fourth edition - solution manual & test bank storesolutions manual to accompany introduction to...
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SolutionS Manual to accoMpany
introduction to HydraulicS and Hydrology witH
applicationS for StorMwater ManageMent
Fourth Edition
John E. Gribbin, P.E.Essex County College
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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© 2014, 2007 Delmar, Cengage Learning
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ISBN-13: 978-1-133-69269-0
ISBN-10: 1-133-69269-9
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Solutions Manual to Accompany Introduction to Hydraulics and Hydrology with Applications for Stormwater Management, 4EJohn E. Gribbin
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iii
Contents
Solutions:Chapter 1 - Hydraulics and Hydrology in Engineering ..............................................1
Chapter 2 - Fluid Mechanics ......................................................................................4
Chapter 3 - Fundamental Hydrostatics .....................................................................6
Chapter 4 - Fundamental Hydrodynamics ..............................................................23
Chapter 5 - Hydraulic Devices ................................................................................39
Chapter 6 - Open Channel Hydraulics ....................................................................51
Chapter 7 - Uniform Flow in Channels ...................................................................58
Chapter 8 - Varied Flow in Channels ......................................................................67
Chapter 9 - Culvert Hydraulics ...............................................................................75
Chapter 10 - Fundamental Hydrology ......................................................................81
Chapter 11 - Runoff Calculations ..............................................................................97
Chapter 12 - Storm Sewer Design ............................................................................126
Chapter 13 - Culvert Design ...................................................................................140
Chapter 14 - Stormwater Detention .........................................................................150
Chapter 15 - Detention Design ................................................................................156
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1
C h a p t e r
1Hydraulics and Hydrology
in EnginEEring
1. A 5pd2
4
A 5p(3.04)2
4
A 5 7.26ft2 (3sig.figures) (Answer)
2. 1.0mi 35280ft1.0mile
5 5280ft
V 5 (L)(W)(T)V 5 (5280)(22.0)(.650)V 5 75,504ft3
V 5 2796yd3
V 5 2800yd3 (2sig.figures) (Answer)
3. 61/2s 5 13/2s (2sig.figures)
13/2in 31ft
12in5 13/24ft 5 0.5417ft
Depth 5 0.54ft (2sig.figures) (Answer)
4. V 5pd
2L4
V 5p(1.30)2(60)
4
V 5 79.64ft3
V 5 80ft3 (2sig.figures) (Answer)
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2 CHAPTER 1 — HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL
5. 12.25151
25.0188.25
Answeris188ft.
6. D 5 36in 3.02540m
1in5 0.9144m
A 5 pD2/4 5 p(.9144)2/4
A 5 0.66m2 (2sig.figures) (Answer)
7. a) A 5 (45.00)(125.00) 5 5625ft2 (4sig.figures)
b) A 5 5625ft2 31acre
43560ft2 5 0.1291acres (4sig.figures)
c) A 5 5625ft2 3.09291ft2 m2 5 522.6m2 (4sig.figures)
d) A 5 5625ft2 31acre
43560ft2 3.40469hectare
1acre5 .05226hectare (4sig.figures)
8. Designaconnectorroadway.
Designconsiderations:
1. Intersectionconfigurations
2. Widthofroadbaseduponexpectedtraffic
3. Typeofcurb
4. Amountofcrown
5. Gradeofprofile
6. Gradingofadjacentground
7. Sightdistances
8. Propertylines
9. Pavementthickness
10. Drainage
11. Stopsignsandpaintedstoplines
12. Signalization(consideration)
13. Considerationofsidewalks
14. Considerationofguiderails
15. Considerationofsnowremoval
9. Designapedestrianwalkway.
Designconsiderations:
1. Sizeandlocationofwalkwaytoconsideramountofpedestriantrafficandconvenienceoftrafficrouting
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HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL 3
2. Considerationofconflictswithexistingutilities,trees,etc.
3. Gradingtoprovidedrainage
4. Handicapaccess
5. Concretemixtureandthickness
6. Crushedstonebasecourse
7. Expansionandcontroljoints
8. Drivewaytreatment:reinforcement,addedthickness
10. Designaculvertpipe.
Designconsiderations:
1. Materialofpipe
2. Diameterbaseduponexpectedfloodflow
3. Coveroverpipe
4. Gradientforgravityflow
5. Erosionprotectionatinletandoutlet
6. Headwalls
7. Trench:stonebedding,shoringifneeded
8. Alignmentofculverttomatchstream
9. Considerationofpossiblepermitsforwetlands,etc.
10. Trafficcontrol
11. Floodingduringconstruction
12. Fishhabitat
13. Upstreamwaterlevelaftercompletion
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4
C h a p t e r
2Fluid Mechanics
1. W 5 gV (Equation2-1)W 5 (62.4)(1.0)W 5 62.4lb. (Answer)
2. W 5 gV (Equation2-1)
ButW 5 mg
Thus,gV 5 mg
Density 5mV
Substituting,Density 5g
g
Therefore,Density 562.432.2
5 1.94slugs/ft3 (Answer)
3. Dimensionsofcan 54.012
ftdia. 36.012
fthigh
V 5pd2
4h
V 5p(.333)2
4(.50)
V 5 0.0428ft2
g 5WV
52.0
.04285 46.77lb/ft2
g 5 47lb/ft3 (Answer)
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HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL 5
4. Dimensionsofcontainer 5 0.100m 3 0.200m 3 0.150m
V 5 (.100)(.200)(.150)
V 5 0.00300m3
g 5WV
5450
.003005 150,000N/m3
g 5 150kN/m3 (Answer)
5. S.G. 5S.W.
62.4lb/ft3
S.G. 557.462.4
5 0.92 (Answer)
6. S.G. 5S.W.
9.81kN/m3
S.G. 57.85 3 103
9.81 3 103 5 0.800 (Answer)
7. Thewaterriseshigherinthe2.0mmdiametertubebecauseitisthenarrowertube.
8. t 5FA
(Equation2-4)
t 51.5 3 1024
.75
t 5 2.0 3 1024lb
m 5 td
v (Equation2-8)
m 5(2.0 3 1024)(.0417)
10 ad 5
.5012
ftb
m 5 8.3 3 1027lb-s/ft2 (Answer)
9. S.W. 5 45lb/ft3
Density 5g
g5
4532.2
5 1.40slugs/ft3
v 5m
r
v 52.2 3 1025
1.40
v 5 1.57 3 1025ft2/s (Answer)
10. S.W. 5 7.85 3 103N/m3
Density 5g
g5
7.85 3 103
9.815 0.800 3 103kg/m3
v 5m
r5
2.4 3 1023
.800 3 103 5 3.00 3 1026m2/s (Answer)
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6
C h a p t e r
3Fundamental Hydrostatics
1. p 5 gz (Equation3-2)
p 5 162.42 13502p 5 21,840lb/ft2
p 5 21,800lb/ft2 (Answer)
2. a) p 5 gz (Equation3-2) b) p 5 gz (Equation3-2)
p 5 162.42 14.02 p 5 162.42 112.02 p 5 250lb/ft2 (Answer) p 5 749lb/ft2 (Answer)
3. z 5 82.5 2 38.0
z 5 44.5ft
p 5 gz (Equation3-2)
p 5 162.42 14.02p 5 2776.8lb/ft2
p 5 2780lb/ft2 (Answer)
4. p 5 gz (Equation3-2)
p 5 162.42 18.502p 5 530.4lb/ft2
p 5 530lb/ft2 (Answer)
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HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL 7
5. Resultantforce:
FR 5gz2
2w (Equation3-4)
FR 5162.42 18.022
2110.02
FR 5 19,968lb
FR 5 20,000lb (Answer)
Locationofresultantforce:
yR 513
z (Equation3-5)
yR 513
18.02
yR 5 2.67ft
yR 5 2.7ft (Answer)
8.0′
A
B
FR
yR
6. Resultantforce:
FR 5 gzlw (Equation3-3)
FR 5 162.42 18.02 112.02 110.02FR 5 59,904lb
FR 5 60,000lb (Answer)
Locationofresultantforce:
FRlocatedatcentroidofpressure
xR 512.0
2
xR 5 6.0ft (Answer)
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8 CHAPTER 3 — HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL
B C
xR
FR
7. u 5 tan215.08.0
u 5 32.0°
FH 5 gz1lwcosu (Equation3-8)
FH 5 162.42 13.02 110.02 19.4342cos32.0°
FH 5 14,976lb
FV 5gw2
1z1 1 z22lsinu (Equation3-9)
FV 5(62.4)(10.0)
2 33.0 1 8.0 4(9.434)sin32.0°
FV 5 17,160lb
W 5gwl2
2sinucosu (Equation3-10)
W 5162.42 110.02 19.43422
2sin32.0°cos32.0°
W 5 12,480lb
yR 5Iy
3c2z1 1 z2
z1 1 z2d (Equation3-7)
yR 55.03
c (2)(3.0) 1 8.03.0 1 8.0
d
yR 5 2.12ft
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HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL 9
D
W = 10.0′W
C
yR
FH
xW
FV
xR
3.0′
8.0′
8.0′
9.43′C
D
FR
lR
xR 5 one-halfhorizontalprojection
xR 512
lcosu
xR 512
(9.434)cos32.0°
xR 5 4.00ft
xW 5 one-thirdhorizontalprojection
xW 513
(9.434)cos32.0°
xW 5 2.67ft
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10 CHAPTER 3 — HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL
FR 5 "Fv2 1 (FH 1 W)2 (Equation3-11)
FR 5 "17,1602 1 (14,976 1 12,480)2
FR 5 32,377lb
FR 5 32,000lb (Answer)
lR 51FR
3Fv(yR) 1 W(xW) 1 FH(xR) 4 (Equation3-12)
lR 51
32,377 3(17,160)(2.12) 1 (12,480)(2.67) 1 (14,976)(4.00) 4
lR 5 4.00ft (Answer)
8. Sincethelengthofthedamisnotindicated,theforcewillbecomputedperlinearfootoflength(w 5 1ft).
u 5 tan2113
u 5 18.435°
FH 5 0
FV 5gw2
(z1 1 z2)lsinu (Equation3-9a)
FV 5(62.4)(1)
2(0 1 15)(47.434)sin18.435°
FV 5 7,020lb/L.F.
W 5gwl2
2sinucosu (Equation3-10)
W 5(62.4)(1)(47.434)
2sin18.435°cos18.435°
W 5 21,060lb/L.F.
xR 5 0
yR 5ly3c2z1 1 z2
z1 1 z2d (Equation3-7)
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HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL 11
15.0′
45.0′
W
θ
yR
Fv
xW
47.434′
θF R
l R
yR 5153
c (2)(0) 1 150 1 15
d
yR 5 5.0ft
xW 5 one-thirdhorizontalprojection
xW 5 15.0ft
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12 CHAPTER 3 — HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL
FR 5 "FV2 1 (FH 1 W)2 (Equation3-11)
FR 5 "7,0202 1 21,0602
FR 5 22,199lb/L.F.
FR 5 22,200lb/L.F. (Answer)
lR 51FR
3FV(yR) 1 W(xw) 1 FH(xR) 4 (Equation3-12)
lR 51
22,199 3(7,020)(5.0) 1 (21,060)(15.0) 1 0 4
lR 5 15.81ft
lR 5 15.8ft (Answer)
9. Forthisproblem,w 5 2.5ft.
7.5′
11.5′
yR
Fv
FR 5glyw
2(z1 1 z2) (Equation3-6)
FR 5(62.4)(4.0)(2.5)
2(7.5 1 11.5)
FR 5 5,928lb (Answer)
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HYDRAULICS AND HYDROLOGY FOR STORMWATER MANAGEMENT - SOLUTIONS MANUAL 13
yR 5ly3c2z1 1 z2
z1 1 z2d (Equation3-7)
yR 54.03
c2(7.5) 1 11.57.5 1 11.5
d
yR 5 1.86ft (Answer)
10. Forthisproblem,w 5 16ft,f 5 90°.
Fv
yv
xW
FH
A
W
B
xH
z2
z1
ϕR
r = 2.0
FR
A
B
ϕ=90˚
′
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