Section 10.4.3 Uniform Depth Examples—Determine Flowrate 10.45 A 2-m-diameter pipe made of finished concrete lies on a slope of 1-m elevation change per 1000-m horizontal distance.. Sect
Trang 1Bài tập Dòng đều
Tính độ nhám Manning:
1) Nước trong kênh có bề rộng 5m, sâu 1m, với vận tốc nước bằng 2m/s Kênh có độ dốc 1m/1000m
Hãy tính hệ số Manning của kênh này
Tính lưu lượng:
2) Ống tròn, đường kính d=2m, có độ dốc 1m/100m, làm bằng bê-tông tô Hãy tính lưu luợng khi nước chảy đầy ½ ống
3) Khi thêm vào tấm chắn giữa kênh, lưu lượng tăng hay giảm, bao nhiêu %?
10.42 The following data are obtained for a particular reach
of the Provo River in Utah: A ! 183 ft2, free-surface width ! 55 ft,
average depth ! 3.3 ft, R h ! 3.32 ft, V ! 6.56 ft/s, length of
reach ! 116 ft, and elevation drop of reach ! 1.04 ft Determine
(a) the average shear stress on the wetted perimeter, (b) the
Manning coefficient, n, and (c) the Froude number of the flow.
10.43 At a particular location, the cross section of the Co-lumbia River is as indicated in Fig P10.43 If on a day without wind it takes 5 min to float 0.5 mi along the river, which drops 0.46 ft in that distance, determine the value of the Manning
coef-ficient, n.
that logs would travel the length of the flume in 15 hours Do you agree with this claim? Provide appropriate calculations to support your answer
10.48 Water flows in a channel as shown in Fig P10.48 The velocity is 4.0 ft/s when the channel is half full with depth
d Determine the velocity when the channel is completely full,
depth 2d.
10.44 If the free surface of the Columbia River shown in Fig P10.43 were 20 ft above the bottom rather than 44 ft, as is in-dicated in the figure, how long would it take to float the 0.5-mi stretch considered in Problem 10.43? Assume the elevation change remains 0.46 ft
Section 10.4.3 Uniform Depth Examples—Determine Flowrate
10.45 A 2-m-diameter pipe made of finished concrete lies
on a slope of 1-m elevation change per 1000-m horizontal distance
Determine the flowrate when the pipe is half full
10.46 By what percent is the flowrate reduced in the rec-tangular channel shown in Fig P10.46 because of the addition of the thin center board? All surfaces are of the same material
10.47 The great Kings River flume in Fresno County, California, was used from 1890 to 1923 to carry logs from an elevation of 4500 ft where trees were cut to an elevation of 300 ft
at the railhead The flume was 54 miles long, constructed of wood, and had a V-cross section as indicated in Fig P10.47 It is claimed
594 Chapter 10 ■Open-Channel Flow
10.49 A natural riverbed has an approximate parabolic cross sec-tion such that the free-surface width is 200 ft when the center depth
is 5 ft Determine the flowrate if n ! 0.035 and the slope is 1.5
ft/mi
10.50 A trapezoidal channel with a bottom width of 3.0 m and sides with a slope of 2 : 1 (horizontal:vertical) is lined with
fine gravel (n ! 0.020) and is to carry 10 m3/s Can this channel
be built with a slope of S0!0.00010 if it is necessary to keep the velocity below 0.75 m/s to prevent scouring of the bottom? Explain
10.51 Water flows in a 2-m-diameter finished concrete pipe
so that it is completely full and the pressure is constant all along
the pipe If the slope is S0!0.005, determine the flowrate by us-ing open-channel flow methods Compare this result with that ob-tained by using pipe flow methods of Chapter 8
10.52 Water flows in a weedy earthen channel at a rate of
30 m3/s What flowrate can be expected if the weeds are removed and the depth remains constant?
10.53 Water flows in an unfinished concrete channel at a rate of
30 m3/s What flowrate can be expected if the concrete were fin-ished and the depth remains constant?
10.54 The Blue Ridge Flume, constructed in Shasta County, Cal-ifornia, in 1872 to supply water for gold mining operations, was built of planed wood and had a cross section as shown in Fig P10.54 Determine the water velocity in a section of this flume if
it was full and the elevation change was 27 ft per mile
GO
10.55 A round concrete storm sewer pipe used to carry rain-fall runoff from a parking lot is designed to be half full when the rainfall rate is a steady 1 in./hr Will this pipe be able to handle the flow from a 2-in./hr rainfall without water backing up into the park-ing lot? Support your answer with appropriate calculations
60 40 20 0
400 800 1200 1600 2000
Width, ft
■Figure P10.43
■Figure P10.46
b/2
b/2
b
Center board
1 ft
1 ft
■Figure P10.47
2 d
d
10 d
■Figure P10.48
■Figure P10.54
48 in.
32 in.
16 in.
4) Nước trong kênh chữ nhật như hình vẽ Vận tốc nước bằng 1.2m/s khi độ sâu mực nước bằng d
Tính vận tốc khi kênh chảy đầy kênh với độ sâu 2d
10.42 The following data are obtained for a particular reach
of the Provo River in Utah: A ! 183 ft2, free-surface width ! 55 ft,
average depth ! 3.3 ft, Rh ! 3.32 ft, V ! 6.56 ft/s, length of
reach ! 116 ft, and elevation drop of reach ! 1.04 ft Determine
(a) the average shear stress on the wetted perimeter, (b) the
Manning coefficient, n, and (c) the Froude number of the flow.
10.43 At a particular location, the cross section of the
Co-lumbia River is as indicated in Fig P10.43 If on a day without
wind it takes 5 min to float 0.5 mi along the river, which drops
0.46 ft in that distance, determine the value of the Manning
coef-ficient, n.
that logs would travel the length of the flume in 15 hours Do you agree with this claim? Provide appropriate calculations to support your answer.
10.48 Water flows in a channel as shown in Fig P10.48.
The velocity is 4.0 ft/s when the channel is half full with depth
d Determine the velocity when the channel is completely full,
depth 2d.
10.44 If the free surface of the Columbia River shown in
Fig P10.43 were 20 ft above the bottom rather than 44 ft, as is
in-dicated in the figure, how long would it take to float the 0.5-mi
stretch considered in Problem 10.43? Assume the elevation change
remains 0.46 ft.
Section 10.4.3 Uniform Depth Examples—Determine
Flowrate
10.45 A 2-m-diameter pipe made of finished concrete lies
on a slope of 1-m elevation change per 1000-m horizontal distance.
Determine the flowrate when the pipe is half full.
10.46 By what percent is the flowrate reduced in the
rec-tangular channel shown in Fig P10.46 because of the addition of
the thin center board? All surfaces are of the same material.
10.47 The great Kings River flume in Fresno County,
California, was used from 1890 to 1923 to carry logs from an
elevation of 4500 ft where trees were cut to an elevation of 300 ft
at the railhead The flume was 54 miles long, constructed of wood,
594 Chapter 10■Open-Channel Flow
10.49 A natural riverbed has an approximate parabolic cross sec-tion such that the free-surface width is 200 ft when the center depth
is 5 ft Determine the flowrate if n ! 0.035 and the slope is 1.5
ft/mi.
10.50 A trapezoidal channel with a bottom width of 3.0 m and sides with a slope of 2 : 1 (horizontal:vertical) is lined with
fine gravel (n ! 0.020) and is to carry 10 m3/s Can this channel
be built with a slope of S0! 0.00010 if it is necessary to keep the velocity below 0.75 m/s to prevent scouring of the bottom?
Explain.
10.51 Water flows in a 2-m-diameter finished concrete pipe
so that it is completely full and the pressure is constant all along
the pipe If the slope is S0! 0.005, determine the flowrate by us-ing open-channel flow methods Compare this result with that ob-tained by using pipe flow methods of Chapter 8.
10.52 Water flows in a weedy earthen channel at a rate of
30 m3/s What flowrate can be expected if the weeds are removed and the depth remains constant?
10.53 Water flows in an unfinished concrete channel at a rate of
30 m3/s What flowrate can be expected if the concrete were fin-ished and the depth remains constant?
10.54 The Blue Ridge Flume, constructed in Shasta County, Cal-ifornia, in 1872 to supply water for gold mining operations, was built of planed wood and had a cross section as shown in Fig.
P10.54 Determine the water velocity in a section of this flume if
it was full and the elevation change was 27 ft per mile.
GO
60
40
20
0
Width, ft
■ Figure P10.43
■ Figure P10.46
b/2
b/2
b
Center board
2 d d
10 d
■ Figure P10.48
48 in
32 in
c10Open-ChannelFlow.qxd 2/23/12 7:27 PM Page 594
5) Kênh hình thang có đáy rộng 3.0m, cạnh bên có độ nghiêng bằng 2:1 (phương ngang: phương đứng)
và được trám bằng sỏi (n=0.020) và lưu lượng 10m3/s Nếu muốn vận tốc trong kênh nhỏ hơn hoặc bằng 0.75m/s thì độ dốc kênh tối đa bằng bao nhiêu?
6) Nước chảy đầy trong đường ống tròn, đường kính bằng 2m, áp suất là hằng số dọc theo ống Với độ dốc So=0.005, hãy tính lưu lượng
7) Nước chảy trong kênh tự nhiên, bề mặt phủ cỏ với lưu lượng 30m3/s Nếu cỏ được làm sạch và độ sâu của mực nước không đổi, lưu lượng mới bằng bao nhiêu?
8) Kênh bê-tông tô có độ dốc 2m/km như trên hình Hãy tính lưu lượng khi mực nước trong kênh sâu y=1.5m
0.5 m 1.0 m
6 m
3 m
Concrete
Tính độ sâu hay kích thước:
9) Nước trong kênh chữ nhật, làm bằng bê tông tô, có lưu lượng 2m3/s Độ dốc đáy kênh bằng 0.001
Hãy tính chiều rộng kênh, nếu độ sâu mực nước bằng chiều rộng
10) Đường ống tròn, làm bằng bê tông cũ có đường kính bằng 2.0m với hệ số Manning bằng 0.025 và lưu lượng bằng 5.0m3/s khi chảy ½ ống Nếu thay bằng một đường ống mới có độ nhám bằng 0.012, chảy ½ ống với cùng lưu lượng, hãy tính đường kính ống mới
Trang 211) Bốn đường ống nước thải với đường kính bằng 0.5m hợp vào một đường ống có đường kính D Nếu
hệ số Manning, độ dốc của các ống là như nhau, nước chảy đầy ½ ống, hãy tính D
12) Kênh có bề mặt làm bằng đất sét (n=0.025) như trên hình Lưu lượng Q=8.1m3/s Để tránh xói mòn
thành và đáy kênh, vận tốc nước không được quá 1.5m/s Hãy tính bề rộng đáy kênh, b, và độ dốc
đáy kênh
b
2 ft
45°
30°
13) Kênh chữ nhật làm bằng bê tông trát vữa có chiều rộng bằng 8.4m và độ dốc 8/1000 Hãy tính độ sâu
và số Froude nếu lưu lượng bằng 10.8m3/s
14) Một kỹ sư thiết kế kênh làm bằng gỗ bào nhẵn với lưu lượng 2m3/s và độ dốc 10m/800m Mặt cắt
kênh có thể là tam giác vuông hoặc hình chữ nhật với bề rộng bằng 2 lần độ sâu Phương án nào tốn
ít gỗ hơn, bao nhiêu %?
15) Kênh có mặt cắt hình chữ nhật được đổi thành hình tròn có đường kính D khi đi qua hầm xuyên núi
Tính đường kính D, nếu vật liệu làm kênh và độ dốc không đổi, nước chảy đầy ống
10.69 The flowrate in the clay-lined channel (n ! 0.025)
shown in Fig P10.69 is to be 300 ft3/s To prevent erosion of the sides, the velocity must not exceed 5 ft/s For this maximum
velocity, determine the width of the bottom, b, and the slope, S0
596 Chapter 10■Open-Channel Flow
10.78 When the channel of triangular cross section shown
in Fig P10.78 was new, a flowrate of Q caused the water to reach
L !2 m up the side as indicated After considerable use, the walls
of the channel became rougher and the Manning coefficient, n, dou-bled Determine the new value of L if the flowrate stayed the same.
10.70 Water flows in a rectangular, brick-lined aqueduct of width 1.2 m at a rate of 73,000 m3/day Determine the water depth if the change in elevation over the 16-km length of this channel is 9.6 m
10.71 A rectangular, unfinished concrete channel of 28-ft width is laid on a slope of 8 ft/mi Determine the flow depth and Froude number of the flow if the flowrate is 400 ft3/s
10.72 An engineer is to design a channel lined with planed wood to carry water at a flowrate of 2 m3/s on a slope of 10 m/
800 m The channel cross section can be either a 90" triangle or a rectangle with a cross section twice as wide as its depth Which would require less wood and by what percent?
10.73 A circular finished concrete culvert is to carry a discharge
of 50 ft3/s on a slope of 0.0010 It is to flow not more than half full The culvert pipes are available from the manufacturer with di-ameters that are multiples of 1 ft Determine the smallest suitable culvert diameter
10.74 At what depth will 50 ft3/s of water flow in a 6-ft-wide rectangular channel lined with rubble masonry set on a slope
of 1 ft in 500 ft? Is a hydraulic jump possible under these condi-tions? Explain
10.75 The rectangular canal shown in Fig P10.75 changes
to a round pipe of diameter D as it passes through a tunnel in a mountain Determine D if the surface material and slope remain
the same and the round pipe is to flow completely full
10.76 An 8-ft-diameter concrete drainage pipe that flows half full is to be replaced by a concrete-lined V-shaped open chan-nel having an interior angle of 90" Determine the depth of fluid that will exist in the V-shaped channel if it is laid on the same slope and carries the same discharge as the drainage pipe
10.77 Water flows in the symmetrical, unfinished concrete trape-zoidal channel shown in Fig P10.77 at a rate of 120 ft3/s The slope
is 4.2 ft/2000 ft Determine the number of cubic yards of concrete needed to line each 1000 ft of the channel
10.79 Water flows in a channel with an equilateral triangle cross section as shown in Fig P10.79 For a given Manning coefficient,
n, and channel slope, determine the depth that gives the maximum flowrate
10.80 Two canals join to form a larger canal as shown in
Video V10.6and Fig P10.80 Each of the three rectangular canals
is lined with the same material and has the same bottom slope The water depth in each is to be 2 m Determine the width of the merged
canal, b Explain physically (i.e., without using any equations) why
it is expected that the width of the merged canal is less than the
combined widths of the two original canals (i.e., b # 4 m $ 8 m
!12 m)
b
2 ft
45°
30°
■ Figure P10.69
■ Figure P10.75
D b
b
2
■ Figure P10.77
35°
10 ft
2 ft
4-in.-thick concrete lining
■ Figure P10.78
2m
L
■ Figure P10.79
y h
■ Figure P10.80
8 m
4 m
b
Q2
Q1
Q3
16) Lưu lượng trong kênh hình thang như hình vẽ là Q Nếu muốn tăng lưu lượng lên gấp đôi mà không
thay đổi độ sâu, hãy tính bề rộng L cần thêm, biết rằng độ dốc, vật liệu kênh là không đổi
10.81 Water flows uniformly at a depth of 1 m in a channel that is 5 m wide as shown in Fig P10.81 Further downstream, the channel cross section changes to that of a square of width and
height b Determine the value of b if the two portions of this
chan-nel are made of the same material and are constructed with the same bottom slope
Problems 597
10.82 Determine the flow depth for the channel shown in Fig P10.60 if the flowrate is 15 m3/s
10.83 Rainwater runoff from a 200-ft by 500-ft parking lot
is to drain through a circular concrete pipe that is laid on a slope
of 3 ft/mi Determine the pipe diameter if it is to be full with a steady rainfall of 1.5 in./hr
10.84 (See Fluids in the News article titled “Plumbing the Everglades,” Section 10.4.1.) The canal shown in Fig P10.84 is to
be widened so that it can carry twice the amount of water
Deter-mine the additional width, L, required if all other parameters (i.e.,
flow depth, bottom slope, surface material, side slope) are to remain the same
Section 10.4.3 Uniform Depth Examples—Determine Slope
10.85 Water flows 1 m deep in a 2-m-wide finished con-crete channel Determine the slope if the flowrate is 3 m3/s
10.86 Water flows in the channel shown in Fig P10.86 at a rate of 90 ft3/s Determine the minimum slope that this channel can have so that the water does not overflow the sides The Manning
coefficient for this channel is n ! 0.014.
10.88 To prevent weeds from growing in a clean earthen-lined canal, it is recommended that the velocity be no less than 2.5 ft/s For the symmetrical canal shown in Fig P10.88, determine the minimum slope needed
10.89 The smooth, concrete-lined, symmetrical chan-nel shown in Video V10.7and Fig P10.88 carries water from the silt-laden Colorado River If the velocity must be 4.0 ft/s to pre-vent the silt from settling out (and epre-ventually clogging the chan-nel), determine the minimum slope needed
10.90 The symmetrical channel shown in Fig P10.88 is dug
in sandy loam soil with n ! 0.020 For such surface material it is
recommended that to prevent scouring of the surface the average velocity be no more than 1.75 ft/s Determine the maximum slope allowed
10.91 The depth downstream of a sluice gate in a rectangu-lar wooden channel of width 5 m is 0.60 m If the flowrate is 18
m3/s, determine the channel slope needed to maintain this depth Will the depth increase or decrease in the flow direction if the slope
is (a) 0.02; (b) 0.01?
10.92 A 50-ft-long aluminum gutter (Manning coefficient n
!0.011) on a section of a roof is to handle a flowrate of 0.15 ft3/s during a heavy rainstorm The cross section of the gutter is shown
in Fig P10.92 Determine the vertical distance that this gutter must
be pitched (i.e., the difference in elevation between the two ends
of the gutter) so that the water does not overflow the gutter As-sume uniform depth channel flow
■Figure P10.81
1 m
b
Width = 5 m
■Figure P10.84
5 ft
2 ft
10 ft
L
2 ft
■Figure P10.88
12 ft
3 ft
4 ft
60"
5 in.
c10Open-ChannelFlow.qxd 2/23/12 7:27 PM Page 597
17) Khi con kênh hình tam giác vuông như hình vẽ còn mới, nước dâng lên 2m dọc theo thành kênh Sau
một thời gian sử dụng, bề mặt đáy kênh trở nên nhám hơn và hệ số Manning tăng lên gấp đôi Hãy
tính L khi lưu lượng không đổi
18) Hãy tính độ sâu khi lưu lượng bằng 15m3/s
Trang 30.5 m 1.0 m
6 m
3 m
Concrete
19) Kênh hình thang cân, đáy nhỏ 1.5m, đáy lớn 3m, nước sâu 0.6m Người ta muốn mở rộng đáy nhỏ thêm L để có thể tăng lưu lượng gấp đôi Hãy tính L khi các yếu tố khác không đổi
20) Kênh hình tròn được làm bằng bê-tông tô có đường kính bằng 1,5m và lưu lượng bằng 2,0m3/s Độ dốc đáy kênh bằng 1/500 Hãy tính độ sâu mực nước trong kênh
21) Nếu độ sâu mực nước trong kênh tròn bằng ¾ đường kính, độ nhám Manning bằng 0,014, độ dốc đáy bằng 1/1000, lưu lượng bằng 3,0 m3/s, đường kính kênh bằng bao nhiêu?
Tính độ dốc:
22) Nước chảy trong kênh chữ nhật, sâu 1m, rộng 2m, làm bằng bê-tông tô Hãy tính độ dốc nếu lưu lượng bằng 3m3/s
23) Nước trong kênh có lưu lượng 2.4m3/s Biết hệ số Manning bằng 0.014, hãy tính độ dốc để nước không bị tràn
10.81 Water flows uniformly at a depth of 1 m in a channel that is 5 m wide as shown in Fig P10.81 Further downstream, the channel cross section changes to that of a square of width and
height b Determine the value of b if the two portions of this
chan-nel are made of the same material and are constructed with the same bottom slope
Problems 597
10.82 Determine the flow depth for the channel shown in Fig P10.60 if the flowrate is 15 m3/s
10.83 Rainwater runoff from a 200-ft by 500-ft parking lot
is to drain through a circular concrete pipe that is laid on a slope
of 3 ft/mi Determine the pipe diameter if it is to be full with a steady rainfall of 1.5 in./hr
10.84 (See Fluids in the News article titled “Plumbing the Everglades,” Section 10.4.1.) The canal shown in Fig P10.84 is to
be widened so that it can carry twice the amount of water
Deter-mine the additional width, L, required if all other parameters (i.e.,
flow depth, bottom slope, surface material, side slope) are to remain the same
Section 10.4.3 Uniform Depth Examples—Determine Slope
10.85 Water flows 1 m deep in a 2-m-wide finished con-crete channel Determine the slope if the flowrate is 3 m3/s
10.86 Water flows in the channel shown in Fig P10.86 at a rate of 90 ft3/s Determine the minimum slope that this channel can have so that the water does not overflow the sides The Manning
coefficient for this channel is n ! 0.014.
10.87 It is claimed that on steep portions of the Blue Ridge Flume (see Problem 10.54 for the flume cross section), the water would rush along at 50 mph Is this possible? If so, determine the slope;
if not, explain why not Note: Use a flowrate of 52 ft3/s, which is that obtained for the conditions (slope) of Problem 10.54
10.88 To prevent weeds from growing in a clean earthen-lined canal, it is recommended that the velocity be no less than 2.5 ft/s For the symmetrical canal shown in Fig P10.88, determine the minimum slope needed
10.89 The smooth, concrete-lined, symmetrical chan-nel shown in Video V10.7and Fig P10.88 carries water from the silt-laden Colorado River If the velocity must be 4.0 ft/s to pre-vent the silt from settling out (and epre-ventually clogging the chan-nel), determine the minimum slope needed
10.90 The symmetrical channel shown in Fig P10.88 is dug
in sandy loam soil with n ! 0.020 For such surface material it is
recommended that to prevent scouring of the surface the average velocity be no more than 1.75 ft/s Determine the maximum slope allowed
10.91 The depth downstream of a sluice gate in a rectangu-lar wooden channel of width 5 m is 0.60 m If the flowrate is 18
m3/s, determine the channel slope needed to maintain this depth Will the depth increase or decrease in the flow direction if the slope
is (a) 0.02; (b) 0.01?
10.92 A 50-ft-long aluminum gutter (Manning coefficient n
!0.011) on a section of a roof is to handle a flowrate of 0.15 ft3/s during a heavy rainstorm The cross section of the gutter is shown
in Fig P10.92 Determine the vertical distance that this gutter must
be pitched (i.e., the difference in elevation between the two ends
of the gutter) so that the water does not overflow the gutter As-sume uniform depth channel flow
■ Figure P10.81
1 m
b
Width = 5 m
■ Figure P10.84
5 ft
2 ft
10 ft
L
■ Figure P10.86
2 ft
2 ft
■ Figure P10.88
12 ft
3 ft
4 ft
■ Figure P10.92
60"
3 in.
5 in.
10.93 Water flows in a rectangular channel of width b and depth
y with a Froude number of unity The slope, S 0c, of the channel
needed to produce this critical flow is a function of y Show that
as yS the slope becomes proportional to y (i.e., S 0c !C1y,
where C1is a constant) and that as yS 0 the slope becomes
pro-portional to y#1/3(i.e., S 0c!C2/y1/3, where C2is a constant) Show
that the channel with an aspect ratio of b/y ! 6 gives the minimum value of S 0c
q
24) Để ngăn cỏ mọc trong kênh tự nhiên, đáy sạch, vận tốc nước được khuyến cáo không nên nhỏ hơn 0.75m/s Hãy tính độ dốc tối thiểu của kênh
10.81 Water flows uniformly at a depth of 1 m in a channel that is 5 m wide as shown in Fig P10.81 Further downstream, the channel cross section changes to that of a square of width and
height b Determine the value of b if the two portions of this
chan-nel are made of the same material and are constructed with the same bottom slope
Problems 597
10.82 Determine the flow depth for the channel shown in Fig P10.60 if the flowrate is 15 m3/s
10.83 Rainwater runoff from a 200-ft by 500-ft parking lot
is to drain through a circular concrete pipe that is laid on a slope
of 3 ft/mi Determine the pipe diameter if it is to be full with a steady rainfall of 1.5 in./hr
10.84 (See Fluids in the News article titled “Plumbing the Everglades,” Section 10.4.1.) The canal shown in Fig P10.84 is to
be widened so that it can carry twice the amount of water
Deter-mine the additional width, L, required if all other parameters (i.e.,
flow depth, bottom slope, surface material, side slope) are to remain the same
Section 10.4.3 Uniform Depth Examples—Determine Slope
10.85 Water flows 1 m deep in a 2-m-wide finished con-crete channel Determine the slope if the flowrate is 3 m3/s
10.86 Water flows in the channel shown in Fig P10.86 at a rate of 90 ft3/s Determine the minimum slope that this channel can have so that the water does not overflow the sides The Manning
coefficient for this channel is n ! 0.014.
10.88 To prevent weeds from growing in a clean earthen-lined canal, it is recommended that the velocity be no less than 2.5 ft/s For the symmetrical canal shown in Fig P10.88, determine the minimum slope needed
10.89 The smooth, concrete-lined, symmetrical chan-nel shown in Video V10.7and Fig P10.88 carries water from the silt-laden Colorado River If the velocity must be 4.0 ft/s to pre-vent the silt from settling out (and epre-ventually clogging the chan-nel), determine the minimum slope needed
10.90 The symmetrical channel shown in Fig P10.88 is dug
in sandy loam soil with n ! 0.020 For such surface material it is
recommended that to prevent scouring of the surface the average velocity be no more than 1.75 ft/s Determine the maximum slope allowed
10.91 The depth downstream of a sluice gate in a rectangu-lar wooden channel of width 5 m is 0.60 m If the flowrate is 18
m3/s, determine the channel slope needed to maintain this depth
Will the depth increase or decrease in the flow direction if the slope
is (a) 0.02; (b) 0.01?
10.92 A 50-ft-long aluminum gutter (Manning coefficient n
!0.011) on a section of a roof is to handle a flowrate of 0.15 ft3/s during a heavy rainstorm The cross section of the gutter is shown
in Fig P10.92 Determine the vertical distance that this gutter must
be pitched (i.e., the difference in elevation between the two ends
of the gutter) so that the water does not overflow the gutter As-sume uniform depth channel flow
■ Figure P10.81
b
Width = 5 m
■ Figure P10.84
5 ft
2 ft
10 ft
L
2 ft
■ Figure P10.88
12 ft
3 ft
4 ft
60"
5 in.
c10Open-ChannelFlow.qxd 2/23/12 7:27 PM Page 597
25) Nếu kênh trong Bài 22 có vật liệu kênh là cát với n=0.02, để tránh xói mòn đáy kênh, vận tốc nước không được quá 0.525m/s Hãy tính độ dốc tối đa cho phép của kênh