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546
61483 Lqirupdwlrq dqg dvvxpswlrqv
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61484 Lqirupdwlrq dqg dvvxpswlrqv
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548
61485 Lqirupdwlrq dqg dvvxpswlrqv
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549
61486 Lqirupdwlrq dqg dvvxpswlrqv
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554
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556
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557
71; Lqirupdwlrq dqg dvvxpswlrqv
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558
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566
6
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7149
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7163 Lqirupdwlrq dqg dvvxpswlrqv
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7165 Lqirupdwlrq dqg dvvxpswlrqv
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7173 Lqirupdwlrq dqg dvvxpswlrqv
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7176 Lqirupdwlrq dqg dvvxpswlrqv
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7178 Lqirupdwlrq dqg dvvxpswlrqv
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0
Elevation, m
-2
-4
-6
-8
-10
-12
0
10
20
30
Radius, m
75:
40
50
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iru u 83 p
102
Pressure (kPa)
100
98
96
94
92
90
88
0
50
100
150
Radius (m)
75<
200
250
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Pressure coefficient
Fs
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0
1
2
3
4
Nondimensional radius (r/rc)
764
5
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81433 Dv wkh suhvvxuh ghfuhdvhv wkh ghqvlw| ehfrphv ohvv1 Wklv phdqv wkdw d vpdoohu suhvvxuh judglhqw lv qhhghg
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81434 Lqirupdwlrq dqg dvvxpswlrqv
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767
81435 Lqirupdwlrq dqg dvvxpswlrqv
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768
81436 Lqirupdwlrq dqg dvvxpswlrqv
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81437 Lqirupdwlrq dqg dvvxpswlrqv
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81438 Lqirupdwlrq dqg dvvxpswlrqv
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81439 Lqirupdwlrq dqg dvvxpswlrqv
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774
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81443 d, Vxevwlwxwlqj wkh htxdwlrq iru wkh vwuhdpolqh lqwr wkh Hxohu htxdwlrq jlyhv
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777
81445 Rqh srvvleoh ghvljq lv vkrzq1 Wkh pdqrphwhu lv dq dlu0zdwhu pdqrphwhu1 Wkhq iru wklv vhwxs1
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water
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kO
@ T@D @ 3=83@++@7, 3=85 , @ 5=879 p2v
@ Y 5 @5j @ +5=879,5 @+5 <=;4, @ 3=663 p
957
:189 Lqirupdwlrq dqg dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
pd{lpxp doorzdeoh glvfkdujh ehiruh fdylwdwlrq
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s4 @ . Y45 @5j . }4 @ s5 @ . Y55 @5j . }5
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Y55 @5j @ 8 . <:> 993@<> :<3 @ 47=<: p> Y5 @ 4:=4 p2v
T @ Y5 D5 @ 4:=4 @7 3=485 @ 3=636 p6 2v
958
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surylghg lq sureohp vwdwhphqw
Ilqg
glvfkdujh dw lqflslhqw fdylwdwlrq
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s4 @ . Y45 @5j . }4
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4=<Y55 @5j> Y5 @ 9=7< p2v
Y5 D5 @ 9=7< @7 3=75 @ 3=;48 p6 @v
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959
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g,
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95:
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surylghg lq sureohp vwdwhphqw
Ilqg
glvfkdujh iru zdwhu
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s4 @ . Y45 @5j . }4 @ s5 @ . Y55 @5j . }5 . kO
5 @5j
3 . 3 . 433 @ 3 . Y95 @5j . 93 . 3=35+4> 333@4,Y45
Frqwlqxlw| htxdwlrq=
Y9 D9
Y9
Y9
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Y45
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EGL
HGL
95;
:193
E1.=610m
EGL
1.52 m
2
HGL
V /2g
EGL
HGL
95<
:194
EGL
HGL
0.71m
10 m (approx.)
963
:195
37.2 m
80 m
42.6 m
2000 m
964
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969
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@ :;=8 iw
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76=: ks
EGL
EGL
HGL
HGL
96:
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V2/2g=4 m
EGL
HGL
p/γ
96;
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11.9 m
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hp=535 m
HGL
0.794 m
973
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3 . 3 . 533 @ sp @ . Yp5 @5j . 533 . 3=35+433@3=63,Y 5 @5j
sp @ @ +Y 5 @5,+4 . 9=99:,
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sp @ ;=35: @ :;> :78 Sd @ :;=: nSd
974
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s4 @ . Y45 @5j . }4 @ s5 @ . Y55 @5j . }5 . kO
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433 @ 3 . Y55 @5j . 63 . 3=347+833@3=93,Ys5 @5j
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pmin
EGL
HGL
40.5 m
p max
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433 @ splq @ . 433 . 6=66 5=86
splq @ ;5=9 nSd/ jdjh
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66=36 p
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979
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A
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N @ 3=7 . 3=38 @ 3=7 . 3=38 @ 3=758
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s
s
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wkh rz yhorflw| zrxog eh
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20
18
16
14
12
10
8
6
4
2
0
0
20
40
60
80
100
Angle, deg
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44<9
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eh wr frqqhfw wkh rz wr d h{leoh edj lpphuvhg lq d zdwhu +ru vrph oltxlg, edwk dv vkrzq1 Dv wkh jdv hqwhuv
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d judgxdwhg f|olqghu wr phdvxuh wkh glvsodfhphqw dv d ixqfwlrq ri wlph1
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v
5s
Fi @ NDr
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5s+NDr ,5
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nqrzq h{dfwo|1 Li wkh ylvfrvlw| ri wkh xlg lv nqrzq/ wkh Uh|qrogv qxpehu frxog eh fdofxodwhg dqg wkh deryh htxdwlrq
frxog eh xvhg iru dq lwhudwlyh vroxwlrq1
44<;
@T|ih 6Lh|ii?
4714 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
wkuxvw rewdlqhg iurp surshoohu
Vroxwlrq
FW @ IW @G7 q5 @ 3=37;
Wkxv/
IW @ 3=37;G7 q5 @ 3=37; 4=38 67 +4> 733@93,5 @ 5> 556 Q
44<<
4715 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
wkuxvw rewdlqhg iurp surshoohu
Vroxwlrq
Y3 @qG @ +;3> 333@6> 933,@++4> 733@93, 6, @ 3=64:
Iurp Ilj1 4706/ FW @ 3=3531 Wkhq
IW @ 3=353 G7 q5 @ 3=353 4=38 67 +4> 733@93,5 @ <59 Q
Dovr iurp Ilj1 4706/ Fs @ 3=344 dqg
S @ 3=344G8 q6 @ 3=344 4=38 68 +4> 733@93,6 @ 68=: nZ
4533
4716 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
wkuxvw surgxfhg e| surshoohu
Vroxwlrq
q @ 4> 333@93 @ 49=9: uhy2vhf
Y3 @ 63 psk @ 77 isv
Y3 @qG @ 77@+49=9: ;, @ 3=66
Iurp Ilj1 4706 FW @ 3=34;5> Fs @ 3=344 vr
IW
S
@ 3=34;5 3=3357 ;7 49=9:5 @ 7<=: oei
@ 3=344 3=3357 ;8 49=9:6 @ 7> 338 iw0oe2vhf @ :=6 ks
Li Y3 @ 3> FW @ 3=37:8 vr
IW @ 3=37:8 3=3357 ;7 49=9:5 @ 463 oei
4534
4717 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
dqjxodu vshhg ri surshoohu
Vroxwlrq
Y3 @ 63 psk @ 77 isv
Iurp Ilj1 4706/ dw pd{lpxp hflhqf|/ Y3 @+qG, @ 3=5;8
q @ 77@+3=5;8 ;, @ 4<=63 usv
Q @ 4> 48; usp
4535
4718 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
wkuxvw dqg srzhu rxwsxw
Vroxwlrq
Dw pd{lpxp hflhqf| FW @ 3=356 dqg Fs @ 3=345
IW
S
@ 3=356 3=3357 97 58=:65 @ 7:=7 oei
@ 3=345 3=3357 98 58=:66 @ 6> ;48 iw0oei2v @ 9=<7 ks
4536
4719 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
gldphwhu ri surshoohu dqg vshhg ri dlufudiw
Vroxwlrq
S
W
W
6<5
G
@
@
@
@
@
@
O
O@+FO V,
Y35
Y3
@
@
@
@
Fs q6 G8
s@UW @ 93 436 @++5;:,+5:6,, @ 3=:99 nj2p6
FW q5 G7
Gudj @ Oliw@63 @ +4> 533,+<=;4,@+63, @ 6<5 Q
+3=358,+3=:99,+6> 333@93,5 G7
4=9< p
Z @ FO +4@5,Y35 V
+Y35 @5, @ +4> 533,+<=;4,@++3=73,+43,, @ 5> <75
+5> <75,+5,@+3=:99, @ :> 9;4
;:=9 p2v
4537
471: Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
pd{lpxp doorzdeoh dqjxodu vshhg
Vroxwlrq
Ywls
Ywls
q
Q
@
@
@
@
3=<f @ 3=< 668 @ 634=8 p2v
$u @ q+5,u
634=8@+5u, @ 634=8@+G, uhy2v
93 q usp
G +p, Q +usp,
5
5> ;:<
6
4> <4<
7
4> 773
4538
471; Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
dqjxodu vshhg ri surshoohu
Dw pd{lpxp hflhqf| Y3 @+qG, @ 3=5;8= Wkhq
q @ Y3 @+3=5;8G, @ +73> 333@6> 933,@+3=5;8 5, @ 4<=8 uhy2v
Q @ 4<=8 93 @ 4> 4:3 usp
4539
471< Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
wkuxvw dqg srzhu lqsxw
Vroxwlrq
Dw pd{lpxp hflhqf| FW @ 3=356 dqg Fs @ 3=345
IW
S
@ 3=356 4=4 57 +4<=8,5 @ 487 Q
@ 3=345 4=4 58 +4<=8,6 @ 6=46 nZ
453:
47143 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
lqlwldo dffhohudwlrq
Vroxwlrq
FW @ 3=37;
Wkxv
IW @ 3=37;G7 q5 @ 3=37; 4=4 57 +4> 333@93,5 @ 568 Q
d @ I@p @ 568@633 @ 3=:;5 p2v5
453;
47144 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
wkh glvfkdujh
Vroxwlrq
q @ 4> 333@93 @ 49=9: uhy2v
FK @ kj@G5 q5 @ 6 <=;4@++3=7,5 +49=9:,5 , @ 3=995
Iurp Ilj1 4709/ FT @ T@+qG6 , @ 3=958= Wkhq
T @ 3=958 49=9: +3=7,6 @ 3=99: p6 2v
453<
47145 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
glvfkdujh dqg srzhu ghpdqg
Vroxwlrq
q
FK
iurp Ilj1 4709/ FT
T FT qG6
Srzhu
@
@
@
@
9<3@93 @ 44=8 uhy2v
kj@+q5 G5 , @ 43 <=;4@++3=:45,5 +44=8,5 , @ 4=9
3=73 dqg Fs @ 3=:9
3=73 44=8 3=:456 @ 4=99 p6 2v
@ Fs G8 q6 @ 3=:9 4> 333 3=:458 44=86 @ 544 nZ
Iurp Ilj1 4709/ FT @ 3=73 dqg Fs @ 3=:9= Wkhq
T @ FT qG6 @ 3=73 44=8 3=:456 @ 4=99 p6 2v
S
@ Fs G8 q6 @ 3=:9 4> 333 3=:458 44=86 @ 544 nZ
4543
47146 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
glvfkdujh dqg srzhu uhtxluhg
Vroxwlrq
G @ 68=9 fp
q @ 44=8 uhy2v
Hqhuj| htxdwlrq iurp wkh uhvhuyrlu vxuidfh wr wkh fhqwhu ri wkh slsh dw wkh rxwohw/
[
kO
s4 @ . Y45 @+5j, . }4 . ks @ s5 @ . Y55 @+5j, . }5 .
ks @ 54=8 53 . ^T5 @+D5 5j,`+4 . iO@G . nh . ne ,
O @ 97 p
Dvvxph i @ 3=347> ue @G @ 4= Iurp Wdeoh 4306/ ne @ 3=68> nh @ 3=4
ks
FT
ks
@ 4=8 . ^T5 ++3=347+97,@3=689, . 3=68 . 3=4 . 4,`@^5+<=;4,+@7,5 +3=689,7 ` @ 4=8 . 53=75
@ T@+qG6 , @ T@^+44=8,+3=689,6 ` @ 4=<6T
@ FK q5 G5 @j @ FK +44=8,5 +3=689,5 @<=;4 @ 4=:4FK
T+p6 @v,
3143
3148
3153
3158
3163
3168
FT
314<6
315;<
316;8
317;5
318:;
319:8
ks4 +p,
41:3
41<9
5165
51:;
6167
7133
FK
5138
41:3
4188
4158
31<8
3188
ks5 +p,
6183
51<4
5198
5146
4195
31<7
Wkhq sorwwlqj wkh v|vwhp fxuyh dqg wkh sxps fxuyh/ zh rewdlq wkh rshudwlqj frqglwlrq=
T @ 3=55 p6 2v
Iurp Ilj1 471:
S @ 9=8 nZ
5
hp(m)
4
pump curve
3
2
1
system curve
operating point
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Q (m 3 /s)
4544
47147 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
glvfkdujh dqg srzhu uhtxluhg
Vroxwlrq
Wkh v|vwhp fxuyh zloo eh wkh vdph dv lq Sure1 47146
FT
ks
@ T@^qG6 ` @ T@^48+3=689,6 ` @ 4=7;T
@ FK q5 G5 @j @ FK +48,5 +3=689,5 @<=;4 @ 5=<4FK
T
3153
3158
3163
3168
FT
315<9
316:3
31777
3184;
FK
4198
4188
4168
4148
ks
71:<
7184
61<5
6167
Sorwwlqj wkh sxps fxuyh zlwk wkh v|vwhp fxuyh jlyhv wkh rshudwlqj frqglwlrq>
T @ 3=65 p6 2v
FT
@ 4=7;+3=65, @ 3=7:7
Wkhq iurp Ilj1 4709/ Fs @ 3=:3
Fs q6 G6 @ 3=:3+48,6 +3=689,8 4> 333 @ 46=8 nZ
5
Pump curve
hp(m)
4
3
System curve
2
0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36
2
Q (m /s)
4545
47148 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
srzhu uhtxluhg
Vroxwlrq
Dw pd{lpxp hflhqf|/ iurp Ilj1 4709/ FT @ 3=97> Fs @ 3=93> dqg FK @ 3=:8
G @ 4=9: iw
q @ 4> 433@93 @ 4;=66 uhy2v
T @ FT qG6 @ 3=97 4;=66 4=9:6 @ 87=9 fiv
k @ FK q5 G5 @j @ 3=:8 4;=665 4=9:5 @65=5 @ 54=; iw
S
@ Fs G8 q6 @ 3=93 4=<7 4=9:8 4;=666 @ <6> 449 iw0oei2vhf @ 49<=6 ks
4546
47149 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
srzhu uhtxluhg
Vroxwlrq
Dw pd{lpxp hflhqf|/ iurp Ilj1 4709/ FT @ 3=97> Fs @ 3=93> FK @ 3=:8
T @ FT qG6 @ 3=97 78 3=86 @ 6193 p6 2v
k @ FK q5 G5 @j @ 3=:8 785 3=85 @<=;4 @ 6;1: p
S @ Fs G8 q6 @ 3=93 4> 333 3=88 786 @ 4> :3< PZ
4547
4714:
G @ 47@45 @ 4=49: iw
q @ 4> 333@93 @ 49=: uhy2v
5
5
5
k @ FK q G @j @ FK +49=:, +4=49:,5 @65=5 @ 44=;FK iw
T @ FT qG6 @ FT 49=:+4=49:,6 @ 59=8FT fiv
FT
313
314
315
316
317
318
319
FK
51<
5188
513
41:
418
415
31;8
T+fiv,
3
5198
816
:1<8
4319
4615
481<
k+iw,
6715
6314
5619
5314
4:1:
4715
4313
40
35
Head, ft
30
25
20
15
10
5
0
2
4
6
8
10
12
D ischarge, cfs
4548
14
16
18
4714;
G @ 93 fp @ 3=93 p
Q @ 9<3 usp @ 44=8 uhy2v
Wkhq
k @ FK G5 q5 @j @ 7=;86FK
T @ FT qG6 @ 5=7;7FT
FT
313
314
315
316
317
318
319
FK
51<3
5188
5133
41:3
4183
4153
31;8
T+p6 2v,
313
3157;
317<:
31:78
31<<7
41575
417<3
k+p,
4714
4517
<1:
;16
:16
81;
715
16
14
Head, m
12
10
8
6
4
2
0
1
3
D ischarge, m /s
4549
2
4714< Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
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khdg dqg glvfkdujh dw pd{lpxp hflhqf|
Vroxwlrq
G @ 3=6:4 5 @ 3=:75 p
q @ 5> 466=8@+5 93, @ 4:=:: usv
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k @ FK q5 G5 @j @ 8=48+4:=::,5 +3=:75,5 @<=;4 @ <4=6 p
T @ FT qG6 @ 3=454+4:=::,+3=:75,6 @ 3=;:; p6 2v
454:
47153 Lqirupdwlrq dqg Dvvxpswlrqv
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srzhu qhhghg wr rshudwh idq
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T @ Y D @ +93,+@7,+4=5,5 @ 9:=; p6 2v
FT @ T@+qG6 , @ +9:=;,@++4> ;33@93,+5,6 @ 3=5;5
Iurp Ilj1 47049 Fs @ 5=9= Wkhq
S @ Fs G8 q6 @ +5=9,+4=5,+5,8 +63,6 , @ 5=:3 PZ
454;
47154 Lqirupdwlrq dqg Dvvxpswlrqv
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glvfkdujh wkurxjk slsh
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Dvvxph k @ <3 p^A}`> wkhq iurp Ilj1 470</ T @ 3=57 p6 2v
Y @ t@D @ 3=57@^+@7,+3=69,5 ` @ 5=69 p2v> nv @G @ 3=33345
Dvvxplqj W @ 53 F>
Uh @ Y G@ @ 5=69+3=69,@439 @ ;=8 438
iurp Ilj1 430;/ i @ 3=347
ki @ +3=347+943,@3=69,++5=69,5 @+5 <=;4,, @ 9=:6 p
k r ;7 . 9=: @ <3=: p
iurp Ilj1 470<
T @ 3=56 p6 2v> Y @ 3=56@++@7,+3=69,5 , @ 5=59 p2v
ki @ ^3=347+943,@3=69`+5=59,5 @+5 <=;4, @ 9=4; p
vr
k @ ;7 . 9=5 @ <3=5 p
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dqg iurp Ilj1 470<
T @ 3=558 p6 2v
454<
47155 Lqirupdwlrq dqg Dvvxpswlrqv
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G @ 3=6:4 p @ 4=54: iw
q @ 4> 933@93 @ 59=: usv
k @ FK q5 G5 @j
vr
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iurp Ilj1 47043 FT @ 3=478 wkhq
T @ FT qG6 @ 3=478+59=:,+4=54:,6 @ 9=<; fiv
4553
47156 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
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pd{lpxp srvvleoh khdg ghyhorshg
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FK @ Kj@G5 q5 Vlqfh FK zloo eh wkh vdph iru wkh pd{lpxp khdg frqglwlrq/ wkhq
K
q5
ru
K4>833 @ K4>333 +4> 833@4> 333,5
K4>833 @ 435 5=58 @ 55<=8 iw
4554
47157 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
vkxwr khdg
Vroxwlrq
K q5
vr
K63 @K68=9 @ +63@68=9,5
ru
K63 @ 437 +63@68=9,5 @ :6=; p
4555
47158 Lqirupdwlrq dqg Dvvxpswlrqv
surylghg lq sureohp vwdwhphqw
Ilqg
glvfkdujh zkhq khdg lv 83 p
Vroxwlrq
FK @ kj@+q5 G5 , @ 83+<=;4,@^+58,5 +3=73,5 ` @ 7=<4
iurp Ilj1 47043 FT @ 3=469 wkhq
T @ FT qG6 @ 3=469+58+3=73,6 @ 3=54; p6 @v
4556
47159 Lqirupdwlrq dqg Dvvxpswlrqv
iurp wdeoh D17 @ ;47 nj2p6
surylghg lq sureohp vwdwhphqw
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Vroxwlrq
Q @ 8> 333 usp @ ;6=66 usv
iurp Ilj1 47043 dw pd{lpxp hflhqf| FT @ 3=458> FK @ 8=48> Fs @ 3=9<
T @ FT qG6 @ +3=458,+;6=66,+3=53,6 @ 3=3;66 p6 @v
k @ FK G5 q5 @j @ +8=48,+3=53,5 +;6=66,5 @<=;4 @ 478=; p
S @ Fs G8 q6 @ +3=9<,+;47,+3=53,8 +;6=66,6 @ 437=3 nZ
4557
4715: Wkh glvfkdujh frhflhqw lv ghqhg dv
FT @ T@qG6
Wkh urwdwlrqdo vshhg lv 4:83293@5<15 usv1 Wkh gldphwhu iru hdfk lpshoohu lv 31749: iw/ 3178; iw/ 318 iw/ 31875
iw dqg 318;6 iw1 Rqh jdoorq shu plqxwh lv 3133555; iw6 @v1 Vr iru hdfk lpshoohu/ wkh frqyhuvlrq idfwru wr jhw wkh
glvfkdujh frhflhqw lv
8%
8=8%
9%
9=8%
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jsp 3=33438
jsp 3=333:<7
jsp 3=333943
jsp 3=3337:<
jsp 3=3336;8
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iw
iw
iw
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3=4843
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Wkh shuirupdqfh lq whupv ri wkh qrqglphqvlrqdo sdudphwhuv lv vkrzq rq wkh judsk1
6
Head coefficient
5
4
5 inch
5.5 inch
6 inch
6.5 inch
7 inch
3
2
1
0.00
0.02
0.04
0.06
0.08
0.10
D ischa rg e coefficien t
4558
0.12
0.14
4715; Wkh urwdwlrqdo vshhg lq usv lv
q @ 833@93 @ ;=66 usv
Wkh glvfkdujh lv jlyhq e|
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Wkh khdg lv jlyhq e|
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FT
3
3=37
3=3;
3=43
3=45
3=47
3=49
T
FK k
3
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5=67 8=:8 <7=4
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6=84 8=58 ;8=<
7=43 7=; :;=8
7=9; 7=3 98=7
100
95
Head, m
90
85
80
75
70
65
60
0
1
2
3
3
D ischarg e, m /s
4559
4
5
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Q
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3=55 p6 @v 597=5 jdoorqv2v 93 v2plq @ 6> 7;: jsp
9<3 +6> 7;:,4@5 @+66,6@7 @ 5> <93
Qvv lv pxfk ehorz ;/833> wkhuhiruh/ lw lv lq d vdih rshudwlqj udqjh1
455:
47163 Lqirupdwlrq dqg Dvvxpswlrqv
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qv
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455;
47164 Lqirupdwlrq dqg Dvvxpswlrqv
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47165 Lqirupdwlrq dqg Dvvxpswlrqv
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Wkhq iurp Ilj1 47047/ qv ? 3=56 vr xvh d udgldo rz sxps1
4563
47166 Lqirupdwlrq dqg Dvvxpswlrqv
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pd{lpxp vshhg
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Q S VK @ 47=: svl 5=64 iw2svl
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4564
47167 Lqirupdwlrq dqg Dvvxpswlrqv
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qv
q
T
k
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Wkhq
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4@+<=;4 6=47,6@7 @ 3=:9
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4565
47168 Lqirupdwlrq dqg Dvvxpswlrqv
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T @ 73=3 3=69 @ 47=7 p6 2v
@ 4=5 nj2p6 dw 53 F
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4566
47169 Lqirupdwlrq dqg Dvvxpswlrqv
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@ 4=55 nj2p6 dw 93 I
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wkhq
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S
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4567
4716: Lqirupdwlrq dqg Dvvxpswlrqv
iurp Wdeoh D08 iru phwkdqh U @ 84; M2nj2N dqg n @ 4=59
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4568
4716; Lqirupdwlrq dqg Dvvxpswlrqv
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4569
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b
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@ 447=9@3=8 @ 55< nZ
456:
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47174 Lqirupdwlrq dqg Dvvxpswlrqv
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4573
47176 Lqirupdwlrq dqg Dvvxpswlrqv
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4574
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4575
47178 Lqirupdwlrq dqg Dvvxpswlrqv
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4576
47179 Lqirupdwlrq dqg Dvvxpswlrqv
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4577
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4596
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4598
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4599
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Mean Velocity
in reach
Section number Depth Velocity at
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1 at y=yc
0.972
3.086
2
0.980
3.060
3
0.990
3.030
2.941
5
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2.830
6
1.100
2.727
8
1.300
2.308
4.0m
9.272
0.660
1.790 x 10-3
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4.4m
0.669
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1.698 x 10
1.7m
6.1m
8.327
0.684
1.551 x 10-3
4.7m
10.9m
7.721
0.701
1.403 x 10-3
7.7m
18.6m
0.730
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6.828
1.192 x 10
33.2m
51.8m
0.769
9.576 x 10-4
55.3m
107.1m
80.0m
187.1m
107.4m
294.5m
0.750
2.404
5.779
0.788
2.225
1.400
0.1m
0.710
2.613
2.500
1.834 x 10-3
0.693
2.779
1.200
3.9m
0.656
0.675
2.886
7
9.443
Distance upstream
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0.662
2.986
1.020
∆x=((y2+V22/2g)(y1+V1/2g))/Sf
0.658
3.045
4
sf=fV2mean/
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0.654
3.073
9
V2
Solution Table for Problem 15.51
Mean Hydraulic
Hydraulic Radius
Radius
R=A/P,m
Rm=(R1+R2)/2
4.951
2.143
2.072
10
1.500
2.000
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0.806
-4
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0.824
4.291
0.841
0.857
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