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Width, ft ■ Figure P10.43 is ft Determine the flowrate ft/mi 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 indicated 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 10.50 A trapezoidal chan and sides with a slope of : fine gravel (n ! 0.020) and is t be built with a slope of S0 ! 0.0 velocity below 0.75 m/s to p Explain Bài tập Dịng 10.51 GO Water flows in a 2Tính độ nhám Manning: Section 10.4.3 Uniform Depth Examples—Determine so that it is completely full and 1) Nước kênh có bề rộng 5m, sâuFlowrate 1m, với vận tốc nước 2m/s Kênh có độ dốc 1m/1000m the pipe If the slope is S0 ! 0.0 2/23/12 7:27 PM Page 594 10.45 A 2-m-diameter pipe made of finished concrete lies ing open-channel flow methods Hãy tính hệ số Manning kênh on a slope of 1-m elevation change per 1000-m horizontal distance tained by using pipe flow metho Tính lưu lượng: Determine the flowrate when the pipe is half full 10.52 Water flows in a w 2) Ống tròn, đường kính d=2m, có độ dốc 1m/100m, làm bê-tơng tơ Hãy tính lưu luợng nước 10.46 By what percent is the flowrate reduced in the rec- 30 m /s What flowrate can be e chảy đầy ½ ống tangular channel shown in Fig P10.46 because of the addition of and the depth remains constant? the thin center board? surfaces are nhiêu of the same 3) Khi thêm vào chắn kênh, lưu lượng tăng hayAllgiảm, bao %? material 10.53 Water flows in an unfini 10 ■ Open-Channel Flow owing data are obtained for a particular reach Utah: A ! 183 ft2, free-surface width ! 55 ft, ft, Rh ! 3.32 ft, V ! 6.56 ft/s, length of elevation drop of reach ! 1.04 ft Determine ar stress on the wetted perimeter, (b) the n, and (c) the Froude number of the flow 30 m3/s What flowrate can be e ished and the depth remains Center board /2 that logs bwould travel the length of the flume in 15 hours b/2 Provide appropriate calculations to agree with this claim? your answer 10.54 The Blue Ridge Flume, c ifornia, in 1872 to supply water built of planed wood and had Do you P10.54 Determine the water ve support it was full and the elevation cha 10.48 Water flows bin a channel as shown in Fig P10.48 The velocity is 4.0 ft/s when the channel is half full with depth ■ Figure P10.46 d Determine the velocity channel full, d 4) Nước kênh chữ nhật hình vẽ Vận tốc nướcwhen bằngthe 1.2m/s is độcompletely sâu mực nước 10.47 The great Kings River flume in Fresno County, depth 2d ticular location, the cross the CoTính vậnsection tốc khiofkênh chảy đầy kênhCalifornia, với độ sâu 2d was used from 1890 to 1923 to carry logs from an dicated in Fig P10.43 If on a day without elevation of 4500 ft where trees were cut to an elevation of 300 ft to float 0.5 mi along the river, which drops at the railhead The flume was 54 miles long, constructed of wood, e, determine the value of the Manning coefand had a V-cross section as indicated in Fig P10.47 It is claimed 2d d 48 in 16 in 10 d ■ Figure P10.54 Figure P10.48 5) Kênh hình thang có đáy rộng■3.0m, cạnh bên có độ nghiêng 2:1 (phương ngang: phương đứng) 10.55 A round concrete st trám sỏi (n=0.020) lưu lượng ft muốn vận tốc kênh nhỏ ft 10m /s Nếu fall runoff from a parking lot is 0.75m/s độ dốc kênh tối đa nhiêu?has an approximate parabolic cross sec- rainfall rate is a steady in./hr W 10.49 A naturalbao riverbed flow from 6) Nước đầy đườngtion ốngsuch trịn,that đường kính bằngwidth 2m, áp suấtft dọc depth theo ống Vớia 2-in./hr độ rainfall with 800 1200 1600 chảy2000 the free-surface is 200 when thesố center ■ Figure P10.47 ing lot? Support your answer w Width, ft is ft Determine the flowrate if n ! 0.035 and the slope is 1.5 dốc So=0.005, tính lưu lượng ft/mi.bề mặt phủ cỏ với lưu lượng 30m3/s Nếu cỏ làm độ 7) Nước chảy kênh tự nhiên, sâu mực nước không đổi, lưu lượngAmới bao nhiêu?with a bottom width of 3.0 m 10.50 trapezoidal channel ee surface of8)theKênh Columbia River in 2m/km and sides with :tính (horizontal:vertical) is nước lined with bê-tơng tơ shown có độ dốc trêna slope hình of Hãy lưu lượng mực kênh sâu t above the bottom rather than 44 ft, as is infine gravel (n ! 0.020) and is to carry 10 m /s Can this channel y=1.5m how long would it take to float the 0.5-mi Problem 10.43? Assume the elevation change be built with a slope of S0 ! 0.00010 if it is necessary to keep the m velocity below 0.75 m/s to prevent scouring of the bottom? Concrete Explain iform Depth Examples—Determine 10.51 GO Water flows in a 2-m-diameter finished concrete pipe mthe pressure is constant all along m so that it is 0.5 completely full and the pipe If the slope is S0 ! 0.005, determine the flowrate by using open-channel flow methods Compare this result with that obtained by using pipe flow methods of Chapter 1.0 m diameter pipe made of finished concrete lies vation change horizontal distance Tínhper độ1000-m sâu hay kích thước: te when the pipe is half full 10.52 flows in a lượng weedy 2m earthen channel at a kênh rate of 9) Nước kênh chữ nhật, làm bê Water tơng tơ, có lưu /s Độ dốc đáy 0.001 30 m /s What flowrate can be expected if the weeds are removed t percent is the flowrate in thekênh, rec- độ sâu mực nước chiều rộng Hãy tínhreduced chiều rộng and the cũ depth constant? wn in Fig P10.46 becauseống of the addition of bê 10) Đường trịn, làm tơng có remains đường kính 2.0m với hệ số Manning 0.025 ? All surfaces arelưu of the same material 10.53 ½Water in anbằng unfinished concrete channel a rate of 0.012, lượng 5.0m /s chảy ống flows Nếu thay đường ống cóat độ nhám /s What flowrate can be expected if the concrete were fin30 m chảy ½ ống với lưu lượng, tính đường kính ống nter board ished and the depth remains constant? 10.54 The Blue Ridge Flume, constructed in Shasta County, California, 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 bled Determine the new va 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 2/23/12 7:27 PM Page 597 width is laid on a slope of ft/mi Determine the flow depth and đường kính 0.5m hợpif vào đường Froude number of the flow the flowrate is 400ống ft3/s.có đường kính c10Open-ChannelFlow.qxd 11) Bốn đường ống nước thải với D Nếu hệ số Manning, độ dốc ống nhau, nước chảy đầy ½ ống, tính D 10.72 An engineer is to design a channel lined with planed 12) Kênh có bề mặt làm đất sét wood (n=0.025) Lưuoflượng xói mịn on a slope/s.ofĐể 10 tránh m/ to carry water at hình a flowrate m3/sQ=8.1m thành đáy kênh, vận tốc nước không 1.5m/s Hãycan tính rộng đáy kênh,orb,a độ dốc 800 m The channel cross section be bề either a 90" triangle rectangle with a cross section twice as wide as its depth Which ■ Figure P10.78 đáy kênh 2m would require less wood and by what percent? 10.73 A circular finished concrete culvert is to carry a discharge Water flows in a ch of 50 ft310.81 /s on a slope of 0.0010 It is to flow not more than half 10.79 Water 10.88 as shown To in prevent w ft flows uniformly at a depth of m in a channel section Fig P1 full Thethat culvert pipes available from the manufacturer with di-the lined canal, it is recommen is m wideare as shown in Fig P10.81 Further downstream, 45° 30° n, and channel slope, determ ameters channel that are cross multiples of changes ft Determine smallest section to that ofthe a square of suitable width and ft/s For the symmetrical c culvert diameter height b Determine the value of b if the two portions of this chan- flowrate the minimum slope needed b same material and are constructed with the nel are made of the 10.74 same At what depth will 50 ft3/s of water flow in a 6-ftbottom slope rectangular channel with rubble on a slope 13) Kênh chữ nhật làm bê tông wide trát vữa có chiều rộnglined 8.4m vàmasonry độ dốcset 8/1000 Hãy of ft in3 500 ft? Is a hydraulic jump possible under these condivà số Froude lưu lượng bằngtions? 10.8m /s Explain tính độ sâu m lưu lượng 2m /s độ dốc 10m/800m Mặt 14) Một kỹ sư thiết kế kênh làm gỗ bào nhẵn1 với cắt h b 10.75 The rectangular canal shown in Fig P10.75 changes kênh tam giác vng hình chữ nhật với bề rộng lần độ sâu Phương án tốn y to a round pipe of diameter D as it passes through a tunnel in a gỗ hơn, %? mountain Determine D if the surface material and slope remain Width =5m ■ Figure P10.88 the same and the round pipecó is to flow completely full 15) Kênh có mặt cắt hình chữ nhật đổi■thành hình trịn đường kính D qua hầm xuyên núi Figure P10.81 ■ Figure P10.79 Tính đường kính D, vật liệu làm kênh độ dốc không đổi, nước chảy đầy ống ft 10.82 Determine the flow depth for the channel shown in Fig P10.60 if the flowrate is 15 m3/s 10.89 The smo nel shown in Video V10.7 silt-laden Colorado River 10.83 Rainwater runoff from a 200-ft by 500-ft parking lot 10.80 Two canals joi b vent the silt from settling is to drain through a circular concrete pipe that is laid on a slope Video V10.6 and Fig P10 nel), determine the minimu of ft/mi Determine the pipe diameter if it is to be full with a is lined with the same mate D 1.5 in./hr steady rainfall of 10.90 water depth in The eachsymmetri is to be in sandy loam with n ! 10.84 (See Fluids in the News article titled “Plumbing the canal, b Explainsoil physically b thatthe to preve Everglades,” Section 10.4.1.) The canal shown in Fig P10.84 is to it recommended is expected that wid velocity be no more than be widened so that it can carry twice the amount of water Deter- combined widths of the tw mine the additional width, L, required if all other parameters (i.e., ! allowed 12 m) Figure 16) Lưu lượng kênh hình thang■như hình vẽ Q Nếuslope, muốnsurface tăng material, lưu lượng gấpaređôito mà10.91 không The depth dow flowP10.75 depth, bottom sidelên slope) remain the thay đổi độ sâu, tính bề rộng L cần thêm, biếtsame độ dốc, vật liệu kênh không đổi lar wooden channel of wid m3/s, determine the channe 10 ft Will the depth increase or d 10.76 An 8-ft-diameter concrete drainage pipe that flows is (a)Q0.02; 8(b) m 0.01? half full is to be replaced by a concrete-lined V-shaped open chan2 ft nel having an interior angle of 90" Determine the depth of fluid L channel if it is laid on the same slope ftV-shaped that will exist in the and carries the same discharge as the drainage pipe ■ Figure P10.84 10.92 A 50-ft-long a ! 0.011) on a section of a during a heavy rainstorm T 4m in Fig P10.92 Determine t Q 10.77 flows in the symmetrical, unfinished trape17) Khi kênh hình tam giác vng nhưWater hình vẽ10.4.3 cịn mới, nướcDepth dâng lên 2m concrete dọc theo thành kênh Sau be pitched (i.e., the differe Section Uniform Examples—Determine shown in Fig P10.77 at số a rate of 120 ft3tăng /s Thelên slope of the gutter) so that the w thời gian sử dụng, bề mặt đáyzoidal kênhchannel trở nên nhám hệ Manning gấp đôi Hãy Slope is 4.2 ft/2000 ft Determine the number of cubic yards of concrete sume uniform depth chann tính L lưu lượng khơng đổi needed to 10.85 1m deep in a 2-m-wide finished con- ■ Figure P10.80 line each Water 1000 ftflows of the channel crete channel Determine the slope if the flowrate is m /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 in ft 18) Hãy tính độ sâu lưu lượng 15m3/s ft ■ Figure P10.86 in ■ Figure P10.92 10.93 Water flows in a rec y with a Froude number o needed to produce this crit 10.82 Determine the flow depth for the channel shown in Fig P10.60 if the flowrate is 15 m3/s 10.89 The smooth, co nel shown in Video V10.7 and Fi silt-laden Colorado River If the vent the silt from settling out (an nel), determine the minimum slop 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 ft/mi Determine the pipe diameter if it is to be full with a steady rainfall of 1.5 in./hr 1.0 m 10.84 (See Fluids in the News article titled “Plumbing the Everglades,” Section m 10.4.1.) The canal shown in Fig P10.84 is to be widened so that it can carry twice the amount of water DeterConcrete 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 3m 0.5 m 10 ft 10.90 The symmetrical cha in sandy loam soil with n ! 0.02 recommended that to prevent sco velocity be no more than 1.75 ft/s allowed 10.91 The depth downstrea lar wooden channel of width m m3/s, determine the channel slop Will the depth increase or decreas is (a) 0.02; (b) 0.01? rộng đáy nhỏ 19) Kênh hình thang cân, đáy nhỏ 1.5m, đáy lớn ft3m, nước sâu 0.6m Người ta muốn mở 10.92 A 50-ft-long aluminu thêm L để tăng lưu lượng gấp đơi Hãy tính L yếu tố khác không đổi L ft ! 0.011) on a section of a roof is 20) Kênh hình trịn làm bê-tơng tơ cóP10.84 đường kính 1,5m lưu lượng 2,0m Độ rainstorm The cro during a/s heavy ■ Figure in Fig P10.92 Determine the vert dốc đáy kênh 1/500 Hãy tính độ sâu mực nước kênh be pitched (i.e., the difference in Section 10.4.3 Uniform Depth 21) Nếu độ sâu mực nước kênh trịn ¾ đường kính, độ Examples—Determine nhám Manning 0,014, độ dốc of the gutter) so that the water d Slope đáy 1/1000, lưu lượng 3,0 m /s, đường kính kênh bao nhiêu? sume uniform depth channel flow 10.85 Water flows m deep in a 2-m-wide finished conTính độ dốc: crete channel Determine the slope if the flowrate is m /s 22) Nước chảy kênh chữ nhật, sâu 1m, rộng 2m, làm bê-tơng tơ Hãy tính độ dốc lưu 10.86 Water flows in the channel shown in Fig P10.86 at a lượng 3m3/s rate of 90 ft3/s Determine the minimum slope that this channel can 23) Nước kênh có lưu lượng 2.4mhave /s.soBiết Manning 0.014, độ dốc để nước that hệ the số water does not overflow the sides Thetính Manning coefficient for this channel is n ! 0.014 không bị tràn .qxd 2/23/12 7:27 PM Page 597 in ft ft Problems 597 Water flows uniformly at a depth of m in a channel 10.88 To prevent weeds from growing in a clean earthen5 m wide as shown in Fig P10.81 Further downstream, the lined canal, it is recommended that the velocity be no less than 2.5 l cross section changes to that of a square of width and ft/s For the symmetrical canal shown in Fig P10.88, determine 24) Đểofngăn kênh tự nhiên, đáy sạch, vận tốc nước khuyến cáo không ■ Figure P10.86 b Determine the value b if thecỏ twomọc portions of this chanthe minimum slope needed made of the same 0.75m/s material andHãy are constructed withtối thethiểu kênh tính độ dốc ottom slope 10.87 It is claimed that on steep portions of the Blue Ridge Flume 12 ft (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.3 ftNote: Use a flowrate of 52 ft3/s, which is 1m b that obtained for the conditions (slope) of Problem 10.54 in ■ Figure P10.92 10.93 Water flows in a rectangu nên nhỏa y with Froude number of unity needed to produce this critical fl as y S q the slope becomes pr where C1 is a constant) and that a portional to y#1/3 (i.e., S0c ! C2/y1 that the channel with an aspect rat value of S0c ft 5m ure P10.81 25) Nếu kênh Bài 22 có vật liệu kênh làP10.88 cát với n=0.02, để tránh xói mịn đáy kênh, vận tốc nước ■ Figure không 0.525m/s Hãy tính độ dốc tối đa cho phép kênh Determine the flow depth for the channel shown in 10.60 if the flowrate is 15 m3/s Rainwater runoff from a 200-ft by 500-ft parking lot ain through a circular concrete pipe that is laid on a slope /mi Determine the pipe diameter if it is to be full with a rainfall of 1.5 in./hr (See Fluids in the News article titled “Plumbing the ades,” Section 10.4.1.) The canal shown in Fig P10.84 is to ened so that it can carry twice the amount of water Deterhe additional width, L, required if all other parameters (i.e., epth, bottom slope, surface material, side slope) are to the same 10 ft ft ft L ure P10.84 n 10.4.3 Uniform Depth Examples—Determine 10.89 The smooth, concrete-lined, symmetrical channel shown in Video V10.7 and Fig P10.88 carries water from the silt-laden Colorado River If the velocity must be 4.0 ft/s to prevent the silt from settling out (and eventually clogging the channel), 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 rectangular wooden channel of width 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