Permeable dike fields are built from rows of timber piles. They do not block the flow,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Permeable dike fields are built from rows of timber piles. They do not block the flow, but rather slow it down due to the extra drag. They are often used in rivers to provide bank protection, and/or to improve river navigability. An example of a dike field on the upper Mississippi River is provided in the attached photograph. To analyze the effect of permeable dikes, we consider an idealized case. The channel is taken to be straight and rectangular (trapezoidal with m = 0). Dike fields are provided along either bank, as illustrated. D=dike zone central zone C DI C D T plan 7 Part 3 (Normal depth: permeable dikes) D+D = control volume for dike region ca control volume for center regions. = Jel Dikes are now placed in the channel as illustrated. Each row of dikes is constructed from N piles, each with diameter dp, such that one half of the piles are lined on one side of the channel and one-half on the other side. The lateral length of each dike (including both sides) is L. The spacing between the rows is Ad. Channel depth y and slope S are taken to be the same in both the central and dike zones. S takes the same value as it did in the absence of dikes; y may change. The values of A, P, and R in the central and dike zones are seen to be A₁ = y(b-L); Pc = b-L; A₁ = yL; P = L + 2y; d терела Re R₁ = y Rd = yL/(L+2y) Momentum balance is performed on the indicated control volumes of the above figure, yielding the following force balances: (Central zone) a = pgA S Ad Here [a] = resistive force due to boundary (bed and/or bank) friction, and [b] = downstream impelling force of gravity. (Dike zone, both sides lumped) TaPad + Drag + Drag = pgAS d b с (4a) (4b) Drag = p ₁ VA₂ P CD Ap where CD is the drag coefficient for cylinders and (5) Here [a] and [b] have their previous meanings, and [c] = Drag = the drag force on a single row of dikes, as obtained from the following formula: (7a) A₂ = Ny dp P (6) (7b) denotes the projected area normal to the flow of the piles in the row. Here N = the number of piles in one row (both sides of the channel), and d, denotes pile diameter. Water conservation requires that the following equation hold: to F VaA + V₁A = Q (8) Show that equations (5), (6), and (8) reduce with the aid of (1) and (7) 28 v² = 12 R²/³ S n v² = [R²/³ 51/[1 + 1/ n = CDN where denotes water discharge. 22 ngad Q/[V (b-L) + V₂L] FR/3 Pa d (8) (9). (10) Permeable dike fields are built from rows of timber piles. They do not block the flow, but rather slow it down due to the extra drag. They are often used in rivers to provide bank protection, and/or to improve river navigability. An example of a dike field on the upper Mississippi River is provided in the attached photograph. To analyze the effect of permeable dikes, we consider an idealized case. The channel is taken to be straight and rectangular (trapezoidal with m = 0). Dike fields are provided along either bank, as illustrated. D=dike zone central zone C DI C D T plan 7 Part 3 (Normal depth: permeable dikes) D+D = control volume for dike region ca control volume for center regions. = Jel Dikes are now placed in the channel as illustrated. Each row of dikes is constructed from N piles, each with diameter dp, such that one half of the piles are lined on one side of the channel and one-half on the other side. The lateral length of each dike (including both sides) is L. The spacing between the rows is Ad. Channel depth y and slope S are taken to be the same in both the central and dike zones. S takes the same value as it did in the absence of dikes; y may change. The values of A, P, and R in the central and dike zones are seen to be A₁ = y(b-L); Pc = b-L; A₁ = yL; P = L + 2y; d терела Re R₁ = y Rd = yL/(L+2y) Momentum balance is performed on the indicated control volumes of the above figure, yielding the following force balances: (Central zone) a = pgA S Ad Here [a] = resistive force due to boundary (bed and/or bank) friction, and [b] = downstream impelling force of gravity. (Dike zone, both sides lumped) TaPad + Drag + Drag = pgAS d b с (4a) (4b) Drag = p ₁ VA₂ P CD Ap where CD is the drag coefficient for cylinders and (5) Here [a] and [b] have their previous meanings, and [c] = Drag = the drag force on a single row of dikes, as obtained from the following formula: (7a) A₂ = Ny dp P (6) (7b) denotes the projected area normal to the flow of the piles in the row. Here N = the number of piles in one row (both sides of the channel), and d, denotes pile diameter. Water conservation requires that the following equation hold: to F VaA + V₁A = Q (8) Show that equations (5), (6), and (8) reduce with the aid of (1) and (7) 28 v² = 12 R²/³ S n v² = [R²/³ 51/[1 + 1/ n = CDN where denotes water discharge. 22 ngad Q/[V (b-L) + V₂L] FR/3 Pa d (8) (9). (10)
Expert Answer:
Answer rating: 100% (QA)
Answer Ans Here first they use the mathematical formulas related to cross secti... View the full answer
Related Book For
Foundations of Financial Management
ISBN: 978-1259024979
10th Canadian edition
Authors: Stanley Block, Geoffrey Hirt, Bartley Danielsen, Doug Short, Michael Perretta
Posted Date:
Students also viewed these accounting questions
-
A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on the side opposite the river costs $20 per foot, and the fence on the...
-
A trapezoidal channel lined with concrete is required to carry 342 cfs. The channel will have a bottom slope of So = 0.001 and side slopes of m = 1.5. Design (size) the channel using the best...
-
A rectangular channel has b = 3 m and y = 1 m. If n and So are the same, what is the diameter of a semicircular channel which will have the same discharge? Compare the two wetted perimeters.
-
In a small university, the Computer Science Department has six faculty members. However, each faculty member belongs to only the computer science department. This type of relationship is called a....
-
Under Sarbanes- Oxley and PCAOB rules, ensuring that the auditor is independent in appear-ance is the responsibility of a. The public accounting firm. b. Senior management. c. The audit committee. d....
-
A regular room and pillar method is used in a hard rock leadzinc mine. The ore horizon is at a depth of 360 m where the overburden averages 25.2kN/m3. Laboratory tests on core samples (L/D = 2) show...
-
An effective way to learn how companies respond to the competing pressures to be globally integrated and locally responsive is to study them in action. Referring back to Exhibit 6.3, search online...
-
The Broughton Cap Company requires that prenumbered receiving reports be completed when purchased inventory items arrive in the receiving department. At the time of receipt, the receiving clerk...
-
Following are the ledger balances of Titas Pvt. Ltd. as on the date 31 December, 2022. Prepare the Trial Balance using the following balances. Account Name Tk. Bank Overdraft 40,000 Cash 20,000...
-
Public companies are required to file restated financial statements with the SEC when they discover after the audited financial statements have been issued that the financial statements are...
-
The Parent acquired 60% of the sub on Jan 1, paying $480,000. The above balance sheets are for the parent and sub at the date of acquisition. At the time of acquisition, any differential was...
-
Nonfinancial has a greater profit than financial. Manufacturing has the greatest profit with retail trade in second place and transportation and warehousing in last. Durable goods has a greater...
-
Function 1: Password Checker function _one (pwd) Create a JavaScript function that meets the following requirements: Is passed a string representing a potential password The function determines if...
-
Given the function f(x) = 7x + 10 x < 0 7x+20 x > 0 Calculate the following values: f(-1) = f(0) = f(2) =
-
Julie Smith is the principal of Frederick High School in Winchester, VA. During the first full week of fall-semester, the Frederick County Sheriffs Department conducts an Active Shooter Emergency...
-
What was Thomas Malthuss theory? what it has impact on growth ?
-
In a cross-section given below, Manning's roughness coefficients are 70 (ki), 40 (k2), 30 (k3), and 20 (k4), respectively, and hydraulic slope is 0.0001. Calculate the water depths for the first and...
-
Prove that if Σ an is absolutely convergent, then a. an
-
A $1,000 par value bond was issued 15 years ago at a 14 percent coupon rate, paid semiannually. It currently has 10 years remaining to maturity. Interest rates on similar debt obligations are now 8...
-
The Ace Battery Company has forecast its sales in units as follows: Ace always keeps an ending inventory equal to 120 percent of the next month's expected sales. The ending inventory for December...
-
For Russell Container Company, described in the previous problem, assume the yield on the bonds goes up by one percentage point and that the tax rate is now 34 percent. a. What is the new aftertax...
-
On September 29, 2008, the stock market fell almost 7%. How can we reconcile these kinds of huge losses in the stock market with the efficient market hypothesis?
-
In 2018, Germany had the worlds largest current account surplus of US$291 billion. Using this one piece of information, answer the following questions. a. Which was greater, the income Germans earned...
-
In the first quarter of 2019, the output gap in the United States was 0.8%. Make a prediction about what you think the output gap will be in the second quarter of 2019. Explain your reasoning.
Study smarter with the SolutionInn App