Hardy Cross

Trial 1

Pipe Loop 1

1  3 4

L(m) 1000 000 1000 000

D(m) 0.40 0.45 0.30 0.30

Ks(m) 0.00005 0.00005 0.00005 0.00005

q=VA q (l/s) V(m/s) -103.56 -0.84104 00 1.5!51 40 0.565884 -53.56 -0 -0.!5!!1"

Σ

Loop  3 8 " 10

1000 000 500 00

0.30 0.30 0.5 0.5

0.00005 0.00003 0.00003 0.00003

-40 -0.565884 160 .6353! !. 0.14!085 !. 0.14!085

Σ

Loop 3 4 5 6 !

000 1000 !50 00

0.30 0.40 0.30 0.30

0.00005 0.00003 0.00003 0.00003

53.56 0.!5!!1" -50 -0.3"!88! 100.!8 1.45!45 -13.8 -0.1"53

Σ

Trial 

Pipe Loop 1

1  3 4

L(m) 1000 000 1000 000

D(m) 0.40 0.45 0.30 0.30

Ks(m) q (l/s) V(m/s) 0.00005 -10".! -0.8!314 0.00005 1"3.838 1.18!!! 0.00005 8".1648 1.6141! 0.00005 -34.3!358 -0 - 0.4868! Σ

Loop 

8 " 10

000 500 00

0.30 0.5 0.5

0.00003 104.6!38 1.480831 0.00003 -48.1065 -0."8001 0.00003 -48.1065 -0."8001 Σ

Loop 3 4 5 6 !

000 1000 !50 00

0.30 0.40 0.30 0.30

0.00005 34.3!358 0.4868! 0.00003 -!5.34838 -0.5""603 0.00003 !5.4316 1.06!13" 0.00003 -3".14838 -0.553836 Σ

Trial 3

Pipe Loop 1

1  3 4

L(m) 1000 000 1000 000

D(m) 0.40 0.45 0.30 0.30

Ks(m) q (l/s) V(m/s) 0.00005 -133."03 -1.065566 0.00005 16".65! 1.066!36 0.00005 6.00"8 0.8!""64 0.00005 -54.!411 -0.!!448 Σ

Loop  3 8 " 10

1000 000 500 00

0.30 0.30 0.5 0.5

0.00005 -6.00"8 -0.8!""64 0.00003 10!.456 1.501" 0.00003 -45.33"" -0."3333 0.00003 -45.33"" -0."3333 Σ

Loop 3 4 5 6 !

000 1000 !50 00

0.30 0.40 0.30 0.30

0.00005 0.00003 0.00003 0.00003

54.!411 0.!!448 -!".161" -0.6""5 !1.6181 1.01318" -4."61" -0.60!!86

Σ

Trial 4

Pipe Loop 1

1  3 4

L(m) 1000 000 1000 000

D(m) 0.40 0.45 0.30 0.30

Ks(m) q (l/s) V(m/s) 0.00005 -135.68 -1.0!643 0.00005 168."18 1.05815 0.00005 63.5"!85 0.8""!5 0.00005 -48.5464 -0.686!8" Σ

Loop  3 8 " 10

1000 000 500 00

0.30 0.30 0.5 0.5

0.00005 -63.5"!85 -0.8""!5 0.00003 104.6"4 1.48111! 0.00003 -48.0860 -0."!"6 0.00003 -48.0860 -0."!"6 Σ

Loop 3 4 5 6 !

000 1000 !50 00

0.30 0.40 0.30 0 30

0.00005 48.5464 0.686!8" 0.00003 -86.!1"4 -0.6"0111 0.00003 64.05806 0."0636 0 00003 50 51"4 -0 !14!3"

Trial 5

Pipe Loop 1

1  3 4

L(m) 1000 000 1000 000

D(m) 0.40 0.45 0.30 0.30

Ks(m) q (l/s) V(m/s) 0.00005 -13".84 -1.1083!4 0.00005 164.!!6 1.03"1 0.00005 5".8!66 0.84!081 0.00005 -51.50653 -0.!8668 Σ

Loop  3 8 " 10

1000 000 500 00

0.30 0.30 0.5 0.5

0.00005 -5".8!66 -0.84!081 0.00003 104.401 1.4!6"! 0.00003 -48.3!"03 -0."8556" 0.00003 -48.3!"03 -0."8556" Σ

Loop 3 4 5 6 !

000 1000 !50 00

0.30 0.40 0.30 0.30

0.00005 51.50653 0.!8668 0.00003 -8!.!!588 -0.6"84"8 0.00003 63.0041 0.8"136 0.00003 -51.5!588 -0.!"64" Σ

Pipe #o. %&l$ mai# 1  3 4 5 6 ! 8 " 10

'=

L(m) 5000 1000 000 1000 000 1000 !50 00 000 500 00

D(m) 0.65 0.40 0.45 0.30 0.30 0.40 0.30 0.30 0.30 0.5 0.5

$s(m) 0.00010 0.00005 0.00005 0.00005 0.00005 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003

1.13-06 m/s

q = -Σhf/(2Σ(hf/q) *e=VD/' *e "1!18.3 500!8.5 15034.8 01164.3

+ , (m) 0.0154540056 -1.33!354 0.01438!868 5.1538 0.01!345!48 0."43661 0.01663!!80! -3.45!"8 1.51430"

,/q q q o,er q eei' 0.01"1380"! -6.161"65 -6.161"65 0.05!68"""5 -6.161"65 -6.161"65 0.035"15315 -6.161"65 -55.365 4".1648 0.06060115!5 -6.161"65 -5.34838 1".1864 0.18!54"83

15034.8 600"3" 3540.85 3540.85

0.01!345!48 -0."43661 0.013"!"1108 4.33686 0.031646818 0.051085 0.031646818 0.4!!3 3.66"05

0.035"15315 -55.365 -6.161"65 -4".1648 0.151053483 -55.365 -55.365 0.00!0!5460" -55.365 -55.365 0.031130!! -55.365 -55.365 0.13"043684

01164.3 140845.1 3!8516.5 51830.""

0.01663!!80! 3.45!"8 0.016!683"!6 -0.3386 0.0146!4!534 3.800"81 0.00!44445 -0."55! 6.41""

0.06060115!5 -5.34838 -6.161"65 -1".1864 0.006!65344 -5.34838 -5.34838 0.03!!15631" -5.34838 -5.34838 0.01415006 -5.34838 -5.34838 0.164"!0444

*e 30"0!6 485353.5 33488".4 1"10.!

+ , (m) 0.015345063! -1.4"0655 0.0144316368 4.85604 0.0156684441 4.356!6 0.01!!6114 -1.4!136 6.1!3"4

,/q q q o,er q eei' 0.013585!4!" -4.18105 -4.18105 0.0505048" -4.18105 -4.18105 0.04!5041!5 -4.18105 .!855 -6."6331 0.041518406 -4.18105 -3.813515 -0.36!54 0.1!6603!55

3"3140." 16816." 16816."

0.01460"5434 10.885! 0.0160!34 -1.56"10! 0.0160!34 -6."0406" -1.83131

0.103""665"1 .!855 0.0361!5" .!855 0.14351!100" .!855 0.3!6354554

.!855 .!855 .!855

1"10.! 14" 83311.3 14!036.

0.01!!6114 1.4!136 0.01561013 -0.!15118 0.01558"3" .0"35! 0.0168555316 -1."344! 0."88"8

0.041518406 -3.813515 -4.18105 0.36!54 0.00"4"0864 -3.813515 -3.813515 0.0"8"533! -3.813515 -3.813515 0.04"361304 -3.813515 -3.813515 0.1"6608"66

*e 3!!1"1.6 44806.3 33618.! 05600.5

+ , (m) 0.014""8!11" -.16""81 0.014631"0" 3.!!1506 0.016300!0 .146""! 0.01658"616 -3.380!1! 0.36!805

,/q q q o,er q eei' 0.016056181 -1.365161 -1.365161 0.0301835 -1.365161 -1.365161 0.03451!0"14 -1.365161 -.!60" 1.3"686" 0.061!586"4 -1.365161 -!.560044 6.1"4884 0.134!11164

33618.! 4035"0.! 04!!. 04!!.

0.016300!0 -.146""! 0.014565314" 11.43!3! 0.01616!040 -1.405006 0.01616!040 -6.1804 1.!03345

0.03451!0"14 -.!60" -1.365161 -1.3"686" 0.10643!!16 -.!60" -.!60" 0.030"""156! -.!60" -.!60" 0.1363"68"4 -.!60" -.!60" 0.3083505

05600.5 ""1.3 68"88. 16135".

0.01658"616 3.380!1! 0.015485538" -0.!83033 0.01533485"! .005865 0.01658"!1"1 -."05! .31"!"

0.061!586"4 -!.560044 -1.365161 -6.1"4884 0.00"8"153!1 -!.560044 -!.560044 0.0800!!"0! -!.560044 -!.560044 0.05331631" -!.560044 -!.560044 0.15"!3"101

*e 38103!.1 41388 38865. 18333.3

+ , (m) 0.014"83! -.101 0.014643"!41 3.!14!1 0.016!534"5 .38361 0.01686!301 -.!0614 1.03!""8

,/q q q o,er q eei' 0.016358548 -4.01431 -4.01431 0.00!0416 -4.01431 -4.01431 0.0351"5544! -4.01431 -0."3004 -3.!1! 0.0556!0"1" -4.01431 -1.053"4 -."60"1 0.1"8"!43

38865. 3"316." 16!5.8 16!5.8

0.016!534"5 -.38361 0.01460"14" 10.88"68 0.016081"41 -1.56!88 0.016081"41 -6.8"8683 0.184!5!

0.0351"5544! -0."3004 -4.01431 3.!1! 0.1040144163 -0."3004 -0."3004 0.03605!836 -0."3004 -0."3004 0.14346544!! -0."3004 -0."3004 0.315811"3

18333.3 448!. 405"3.! 18"!53 8

0.01686!301 .!0614 0.0556!0"1" -1.053"4 -4.01431 ."60"1 0.015631886 -0."64 0.0106805"! -1.053"4 -1.053"4 0.0155804"6 1.630415 0.05451468 -1.053"4 -1.053"4 0 016154684 3 084581 0 061054813 1 053"4 1 053"4

*e 3"344.8 411336.! 4888.! 1"3451.8

+ , (m) 0.014"35353 -.33!"18 0.01468!6 3.54845 0.0163"81! 1."""061 0.016!568!3 -3.01!543 0.1"05

,/q q q o,er q eei' 0.016!85450" -0.!3668 -0.!3668 0.016003"5 -0.!3668 -0.!3668 0.0333863438 -0.!3668 -0.4308"3 -0.305!36 0.0585856434 -0.!3668 -1.4844 0.6"1813 0.13035!!6!!

4888.! 3"116.4 18046.3 18046.3

0.0163"81! -1."""061 0.014613"8! 10.8335 0.0160141"3! -1.58566 0.0160141"3! -6."!6"11 0.!0!15

0.0333863438 -0.4308"3 -0.!3668 0.305!36 0.103!5!165 -0.4308"3 -0.4308"3 0.03!!5806! -0.4308"3 -0.4308"3 0.1441354"! -0.4308"3 -0.4308"3 0.31413865

1"3451.8 4!56 36635. 1"3!1.

0.016!568!3 3.01!543 0.0153450! -0."4!10" 0.0156180555 1.581034 0.016101815 -3.040"! 0.44!3!

0.0585856434 -1.4844 -0.!3668 -0.6"1813 0.010!"00853 -1.4844 -1.4844 0.050"41"8 -1.4844 -1.4844 0.0613"48 -1.4844 -1.4844 0.1565"38065

#e q (l/s) λ=0.0055[1+(2000 0/+ 〖 10 〗 ^6/)^(1/3)] -10".! 1"3.838 8".1648 -34.3!358

-8".1648 104.6!38 -48.1065 -48.1065

34.3!358 -!5.34838 !5.4316 -3".14838

#e q (l/s) -133."03 16".65! 6.00"8 -54.!411

ℎ_=(8λ^2)/ ( ^2 ^5 )

10!.456 -45.33"" -45.33""

54.!411 -!".161" !1.6181 -4."61"

#e q (l/s) -135.68 168."18 63.5"!85 -48.5464

-63.5"!85 104.6"4 -48.0860 -48.0860

48.5464 -86.!1"4 64.05806 -50.51"4

#e q (l/s) -13".84 164.!!6 5".8!66 -51.50653

-5".8!66 104.401 -48.3!"03 -48.3!"03

51.50653 -8!.!!588 63.0041 -51.5!588

#e q (l/s) -140.01" 163.541 5".5!088 -50.814!1

-5".5!088 103."!01 -48.80"" -48.80""

50.814!1 -8".043 61.5!568 -53.0043