v}}=\omega \times {\bf {v}}+{1 \over {2}}\nabla \|{\bf {v}}\|^{2}}
4329:
4252:
3859:
1735:
69:
3431:
4272:
4237:
2438:
797:
it is possible to decompose the volume integral into a cross-section and length, which leads to the form:
4217:
4196:
4145:
3119:
1261:{\displaystyle \int _{x}{\partial A \over {\partial t}}\;dx=-\int _{x}{\partial Q \over {\partial x}}dx}
305:
1132:
3864:
1920:
1127:
588:
3665:
1925:
4334:
4212:
4093:
1678:
1090:
490:
471:
178:
2283:
4242:
4232:
59:
4079:
3490:
2775:
2938:
375:
4227:
4024:
4007:
3977:
3924:
3897:
1708:
174:
2802:. This leads to a form of the momentum equation, ignoring the external forces term, given by:
2751:
1684:
3839:
2432:
2035:
1702:
790:{\displaystyle {d \over {dt}}\int _{V}\rho \;dV=-\int _{V}\nabla \cdot (\rho {\bf {v}})\;dV}
363:
3702:
3337:
2390:
2055:
564:
466:
To simplify the final form of the equations, it is acceptable to make several assumptions:
4257:
4247:
4222:
4190:
4135:
3968:
3854:
3822:
3692:
3485:
2330:. To account for shear stress along the channel banks, we may define the force term to be:
1660:
939:{\displaystyle {d \over {dt}}\int _{x}\left(\int _{A}\rho \;dA\right)dx=-\int _{x}\leftdx}
333:
214:
31:
2482:, a way of quantifying friction losses, leads to the final form of the momentum equation:
463:, these components correspond to the flow velocity in the x, y, and z axes respectively.
1268:
Finally, this leads to the continuity equation for incompressible, 1D open-channel flow:
4277:
4262:
3849:
3768:
3530:
3525:
3463:
3194:
3176:
2799:
2414:
1636:
683:
624:
619:
341:
311:
287:
267:
146:
142:
51:
4019:
1738:. By invoking the high Reynolds number and 1D flow assumptions, we have the equations:
477:
The
Reynolds number is sufficiently large such that viscous diffusion can be neglected
4318:
4267:
4052:
4047:
3817:
367:
219:
3790:
3738:
that was ignored by discounting the external forces term in the momentum equation.
2408:
554:{\displaystyle {\partial \rho \over {\partial t}}+\nabla \cdot (\rho {\bf {v}})=0}
370:
337:
47:
332:. Depending on the effect of viscosity relative to inertia, as represented by the
1330:{\displaystyle {\partial A \over {\partial t}}+{\partial Q \over {\partial x}}=0}
17:
4140:
3945:
3727:
3301:
3257:
2932:
1600:
1502:
1392:
65:
4130:
4116:
4074:
4069:
4064:
3805:
3773:
3753:
3735:
1345:
The momentum equation for open-channel flow may be found by starting from the
615:
35:
3421:{\displaystyle {\partial E \over {\partial t}}+{\bf {v}}\cdot \nabla (E+p)=0}
3827:
3795:
3778:
3696:
2769:
206:
55:
3731:
1654:
452:{\displaystyle {\bf {v}}={\begin{pmatrix}u&v&w\end{pmatrix}}^{T}}
3748:
946:
Under the assumption of incompressible, 1D flow, this equation becomes:
618:
operator. Under the assumption of incompressible flow, with a constant
582:
210:
2617:
43:
64:
4023:. Water Science and Technology Library. New York, NY: Springer.
205:
The behavior of open-channel flow is governed by the effects of
4089:
4085:
3166:{\displaystyle {\bf {v}}\cdot (\omega \times {\bf {v}})=0}
2380:{\displaystyle F_{x}=-{1 \over {\rho }}{\tau \over {R}}}
3695:. However, realistic systems require the addition of a
474:(this is not a good assumption for rapidly-varied flow)
362:
It is possible to formulate equations describing three
218:
dimensionless parameter. The parameter is known as the
493:, describing the conservation of mass, takes the form:
419:
3705:
3668:
3556:
3533:
3493:
3484:. Of particular interest in open-channel flow is the
3466:
3434:
3360:
3340:
3203:
3179:
3127:
2965:
2941:
2808:
2778:
2754:
2663:
2626:
2491:
2441:
2417:
2393:
2336:
2286:
2085:
2058:
2038:
2032:
is the difference between the free surface elevation
1960:
1928:
1744:
1711:
1687:
1663:
1639:
1355:
1277:
1178:
1135:
1093:
952:
803:
706:
686:
647:
627:
591:
567:
499:
402:
378:
314:
290:
270:
228:
2620:
equation, note that the advective acceleration term
4286:
4205:
4154:
4123:
3718:
3683:
3651:
3539:
3516:
3472:
3452:
3420:
3346:
3326:
3185:
3165:
3110:
2951:
2923:
2790:
2760:
2740:
2649:
2600:
2474:
2423:
2399:
2379:
2322:
2272:
2071:
2044:
2024:
1946:
1911:
1726:
1693:
1669:
1645:
1625:
1329:
1260:
1164:
1118:
1079:
938:
789:
692:
669:
633:
606:
573:
553:
451:
388:
320:
296:
276:
257:{\displaystyle {\text{Fr}}={U \over {\sqrt {gD}}}}
256:
4048:Derivation of the Equations of Open Channel Flow
4006:. IAHR Monograph. Rotterdam, NL: A.A. Balkema.
3947:Basic Hydraulic Principles of Open-Channel Flow
3944:Jobson, Harvey E.; Froehlich, David C. (1988).
3917:Battjes, Jurjen A.; Labeur, Robert Jan (2017).
3354:is time-independent, we arrive at the equation:
2650:{\displaystyle {\bf {v}}\cdot \nabla {\bf {v}}}
2025:{\displaystyle \eta (t,x)=\zeta (t,x)-z_{b}(x)}
4101:
4020:Numerical Modeling in Open Channel Hydraulics
3923:. Cambridge, UK: Cambridge University Press.
2079:. Substitution into the first equation gives:
480:The flow is one-dimensional across the x-axis
54:. The other type of flow within a conduit is
8:
3240:
3229:
3067:
3056:
3009:
2998:
2886:
2875:
2785:
2779:
2729:
2718:
358:Computational methods for free surface flow
4108:
4094:
4086:
2175:
2171:
1209:
1155:
1059:
918:
847:
780:
735:
641:, this equation has the simple expression
3710:
3704:
3667:
3638:
3633:
3614:
3608:
3602:
3582:
3577:
3557:
3555:
3532:
3503:
3492:
3465:
3433:
3385:
3384:
3371:
3361:
3359:
3339:
3313:
3304:
3299:
3284:
3269:
3260:
3255:
3243:
3233:
3232:
3219:
3214:
3211:
3202:
3178:
3148:
3147:
3129:
3128:
3126:
3084:
3079:
3070:
3060:
3059:
3049:
3044:
3027:
3026:
3012:
3002:
3001:
2991:
2986:
2971:
2966:
2964:
2943:
2942:
2940:
2903:
2898:
2889:
2879:
2878:
2868:
2863:
2843:
2842:
2823:
2816:
2815:
2809:
2807:
2777:
2753:
2732:
2722:
2721:
2708:
2703:
2694:
2693:
2678:
2677:
2665:
2664:
2662:
2641:
2640:
2628:
2627:
2625:
2577:
2554:
2544:
2528:
2518:
2502:
2492:
2490:
2458:
2446:
2440:
2416:
2392:
2370:
2365:
2358:
2353:
2341:
2335:
2309:
2303:
2285:
2264:
2238:
2228:
2212:
2202:
2186:
2176:
2165:
2148:
2138:
2122:
2112:
2096:
2086:
2084:
2063:
2057:
2037:
2007:
1959:
1927:
1879:
1869:
1862:
1857:
1844:
1827:
1817:
1810:
1805:
1785:
1775:
1759:
1749:
1745:
1743:
1710:
1686:
1662:
1638:
1612:
1603:
1598:
1588:
1586:
1576:
1561:
1551:
1539:
1538:
1529:
1514:
1505:
1500:
1481:
1476:
1473:
1460:
1448:
1436:
1435:
1423:
1422:
1419:
1404:
1395:
1390:
1376:
1369:
1368:
1361:
1357:
1354:
1311:
1301:
1288:
1278:
1276:
1242:
1232:
1226:
1199:
1189:
1183:
1177:
1146:
1134:
1098:
1092:
1050:
1031:
1026:
1020:
987:
972:
958:
953:
951:
909:
908:
890:
875:
838:
823:
809:
804:
802:
771:
770:
752:
726:
712:
707:
705:
685:
655:
654:
646:
626:
590:
566:
536:
535:
510:
500:
498:
443:
414:
404:
403:
401:
380:
379:
377:
313:
289:
269:
242:
237:
229:
227:
173:The discharge is constant throughout the
4053:Surface Profiles for Steady Channel Flow
3976:. New York, NY: McGraw-Hill. p. 2.
3480:being a constant; this is equivalent to
670:{\displaystyle \nabla \cdot {\bf {v}}=0}
106:The depth of flow does change with time.
4000:Nezu, Iehisa; Nakagawa, Hiroji (1993).
3879:
3118:This equation was arrived at using the
159:The depth changes over a long distance.
1347:incompressible Navier-Stokes equations
3953:. Reston, VA: U.S. Geological Survey.
3896:. Caldwell, NJ: The Blackburn Press.
7:
3962:
3960:
27:Type of liquid flow within a conduit
2475:{\displaystyle S_{f}=\tau /\rho gR}
677:. However, it is possible that the
3394:
3372:
3364:
3341:
3290:
3094:
3036:
2972:
2968:
2913:
2855:
2824:
2812:
2715:
2674:
2637:
2555:
2547:
2529:
2521:
2503:
2495:
2239:
2231:
2213:
2205:
2187:
2179:
2149:
2141:
2123:
2115:
2097:
2089:
1880:
1872:
1828:
1820:
1786:
1778:
1760:
1752:
1712:
1688:
1567:
1564:
1535:
1488:
1432:
1377:
1365:
1312:
1304:
1289:
1281:
1243:
1235:
1200:
1192:
1032:
1028:
896:
758:
648:
592:
523:
511:
503:
25:
3300:
3256:
1599:
1501:
1391:
308:scale for a channel's depth, and
4003:Turbulence in Open-Channel Flows
3386:
3234:
3149:
3130:
3061:
3028:
3003:
2944:
2880:
2844:
2817:
2723:
2695:
2679:
2666:
2642:
2629:
1589:
1540:
1437:
1424:
1370:
1165:{\displaystyle Q=\int _{A}u\;dA}
910:
772:
656:
537:
405:
381:
3524:, which is used to compute the
607:{\displaystyle \nabla \cdot ()}
3920:Unsteady Flow in Open Channels
3684:{\displaystyle \gamma =\rho g}
3409:
3397:
3154:
3138:
2589:
2570:
2435:. Defining the friction slope
2172:
2019:
2013:
1997:
1985:
1976:
1964:
1947:{\displaystyle p=\rho g\zeta }
1919:The second equation implies a
915:
902:
777:
764:
601:
598:
542:
529:
1:
4080:Simulation of Turbulent Flows
4017:Syzmkiewicz, Romuald (2010).
1172:, the equation is reduced to:
1119:{\displaystyle \int _{A}dA=A}
46:flow within a conduit with a
3764:Computational fluid dynamics
2959:with this equation leads to:
2323:{\displaystyle S=-dz_{b}/dx}
2280:where the channel bed slope
209:and gravity relative to the
181:for continuous steady flow.
4356:
4065:Open Channel Flow Concepts
3517:{\displaystyle e=E/\rho g}
2791:{\displaystyle \|\cdot \|}
1954:, where the channel depth
355:
330:gravitational acceleration
4182:Hydrological optimization
4172:Groundwater flow equation
4075:Open Channel Flow Example
4070:What is a Hydraulic Jump?
2952:{\displaystyle {\bf {v}}}
389:{\displaystyle {\bf {v}}}
336:, the flow can be either
3967:Sturm, Terry W. (2001).
1727:{\displaystyle \Phi =gz}
4177:Hazen–Williams equation
4167:Darcy–Weisbach equation
3970:Open Channel Hydraulics
3890:Open-Channel Hydraulics
3845:Darcy-Weisbach equation
2761:{\displaystyle \omega }
2052:and the channel bottom
1736:gravitational potential
1694:{\displaystyle \Delta }
77:Classifications of flow
70:Central Arizona Project
3860:Saint-Venant equations
3835:Other related articles
3726:to account for energy
3720:
3685:
3653:
3541:
3518:
3474:
3454:
3422:
3348:
3328:
3187:
3167:
3112:
2953:
2925:
2792:
2762:
2742:
2651:
2602:
2476:
2425:
2401:
2381:
2324:
2274:
2073:
2046:
2045:{\displaystyle \zeta }
2026:
1948:
1913:
1728:
1695:
1671:
1647:
1627:
1331:
1262:
1166:
1120:
1081:
940:
791:
694:
671:
635:
608:
575:
555:
453:
390:
322:
298:
284:is the mean velocity,
278:
258:
114:Space as the criterion
73:
4340:Hydraulic engineering
4197:Pipe network analysis
4162:Bernoulli's principle
4146:Hydraulic engineering
3887:Chow, Ven Te (2008).
3721:
3719:{\displaystyle h_{f}}
3686:
3654:
3542:
3519:
3482:Bernoulli's principle
3475:
3455:
3453:{\displaystyle E+p=C}
3423:
3349:
3347:{\displaystyle \Phi }
3329:
3188:
3168:
3120:scalar triple product
3113:
2954:
2926:
2793:
2763:
2743:
2657:may be decomposed as:
2652:
2603:
2477:
2426:
2402:
2400:{\displaystyle \tau }
2382:
2325:
2275:
2074:
2072:{\displaystyle z_{b}}
2047:
2027:
1949:
1914:
1729:
1696:
1672:
1648:
1628:
1462:Inertial Acceleration
1332:
1263:
1167:
1121:
1082:
941:
792:
695:
672:
636:
609:
576:
574:{\displaystyle \rho }
556:
461:Cartesian coordinates
454:
391:
356:Further information:
323:
306:characteristic length
299:
279:
259:
187:Spatially-varied flow
155:Gradually-varied flow
87:Time as the criterion
68:
3865:Standard step method
3703:
3666:
3554:
3531:
3491:
3464:
3432:
3358:
3338:
3201:
3177:
3125:
2963:
2939:
2806:
2776:
2752:
2661:
2624:
2489:
2439:
2415:
2391:
2334:
2284:
2083:
2056:
2036:
1958:
1926:
1921:hydrostatic pressure
1742:
1709:
1685:
1670:{\displaystyle \nu }
1661:
1637:
1353:
1275:
1176:
1133:
1128:volumetric flow rate
1091:
950:
801:
704:
684:
679:cross-sectional area
645:
625:
589:
565:
497:
400:
376:
312:
288:
268:
226:
222:, and is defined as:
213:forces of the flow.
3786:Types of fluid flow
3547:that is defined as:
1679:kinematic viscosity
491:continuity equation
485:Continuity equation
179:continuity equation
137:Rapidly-varied flow
3716:
3681:
3649:
3647:
3537:
3514:
3470:
3450:
3418:
3344:
3324:
3323:
3321:
3320:
3297:
3279:
3277:
3276:
3253:
3183:
3163:
3108:
2949:
2921:
2788:
2758:
2738:
2647:
2598:
2472:
2421:
2397:
2377:
2320:
2270:
2069:
2042:
2022:
1944:
1909:
1907:
1724:
1691:
1667:
1643:
1623:
1622:
1620:
1619:
1596:
1581:
1574:
1556:
1549:
1524:
1522:
1521:
1498:
1453:
1446:
1414:
1412:
1411:
1388:
1327:
1258:
1162:
1116:
1077:
936:
787:
690:
667:
631:
604:
571:
551:
449:
437:
386:
318:
294:
274:
254:
74:
60:hydraulic pressure
4325:Civil engineering
4312:
4311:
4187:Open-channel flow
4060:Open-Channel Flow
3801:Transitional flow
3643:
3622:
3590:
3540:{\displaystyle h}
3473:{\displaystyle C}
3379:
3316:
3307:
3285:
3283:
3272:
3263:
3224:
3212:
3210:
3186:{\displaystyle E}
3089:
3054:
2996:
2979:
2908:
2873:
2831:
2713:
2562:
2536:
2510:
2424:{\displaystyle R}
2375:
2363:
2246:
2220:
2194:
2156:
2130:
2104:
1887:
1867:
1835:
1815:
1793:
1767:
1646:{\displaystyle p}
1615:
1606:
1587:
1585:
1579:
1562:
1560:
1554:
1530:
1528:
1517:
1508:
1486:
1474:
1472:
1465:
1463:
1458:
1451:
1420:
1418:
1407:
1398:
1384:
1362:
1360:
1341:Momentum equation
1319:
1296:
1250:
1207:
1126:and defining the
1039:
966:
817:
720:
693:{\displaystyle A}
634:{\displaystyle V}
518:
364:conservation laws
321:{\displaystyle g}
297:{\displaystyle D}
277:{\displaystyle U}
252:
250:
232:
40:open-channel flow
18:Open channel flow
16:(Redirected from
4347:
4110:
4103:
4096:
4087:
3988:
3987:
3975:
3964:
3955:
3954:
3952:
3941:
3935:
3934:
3914:
3908:
3907:
3895:
3884:
3813:Fluid properties
3725:
3723:
3722:
3717:
3715:
3714:
3690:
3688:
3687:
3682:
3658:
3656:
3655:
3650:
3648:
3644:
3642:
3634:
3623:
3621:
3613:
3612:
3603:
3595:
3591:
3589:
3578:
3546:
3544:
3543:
3538:
3523:
3521:
3520:
3515:
3507:
3479:
3477:
3476:
3471:
3459:
3457:
3456:
3451:
3427:
3425:
3424:
3419:
3390:
3389:
3380:
3378:
3370:
3362:
3353:
3351:
3350:
3345:
3333:
3331:
3330:
3325:
3322:
3317:
3314:
3308:
3305:
3298:
3293:
3278:
3273:
3270:
3264:
3261:
3254:
3249:
3248:
3247:
3238:
3237:
3225:
3223:
3215:
3192:
3190:
3189:
3184:
3172:
3170:
3169:
3164:
3153:
3152:
3134:
3133:
3117:
3115:
3114:
3109:
3101:
3097:
3090:
3088:
3080:
3075:
3074:
3065:
3064:
3055:
3053:
3045:
3032:
3031:
3022:
3018:
3017:
3016:
3007:
3006:
2997:
2995:
2987:
2980:
2978:
2967:
2958:
2956:
2955:
2950:
2948:
2947:
2930:
2928:
2927:
2922:
2920:
2916:
2909:
2907:
2899:
2894:
2893:
2884:
2883:
2874:
2872:
2864:
2848:
2847:
2832:
2830:
2822:
2821:
2820:
2810:
2797:
2795:
2794:
2789:
2772:of the flow and
2767:
2765:
2764:
2759:
2747:
2745:
2744:
2739:
2737:
2736:
2727:
2726:
2714:
2712:
2704:
2699:
2698:
2683:
2682:
2670:
2669:
2656:
2654:
2653:
2648:
2646:
2645:
2633:
2632:
2607:
2605:
2604:
2599:
2582:
2581:
2563:
2561:
2553:
2545:
2537:
2535:
2527:
2519:
2511:
2509:
2501:
2493:
2481:
2479:
2478:
2473:
2462:
2451:
2450:
2433:hydraulic radius
2430:
2428:
2427:
2422:
2406:
2404:
2403:
2398:
2386:
2384:
2383:
2378:
2376:
2374:
2366:
2364:
2362:
2354:
2346:
2345:
2329:
2327:
2326:
2321:
2313:
2308:
2307:
2279:
2277:
2276:
2271:
2269:
2268:
2247:
2245:
2237:
2229:
2221:
2219:
2211:
2203:
2195:
2193:
2185:
2177:
2170:
2169:
2157:
2155:
2147:
2139:
2131:
2129:
2121:
2113:
2105:
2103:
2095:
2087:
2078:
2076:
2075:
2070:
2068:
2067:
2051:
2049:
2048:
2043:
2031:
2029:
2028:
2023:
2012:
2011:
1953:
1951:
1950:
1945:
1918:
1916:
1915:
1910:
1908:
1888:
1886:
1878:
1870:
1868:
1866:
1858:
1849:
1848:
1836:
1834:
1826:
1818:
1816:
1814:
1806:
1794:
1792:
1784:
1776:
1768:
1766:
1758:
1750:
1733:
1731:
1730:
1725:
1703:Laplace operator
1700:
1698:
1697:
1692:
1676:
1674:
1673:
1668:
1652:
1650:
1649:
1644:
1632:
1630:
1629:
1624:
1621:
1616:
1613:
1607:
1604:
1597:
1592:
1580:
1577:
1575:
1570:
1555:
1552:
1550:
1545:
1544:
1543:
1523:
1518:
1515:
1509:
1506:
1499:
1494:
1487:
1485:
1477:
1464:
1461:
1459:
1454:
1452:
1449:
1447:
1442:
1441:
1440:
1428:
1427:
1413:
1408:
1405:
1399:
1396:
1389:
1383:
1375:
1374:
1373:
1363:
1358:
1356:
1336:
1334:
1333:
1328:
1320:
1318:
1310:
1302:
1297:
1295:
1287:
1279:
1267:
1265:
1264:
1259:
1251:
1249:
1241:
1233:
1231:
1230:
1208:
1206:
1198:
1190:
1188:
1187:
1171:
1169:
1168:
1163:
1151:
1150:
1125:
1123:
1122:
1117:
1103:
1102:
1086:
1084:
1083:
1078:
1070:
1066:
1055:
1054:
1040:
1038:
1027:
1025:
1024:
1003:
999:
992:
991:
977:
976:
967:
965:
954:
945:
943:
942:
937:
929:
925:
914:
913:
895:
894:
880:
879:
858:
854:
843:
842:
828:
827:
818:
816:
805:
796:
794:
793:
788:
776:
775:
757:
756:
731:
730:
721:
719:
708:
699:
697:
696:
691:
676:
674:
673:
668:
660:
659:
640:
638:
637:
632:
613:
611:
610:
605:
580:
578:
577:
572:
560:
558:
557:
552:
541:
540:
519:
517:
509:
501:
458:
456:
455:
450:
448:
447:
442:
441:
409:
408:
396:with components
395:
393:
392:
387:
385:
384:
327:
325:
324:
319:
303:
301:
300:
295:
283:
281:
280:
275:
263:
261:
260:
255:
253:
251:
243:
238:
233:
230:
21:
4355:
4354:
4350:
4349:
4348:
4346:
4345:
4344:
4315:
4314:
4313:
4308:
4287:Public networks
4282:
4201:
4191:Manning formula
4150:
4136:Hydraulic fluid
4119:
4114:
4082:(p. 26-38)
4044:lecture notes:
4038:
3997:
3995:Further reading
3992:
3991:
3984:
3973:
3966:
3965:
3958:
3950:
3943:
3942:
3938:
3931:
3916:
3915:
3911:
3904:
3893:
3886:
3885:
3881:
3876:
3871:
3855:Manning formula
3823:Reynolds number
3759:Fields of study
3744:
3706:
3701:
3700:
3693:specific weight
3664:
3663:
3660:
3646:
3645:
3604:
3593:
3592:
3564:
3552:
3551:
3529:
3528:
3489:
3488:
3486:specific energy
3462:
3461:
3430:
3429:
3363:
3356:
3355:
3336:
3335:
3319:
3318:
3310:
3309:
3286:
3275:
3274:
3266:
3265:
3239:
3213:
3199:
3198:
3175:
3174:
3123:
3122:
3066:
3043:
3039:
3008:
2985:
2981:
2961:
2960:
2937:
2936:
2885:
2862:
2858:
2811:
2804:
2803:
2774:
2773:
2750:
2749:
2728:
2659:
2658:
2622:
2621:
2614:
2612:Energy equation
2609:
2573:
2546:
2520:
2494:
2487:
2486:
2442:
2437:
2436:
2413:
2412:
2389:
2388:
2337:
2332:
2331:
2299:
2282:
2281:
2260:
2230:
2204:
2178:
2161:
2140:
2114:
2088:
2081:
2080:
2059:
2054:
2053:
2034:
2033:
2003:
1956:
1955:
1924:
1923:
1906:
1905:
1895:
1871:
1851:
1850:
1840:
1819:
1795:
1777:
1751:
1740:
1739:
1707:
1706:
1683:
1682:
1659:
1658:
1635:
1634:
1618:
1617:
1609:
1608:
1563:
1531:
1520:
1519:
1511:
1510:
1475:
1421:
1410:
1409:
1401:
1400:
1364:
1359:
1351:
1350:
1343:
1338:
1303:
1280:
1273:
1272:
1234:
1222:
1191:
1179:
1174:
1173:
1142:
1131:
1130:
1094:
1089:
1088:
1087:By noting that
1046:
1045:
1041:
1016:
983:
982:
978:
968:
948:
947:
886:
885:
881:
871:
834:
833:
829:
819:
799:
798:
748:
722:
702:
701:
682:
681:
643:
642:
623:
622:
587:
586:
563:
562:
502:
495:
494:
487:
436:
435:
430:
425:
415:
413:
398:
397:
374:
373:
360:
354:
334:Reynolds number
310:
309:
286:
285:
266:
265:
224:
223:
215:Surface tension
203:
169:Continuous flow
79:
32:fluid mechanics
28:
23:
22:
15:
12:
11:
5:
4353:
4351:
4343:
4342:
4337:
4332:
4330:Fluid dynamics
4327:
4317:
4316:
4310:
4309:
4307:
4306:
4301:
4296:
4290:
4288:
4284:
4283:
4281:
4280:
4275:
4270:
4265:
4260:
4255:
4250:
4245:
4240:
4235:
4230:
4225:
4220:
4215:
4209:
4207:
4203:
4202:
4200:
4199:
4194:
4184:
4179:
4174:
4169:
4164:
4158:
4156:
4152:
4151:
4149:
4148:
4143:
4138:
4133:
4127:
4125:
4121:
4120:
4115:
4113:
4112:
4105:
4098:
4090:
4084:
4083:
4077:
4072:
4067:
4062:
4057:
4056:
4055:
4050:
4037:
4036:External links
4034:
4033:
4032:
4015:
3996:
3993:
3990:
3989:
3982:
3956:
3936:
3929:
3909:
3903:978-1932846188
3902:
3878:
3877:
3875:
3872:
3870:
3869:
3868:
3867:
3862:
3857:
3852:
3850:Hydraulic jump
3847:
3842:
3832:
3831:
3830:
3825:
3820:
3810:
3809:
3808:
3806:Turbulent flow
3803:
3798:
3793:
3783:
3782:
3781:
3776:
3771:
3769:Fluid dynamics
3766:
3756:
3751:
3745:
3743:
3740:
3713:
3709:
3680:
3677:
3674:
3671:
3641:
3637:
3632:
3629:
3626:
3620:
3617:
3611:
3607:
3601:
3598:
3596:
3594:
3588:
3585:
3581:
3576:
3573:
3570:
3567:
3565:
3563:
3560:
3559:
3549:
3536:
3526:hydraulic head
3513:
3510:
3506:
3502:
3499:
3496:
3469:
3449:
3446:
3443:
3440:
3437:
3417:
3414:
3411:
3408:
3405:
3402:
3399:
3396:
3393:
3388:
3383:
3377:
3374:
3369:
3366:
3343:
3312:
3311:
3303:
3302:
3296:
3292:
3289:
3282:
3268:
3267:
3259:
3258:
3252:
3246:
3242:
3236:
3231:
3228:
3222:
3218:
3209:
3206:
3195:energy density
3182:
3162:
3159:
3156:
3151:
3146:
3143:
3140:
3137:
3132:
3107:
3104:
3100:
3096:
3093:
3087:
3083:
3078:
3073:
3069:
3063:
3058:
3052:
3048:
3042:
3038:
3035:
3030:
3025:
3021:
3015:
3011:
3005:
3000:
2994:
2990:
2984:
2977:
2974:
2970:
2946:
2919:
2915:
2912:
2906:
2902:
2897:
2892:
2888:
2882:
2877:
2871:
2867:
2861:
2857:
2854:
2851:
2846:
2841:
2838:
2835:
2829:
2826:
2819:
2814:
2800:Euclidean norm
2787:
2784:
2781:
2757:
2735:
2731:
2725:
2720:
2717:
2711:
2707:
2702:
2697:
2692:
2689:
2686:
2681:
2676:
2673:
2668:
2644:
2639:
2636:
2631:
2613:
2610:
2597:
2594:
2591:
2588:
2585:
2580:
2576:
2572:
2569:
2566:
2560:
2557:
2552:
2549:
2543:
2540:
2534:
2531:
2526:
2523:
2517:
2514:
2508:
2505:
2500:
2497:
2484:
2471:
2468:
2465:
2461:
2457:
2454:
2449:
2445:
2420:
2396:
2373:
2369:
2361:
2357:
2352:
2349:
2344:
2340:
2319:
2316:
2312:
2306:
2302:
2298:
2295:
2292:
2289:
2267:
2263:
2259:
2256:
2253:
2250:
2244:
2241:
2236:
2233:
2227:
2224:
2218:
2215:
2210:
2207:
2201:
2198:
2192:
2189:
2184:
2181:
2174:
2168:
2164:
2160:
2154:
2151:
2146:
2143:
2137:
2134:
2128:
2125:
2120:
2117:
2111:
2108:
2102:
2099:
2094:
2091:
2066:
2062:
2041:
2021:
2018:
2015:
2010:
2006:
2002:
1999:
1996:
1993:
1990:
1987:
1984:
1981:
1978:
1975:
1972:
1969:
1966:
1963:
1943:
1940:
1937:
1934:
1931:
1904:
1901:
1898:
1896:
1894:
1891:
1885:
1882:
1877:
1874:
1865:
1861:
1856:
1853:
1852:
1847:
1843:
1839:
1833:
1830:
1825:
1822:
1813:
1809:
1804:
1801:
1798:
1796:
1791:
1788:
1783:
1780:
1774:
1771:
1765:
1762:
1757:
1754:
1748:
1747:
1723:
1720:
1717:
1714:
1690:
1666:
1642:
1611:
1610:
1602:
1601:
1595:
1591:
1584:
1573:
1569:
1566:
1559:
1548:
1542:
1537:
1534:
1527:
1513:
1512:
1504:
1503:
1497:
1493:
1490:
1484:
1480:
1471:
1468:
1457:
1445:
1439:
1434:
1431:
1426:
1417:
1403:
1402:
1394:
1393:
1387:
1382:
1379:
1372:
1367:
1342:
1339:
1326:
1323:
1317:
1314:
1309:
1306:
1300:
1294:
1291:
1286:
1283:
1270:
1257:
1254:
1248:
1245:
1240:
1237:
1229:
1225:
1221:
1218:
1215:
1212:
1205:
1202:
1197:
1194:
1186:
1182:
1161:
1158:
1154:
1149:
1145:
1141:
1138:
1115:
1112:
1109:
1106:
1101:
1097:
1076:
1073:
1069:
1065:
1062:
1058:
1053:
1049:
1044:
1037:
1034:
1030:
1023:
1019:
1015:
1012:
1009:
1006:
1002:
998:
995:
990:
986:
981:
975:
971:
964:
961:
957:
935:
932:
928:
924:
921:
917:
912:
907:
904:
901:
898:
893:
889:
884:
878:
874:
870:
867:
864:
861:
857:
853:
850:
846:
841:
837:
832:
826:
822:
815:
812:
808:
786:
783:
779:
774:
769:
766:
763:
760:
755:
751:
747:
744:
741:
738:
734:
729:
725:
718:
715:
711:
689:
666:
663:
658:
653:
650:
630:
620:control volume
603:
600:
597:
594:
570:
550:
547:
544:
539:
534:
531:
528:
525:
522:
516:
513:
508:
505:
486:
483:
482:
481:
478:
475:
472:incompressible
446:
440:
434:
431:
429:
426:
424:
421:
420:
418:
412:
407:
383:
353:
350:
317:
293:
273:
249:
246:
241:
236:
202:
201:States of flow
199:
198:
197:
196:
195:
194:
193:
184:
183:
182:
166:
165:
164:
163:
162:
161:
160:
152:
151:
150:
147:hydraulic drop
143:hydraulic jump
126:
125:
124:
111:
110:
109:
108:
107:
99:
98:
97:
78:
75:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4352:
4341:
4338:
4336:
4333:
4331:
4328:
4326:
4323:
4322:
4320:
4305:
4302:
4300:
4297:
4295:
4292:
4291:
4289:
4285:
4279:
4276:
4274:
4271:
4269:
4266:
4264:
4261:
4259:
4256:
4254:
4253:Power network
4251:
4249:
4246:
4244:
4241:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4210:
4208:
4204:
4198:
4195:
4192:
4188:
4185:
4183:
4180:
4178:
4175:
4173:
4170:
4168:
4165:
4163:
4160:
4159:
4157:
4153:
4147:
4144:
4142:
4139:
4137:
4134:
4132:
4129:
4128:
4126:
4122:
4118:
4111:
4106:
4104:
4099:
4097:
4092:
4091:
4088:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4061:
4058:
4054:
4051:
4049:
4046:
4045:
4043:
4040:
4039:
4035:
4030:
4029:9789048136735
4026:
4022:
4021:
4016:
4013:
4012:9789054101185
4009:
4005:
4004:
3999:
3998:
3994:
3985:
3983:9780073397870
3979:
3972:
3971:
3963:
3961:
3957:
3949:
3948:
3940:
3937:
3932:
3930:9781316576878
3926:
3922:
3921:
3913:
3910:
3905:
3899:
3892:
3891:
3883:
3880:
3873:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3841:
3840:Chézy formula
3838:
3837:
3836:
3833:
3829:
3826:
3824:
3821:
3819:
3818:Froude number
3816:
3815:
3814:
3811:
3807:
3804:
3802:
3799:
3797:
3794:
3792:
3789:
3788:
3787:
3784:
3780:
3777:
3775:
3772:
3770:
3767:
3765:
3762:
3761:
3760:
3757:
3755:
3752:
3750:
3747:
3746:
3741:
3739:
3737:
3733:
3729:
3711:
3707:
3698:
3694:
3678:
3675:
3672:
3669:
3659:
3639:
3635:
3630:
3627:
3624:
3618:
3615:
3609:
3605:
3599:
3597:
3586:
3583:
3579:
3574:
3571:
3568:
3566:
3561:
3548:
3534:
3527:
3511:
3508:
3504:
3500:
3497:
3494:
3487:
3483:
3467:
3447:
3444:
3441:
3438:
3435:
3415:
3412:
3406:
3403:
3400:
3391:
3381:
3375:
3367:
3294:
3287:
3280:
3250:
3244:
3226:
3220:
3216:
3207:
3204:
3196:
3180:
3160:
3157:
3144:
3141:
3135:
3121:
3105:
3102:
3098:
3091:
3085:
3081:
3076:
3071:
3050:
3046:
3040:
3033:
3023:
3019:
3013:
2992:
2988:
2982:
2975:
2934:
2917:
2910:
2904:
2900:
2895:
2890:
2869:
2865:
2859:
2852:
2849:
2839:
2836:
2833:
2827:
2801:
2782:
2771:
2755:
2733:
2709:
2705:
2700:
2690:
2687:
2684:
2671:
2634:
2619:
2616:To derive an
2611:
2608:
2595:
2592:
2586:
2583:
2578:
2574:
2567:
2564:
2558:
2550:
2541:
2538:
2532:
2524:
2515:
2512:
2506:
2498:
2483:
2469:
2466:
2463:
2459:
2455:
2452:
2447:
2443:
2434:
2418:
2410:
2394:
2371:
2367:
2359:
2355:
2350:
2347:
2342:
2338:
2317:
2314:
2310:
2304:
2300:
2296:
2293:
2290:
2287:
2265:
2261:
2257:
2254:
2251:
2248:
2242:
2234:
2225:
2222:
2216:
2208:
2199:
2196:
2190:
2182:
2166:
2162:
2158:
2152:
2144:
2135:
2132:
2126:
2118:
2109:
2106:
2100:
2092:
2064:
2060:
2039:
2016:
2008:
2004:
2000:
1994:
1991:
1988:
1982:
1979:
1973:
1970:
1967:
1961:
1941:
1938:
1935:
1932:
1929:
1922:
1902:
1899:
1897:
1892:
1889:
1883:
1875:
1863:
1859:
1854:
1845:
1841:
1837:
1831:
1823:
1811:
1807:
1802:
1799:
1797:
1789:
1781:
1772:
1769:
1763:
1755:
1737:
1721:
1718:
1715:
1704:
1680:
1664:
1656:
1640:
1593:
1582:
1571:
1557:
1546:
1532:
1525:
1495:
1491:
1482:
1478:
1469:
1466:
1455:
1443:
1429:
1415:
1385:
1380:
1348:
1340:
1337:
1324:
1321:
1315:
1307:
1298:
1292:
1284:
1269:
1255:
1252:
1246:
1238:
1227:
1223:
1219:
1216:
1213:
1210:
1203:
1195:
1184:
1180:
1159:
1156:
1152:
1147:
1143:
1139:
1136:
1129:
1113:
1110:
1107:
1104:
1099:
1095:
1074:
1071:
1067:
1063:
1060:
1056:
1051:
1047:
1042:
1035:
1021:
1017:
1013:
1010:
1007:
1004:
1000:
996:
993:
988:
984:
979:
973:
969:
962:
959:
955:
933:
930:
926:
922:
919:
905:
899:
891:
887:
882:
876:
872:
868:
865:
862:
859:
855:
851:
848:
844:
839:
835:
830:
824:
820:
813:
810:
806:
784:
781:
767:
761:
753:
749:
745:
742:
739:
736:
732:
727:
723:
716:
713:
709:
687:
680:
664:
661:
651:
628:
621:
617:
595:
584:
581:is the fluid
568:
548:
545:
532:
526:
520:
514:
506:
492:
484:
479:
476:
473:
469:
468:
467:
464:
462:
444:
438:
432:
427:
422:
416:
410:
372:
369:
368:flow velocity
365:
359:
351:
349:
347:
343:
339:
335:
331:
315:
307:
291:
271:
247:
244:
239:
234:
221:
220:Froude number
216:
212:
208:
200:
190:
189:
188:
185:
180:
176:
172:
171:
170:
167:
158:
157:
156:
153:
148:
144:
140:
139:
138:
135:
134:
132:
131:
130:
127:
122:
121:
120:
117:
116:
115:
112:
105:
104:
103:
102:Unsteady flow
100:
95:
94:
93:
90:
89:
88:
85:
84:
83:
76:
71:
67:
63:
61:
57:
53:
50:, known as a
49:
45:
42:is a type of
41:
37:
33:
19:
4273:Rescue tools
4238:Drive system
4206:Technologies
4186:
4018:
4001:
3969:
3946:
3939:
3919:
3912:
3889:
3882:
3834:
3812:
3791:Laminar flow
3785:
3758:
3661:
3550:
3334:Noting that
2615:
2485:
2409:shear stress
1344:
1271:
489:The general
488:
470:The flow is
465:
371:vector field
361:
346:transitional
204:
186:
168:
154:
136:
128:
119:Uniform flow
118:
113:
101:
91:
86:
80:
48:free surface
39:
29:
4218:Accumulator
4141:Fluid power
3728:dissipation
2933:dot product
2931:Taking the
352:Formulation
129:Varied flow
92:Steady flow
4335:Hydraulics
4319:Categories
4304:Manchester
4131:Hydraulics
4117:Hydraulics
3874:References
3774:Hydraulics
3754:Streamflow
3736:turbulence
3691:being the
3193:to be the
3173:. Define
616:divergence
36:hydraulics
4294:Liverpool
4213:Machinery
3828:Viscosity
3796:Pipe flow
3779:Hydrology
3697:head loss
3676:ρ
3670:γ
3640:γ
3584:ρ
3509:ρ
3395:∇
3392:⋅
3373:∂
3365:∂
3342:Φ
3306:Potential
3295:⏟
3291:Φ
3288:ρ
3251:⏟
3241:‖
3230:‖
3227:ρ
3145:×
3142:ω
3136:⋅
3095:Φ
3086:ρ
3068:‖
3057:‖
3037:∇
3034:⋅
3010:‖
2999:‖
2973:∂
2969:∂
2914:Φ
2905:ρ
2887:‖
2876:‖
2856:∇
2853:−
2840:×
2837:ω
2825:∂
2813:∂
2786:‖
2783:⋅
2780:‖
2770:vorticity
2756:ω
2730:‖
2719:‖
2716:∇
2691:×
2688:ω
2675:∇
2672:⋅
2638:∇
2635:⋅
2584:−
2556:∂
2551:η
2548:∂
2530:∂
2522:∂
2504:∂
2496:∂
2464:ρ
2456:τ
2395:τ
2368:τ
2360:ρ
2351:−
2294:−
2249:−
2240:∂
2235:η
2232:∂
2214:∂
2206:∂
2188:∂
2180:∂
2173:⟹
2150:∂
2145:ζ
2142:∂
2124:∂
2116:∂
2098:∂
2090:∂
2040:ζ
2001:−
1983:ζ
1962:η
1942:ζ
1936:ρ
1890:−
1881:∂
1873:∂
1864:ρ
1855:−
1829:∂
1821:∂
1812:ρ
1803:−
1787:∂
1779:∂
1761:∂
1753:∂
1713:Φ
1689:Δ
1665:ν
1594:⏟
1572:⏟
1568:Φ
1565:∇
1558:−
1553:Diffusion
1547:⏟
1536:Δ
1533:ν
1496:⏟
1489:∇
1483:ρ
1470:−
1456:⏞
1450:Advection
1444:⏟
1433:∇
1430:⋅
1386:⏟
1378:∂
1366:∂
1313:∂
1305:∂
1290:∂
1282:∂
1244:∂
1236:∂
1224:∫
1220:−
1201:∂
1193:∂
1181:∫
1144:∫
1096:∫
1048:∫
1033:∂
1029:∂
1018:∫
1014:−
985:∫
970:∫
906:ρ
900:⋅
897:∇
888:∫
873:∫
869:−
845:ρ
836:∫
821:∫
768:ρ
762:⋅
759:∇
750:∫
746:−
733:ρ
724:∫
652:⋅
649:∇
596:⋅
593:∇
569:ρ
533:ρ
527:⋅
524:∇
512:∂
507:ρ
504:∂
342:turbulent
207:viscosity
56:pipe flow
4243:Manifold
4233:Cylinder
4155:Modeling
4124:Concepts
3742:See also
3732:friction
1655:pressure
1605:External
1516:Gradient
1507:Pressure
211:inertial
145:and the
72:channel.
4228:Circuit
4042:Caltech
3749:HEC-RAS
3730:due to
3262:Kinetic
2798:is the
2768:is the
2431:is the
2407:is the
1734:is the
1701:is the
1677:is the
1653:is the
1578:Gravity
1349: :
614:is the
583:density
338:laminar
328:is the
304:is the
52:channel
4299:London
4027:
4010:
3980:
3927:
3900:
3315:Energy
3271:Energy
2748:where
2618:energy
2387:where
1705:, and
1633:where
1614:Forces
1406:Change
561:where
264:where
44:liquid
4258:Press
4248:Motor
4223:Brake
3974:(PDF)
3951:(PDF)
3894:(PDF)
3699:term
3662:with
3460:with
1397:Local
459:. In
344:, or
175:reach
4278:Seal
4263:Pump
4025:ISBN
4008:ISBN
3978:ISBN
3925:ISBN
3898:ISBN
3734:and
2411:and
585:and
34:and
4268:Ram
2935:of
30:In
4321::
3959:^
1681:,
1657:,
340:,
231:Fr
62:.
38:,
4193:)
4189:(
4109:e
4102:t
4095:v
4031:.
4014:.
3986:.
3933:.
3906:.
3712:f
3708:h
3679:g
3673:=
3636:p
3631:+
3628:z
3625:+
3619:g
3616:2
3610:2
3606:u
3600:=
3587:g
3580:p
3575:+
3572:e
3569:=
3562:h
3535:h
3512:g
3505:/
3501:E
3498:=
3495:e
3468:C
3448:C
3445:=
3442:p
3439:+
3436:E
3416:0
3413:=
3410:)
3407:p
3404:+
3401:E
3398:(
3387:v
3382:+
3376:t
3368:E
3281:+
3245:2
3235:v
3221:2
3217:1
3208:=
3205:E
3197::
3181:E
3161:0
3158:=
3155:)
3150:v
3139:(
3131:v
3106:0
3103:=
3099:)
3092:+
3082:p
3077:+
3072:2
3062:v
3051:2
3047:1
3041:(
3029:v
3024:+
3020:)
3014:2
3004:v
2993:2
2989:1
2983:(
2976:t
2945:v
2918:)
2911:+
2901:p
2896:+
2891:2
2881:v
2870:2
2866:1
2860:(
2850:=
2845:v
2834:+
2828:t
2818:v
2734:2
2724:v
2710:2
2706:1
2701:+
2696:v
2685:=
2680:v
2667:v
2643:v
2630:v
2596:0
2593:=
2590:)
2587:S
2579:f
2575:S
2571:(
2568:g
2565:+
2559:x
2542:g
2539:+
2533:x
2525:u
2516:u
2513:+
2507:t
2499:u
2470:R
2467:g
2460:/
2453:=
2448:f
2444:S
2419:R
2372:R
2356:1
2348:=
2343:x
2339:F
2318:x
2315:d
2311:/
2305:b
2301:z
2297:d
2291:=
2288:S
2266:x
2262:F
2258:=
2255:S
2252:g
2243:x
2226:g
2223:+
2217:x
2209:u
2200:u
2197:+
2191:t
2183:u
2167:x
2163:F
2159:=
2153:x
2136:g
2133:+
2127:x
2119:u
2110:u
2107:+
2101:t
2093:u
2065:b
2061:z
2020:)
2017:x
2014:(
2009:b
2005:z
1998:)
1995:x
1992:,
1989:t
1986:(
1980:=
1977:)
1974:x
1971:,
1968:t
1965:(
1939:g
1933:=
1930:p
1903:0
1900:=
1893:g
1884:z
1876:p
1860:1
1846:x
1842:F
1838:+
1832:x
1824:p
1808:1
1800:=
1790:x
1782:u
1773:u
1770:+
1764:t
1756:u
1722:z
1719:g
1716:=
1641:p
1590:F
1583:+
1541:v
1526:+
1492:p
1479:1
1467:=
1438:v
1425:v
1416:+
1381:t
1371:v
1325:0
1322:=
1316:x
1308:Q
1299:+
1293:t
1285:A
1256:x
1253:d
1247:x
1239:Q
1228:x
1217:=
1214:x
1211:d
1204:t
1196:A
1185:x
1160:A
1157:d
1153:u
1148:A
1140:=
1137:Q
1114:A
1111:=
1108:A
1105:d
1100:A
1075:x
1072:d
1068:)
1064:A
1061:d
1057:u
1052:A
1043:(
1036:x
1022:x
1011:=
1008:x
1005:d
1001:)
997:A
994:d
989:A
980:(
974:x
963:t
960:d
956:d
934:x
931:d
927:]
923:A
920:d
916:)
911:v
903:(
892:A
883:[
877:x
866:=
863:x
860:d
856:)
852:A
849:d
840:A
831:(
825:x
814:t
811:d
807:d
785:V
782:d
778:)
773:v
765:(
754:V
743:=
740:V
737:d
728:V
717:t
714:d
710:d
688:A
665:0
662:=
657:v
629:V
602:)
599:(
549:0
546:=
543:)
538:v
530:(
521:+
515:t
445:T
439:)
433:w
428:v
423:u
417:(
411:=
406:v
382:v
316:g
292:D
272:U
248:D
245:g
240:U
235:=
149:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
