Most efficient trapezoidal channel is half of. The lining of the channel is to be float-finished concrete.

Most efficient trapezoidal channel is half of It is the equation beginning with V= above. 5 carries the water at 15 m/s with the velocity of 1 m/s. The channel has a trapezoidal section with bottom slope S0 =0. Example: A trapezoidal channel having side slope (1:1) it is required to discharge 13. The most efficient section must have a minimum wetted perimeter and hence minimum resistance to flow. 0004, which is made in the shape of a half- hexagon for maximum efficiency. 015. For most efficient trapezoidal channel section with fixed side slope having depth of flow=y and fixed side slope 1:m all the condition should be satisfied. If this channel is unlined and the value of C=44 and when this channel is lined with concrete the value C=60. Dec 17, 2024 · Final Answer The most economical section in open channel flow is the one that minimizes the wetted perimeter for a given discharge and area, effectively maximizing the hydraulic radius (A/P). If the flume is constructed of corrugated Open channels may be either natural channels or man-made channels. Examples of applying the Manning's equation to calculate flow rate and velocity are shown. For rigid boundary channels, the most common design approach is to use Manning's equation to select dimensions that produce non-silting, non-scouring velocities. The document discusses determining the most hydraulically efficient cross-sectional shape for open channel flow. For the case of most efficient cross section, determine the bottom width of the channel if the available vertical drop is 10 ft/mile. Rectangular, trapezoidal, triangular, and flexible sheet channels are analyzed. are artificial channels. Nov 15, 2022 · A channel is said to be the most economical section when, it gives maximum discharge for a given area and slope. 5 m3/s of flow. However, given the multiple choice options, an approximate solution is sufficient. We need to use the general formula A = (b + zy)y = (b + y)y = 50 m². 0135. Using this, and an approximation for area and hydraulic radius, we can estimate the discharge. Determine ) the diameter of channel, using Manning’s Q6) Using equations prove that hydraulic radius of most economical trapezoidal section is equal to half of its water depth. Keep reading Aug 12, 2016 · The most economical section of a trapezoidal channel is one which has hydraulic mean depth equal to half the depth of flow. The half-square shape is found to be most efficient for triangular channels. Design the most economical trapezoidal section to carry 35 m3 /s on a slope of 1 in 5000. 5 m3/s. 00033, a bottom width of 4. The document discusses different channel sections including rectangular, trapezoidal and triangular sections. 3) The most economical section of a triangular channel is one which has its sloping sides an (a) Prove that the most efficient cross section for triangle is half of square channel. Feb 3, 2021 · Hydraulic design engineers can use this paper to determine the most hydraulically efficient trapezoidal open channel section. Sep 1, 2012 · For a flow equation, e. 2) For a rectangular channel with a flow area of 10 m^2, the optimal dimensions are a depth (d) of 2. The lining of the channel is to be float-finished concrete. It emphasizes the importance of minimizing the wetted perimeter to optimize flow conditions and reduce construction costs, while outlining key hydraulic principles and equations, such as the Chezy and Manning equations. 5 m/s of flow. The design of a channel involves the selection of channel alignment, shape, size, and bottom slope and whether the channel should be lined to reduce seepage and/or to prevent the erosion of channel sides and bottom. It is required to carry discharge of 15cumec with a slope of 1in 1500. , P/h) for (i) a triangular section, and (ii) a trapezoidal section, respectively? Question: Please proof that the most efficient hydraulic channel section for the trapezoidal shape is half hexagon. 0 m and a water discharge of 39 m3/s. Best Hydraulic Cross Section Explained Open channel flow refers to the flow of water in a natural or artificial channel with a free water surface, such as rivers, streams, or drainage channels. For example, canals, flumes, culverts etc. To find the bottom width of the most hydraulically efficient trapezoidal channel section, you can use the Manning's equation for open channel flow. 05m) A circular channel conveys 3. e R= y/2 2) The most economical section of a trapezoidal channel is one which has hydraulic mean depth equal to half the depth of flow. Most Economical Circular Section: That for a most economical sections the discharge, for a constant cross-sectional area, slope of bed and resistance co-efficient, is maximum. Jan 9, 2025 · For a most efficient trapezoidal channel (half-hexagon), the hydraulic mean depth (m) is equal to y/2, where y is the depth of flow. It describes the key steps in designing trapezoidal channels including determining depth, bed width, side slopes, and longitudinal slope. 020 is needed to convey 12. The discharge through the channel will be m³/s. The most efficient trapezoidal channel has a half-hexagon shape. There are 2 steps to solve this one. 8m3s and is designed to flow in a trapezoidal Jun 27, 2022 · Which of the following statements are true/false related to most economical trapezoidal channel? Statements: 1 : The most efficient section for a trapezoidal channel is a half-hexagon in the form of a trapezoid. All water ways formed by natural causes are natural channels. Channels constructed for various purposes are artificial channels. It includes numerical and theory of best side slope for trapezoidal section To show that the most efficient section in a trapezoidal section is one half of a hexagon, we need to compare the hydraulic radius of both shapes. Determine the most effective size of the channel if the side slope is restricted to 3 (horizontal) : 1 (vertical). Please proof that the most efficient hydraulic channel section for the trapezoidal shape is half hexagon. Design the section if n=0. Since the side slopes are 45 degrees, the trapezoid is half a regular hexagon. This document discusses the design of open channel sections to convey water flow in the most economical way. Natural channels are of irregular shape, varying from approximately parabolic to approximately trapezoidal (Chow, 1959). B= 1. Compute: i. This is also called the most efficient cross section. The exact solution requires iterative methods or more advanced hydraulics equations. 24 m and a width (b) of 4. Trapezoidal Channel Geometry: We need to express the area and wetted perimeter of the trapezoid in terms of its dimensions. The most efficient channel section depends on various factors including the hydraulic conditions, available space, and construction constraints. Civil Engineering Objective type Questions and Answers. The rectangle, trapezoid, triangle and circle are some of the commonly used shapes in made channels. 013. Find the dimension of the most economical section Determine the side slope of the most hydraulically efficient triangular section. Question: (a) Prove that the most efficient cross section for triangular channel is half of a square. Wetted perimeter for the most economical section. 60 ft. xy 6-sin sin (a) Not the question you’re looking for? 1. Assume side slopes to be 2 H: 1 V and 𝑛 Aug 2, 2025 · A hydraulically most efficient trapezoidal channel section carries water at the optimal depth of 0. Empirical formulas for determining coefficients in the open channel flow equations are presented. 0. Feb 21, 2017 · ? = 2? ? = 𝑑 2 Minimum seepage of Trapezoidal Channel: ? = 4𝑑𝑡?? ɵ 2 Trapezoidal channel will be most economical when either: 1. Helpful Not Helpful Explain Simplify . using Manning's/Chezy's formula. A nomogram and a set of curves, developed from the Manning formula, are provided to facilitate the determination of channel dimensions. Conclusion After comparing the given options, it can be concluded that a half hexagon in the form of a trapezoid (option A) is the most efficient channel section. The canal is lined for which the value of frictional coefficient in Manning’s formula is n=0. e. Calculate the dimensions of the most efficient section if the channel is (a) triangular, (b) rectangular and (c) trapezoidal (2 H: 1 V). - Download as a PDF or view online for free #mosteconomicalchannel #trapezodialchannel #openchannelflowcondition for most economical trapezoidal channel is educational video for better understanding of Introduction Many natural and man-made channels are approximately trapezoidal. Sep 29, 2020 · This video lecture discusses the solution of numerical based on the most economical channel section (Rectangular and Trapezoidal 1. Mar 21, 2025 · When discussing most efficient section of flow into open channels, what is the perimeter P as a proportion of depth of flow h (i. Question: a) A concrete lined channel has a slope of 0. Design the most b) The channel above has to go through a rectangular culvert under a road, also with slope 0. The cost per cubic meter of excavation is four times the cost per square meter of lining. 2m per kilometre. , 60°): Simplified Efficiency Formula For the most efficient trapezoidal section (half-hexagon), the relationships can be expressed in simplified form: ANS: D - half hexagon in the form of trapezoid. The hydraulic radius is a measure of the efficiency of a channel in carrying flow. , m = d/2 The three sides of the trapezoidal section are the tangential to the semi-circle described on the water-line. Aug 18, 2020 · #MostEconomicalSection #MostEconomicalTrapezoidalChannelSection #OpenChannelFlowMost Economical Section of the channel | most economical Trapezoidal channel An irrigation canal of trapezoidal section having side slope 2 in 3 is to carry a flow of 10m3/s on longitudinal slope of 1 in 5000. The Manning equation is best used for uniform steady state flows. Manning, the channel section contains two variables (rectangular and triangular sections) or three variables (trapezoidal and round-bottom triangular sections). A trapezoidal canal section, characterized by its trapezoidal shape, allows for controlled flow and effective sediment transport. 020 and bed slope S=0. The most economical section (also called the best section or most efficient section) is one that gives the maximum discharge for a given amount of excavation. This configuration minimizes the wetted perimeter for a given area, thus minimizing frictional losses and maximizing discharge. The key concept here is hydraulic efficiency, which is directly related to minimizing the wetted Semi-circular open channel will discharge more water than any other shape (assuming that the area, slope and surface roughness are the same). If the flume is constructed of corrugated metal, what should be its dimensions to minimize the Design the most efficient (straight) lined trapezoidal channel to carry 30 m 3 / s on a longitudinal slope of 0. You will also learn about the most efficient cross-sections of open channels. Discharge, Q = A 1 n R 2 3 S 1 2 Discharge is maximum when Hydraulic radius (R) is maximum and wetted perimeter is minimum R = A P A section of a channel is said to Determine the normal depth, bed width and side slopes of a most efficient trapezoidal section to carry a discharge of 25 m³/s. A trapezoidal channel has side slope of 1:1. Provides an optimal balance between flow efficiency, stability of slopes, and ease of construction. The channel has a trapezoidal section with bottom slope S. Jan 6, 2025 · Explanation: The length of the channel boundary (sides and the base of the channel) which comes in contact with the flowing liquid is called the wetted perimeter. Thus a circle with centre $O$ and radius equal to the depth of flow will be tangential to the three sides of a most economical trapezoidal section; this condition stipulates that the most economical section of a trapezoidal channel will be a half-hexagon. Additionally, it provides specific GATE ACADEMY Global is an initiative by us to provide a separate channel for all our technical content using "ENGLISH" as a primary language of communication Question: a) Prove that the most efficient section or the best hydraulic section for a trapezoidal channel is determined when the top water width ( T ) is twice the side length (w) and is half of a hexagon with a side slope of 60° and z is 132 on both sides. Compared to other cross-sections, the semicircular section has the lowest wetted perimeter, and is, therefore, the section of the Even when the channel cross-sectional is trapezoidal, it is still important to de-termine the most economical trapezium, that is, the one giving the maximum discharge for a given amount of excavation, based on dimensions' characteris-tics and side slopes. For the most efficient trapezoidal section, the area is given by A = 2y²√2. (a) Prove that the most efficient cross section for triangular channel is half of a square. (Ans. The total cost of excavation for this Question: Please proof that the most efficient hydraulic channel section for the trapezoidal shape is half hexagon. This shape optimizes the flow by reducing resistance. 3) For a trapezoidal channel with a flow area of 14 m^2 and side slopes of 30°, the The document discusses the design and characteristics of open channels, focusing on rectangular and trapezoidal sections for uniform flow. It provides examples and solutions for calculating discharge and dimensions for channels with different cross-sections given parameters like slope, depth of flow, Manning's n etc. Mar 8, 2019 · most economical trapezoidal channel section || fluid mechanics || h&hm e Tution 44K subscribers Subscribed Take the value of Chery's constant as 70. For what length of L will the channel carry 7. Most economical section is also called the best section or most efficient section as the discharge, passing through a most economical section of channel for a given cross- sectional area A, slope of the bed S and a resistance coefficient, is maximum. 2. Canals excavated in earth must have a trapezoidal shape with slopes less than the angle of repose of the saturated bank material. g. 001 ft/ft. For trapezoidal channels, the most efficient shape is a half hexagon with the inscribed circle tangent to the sides. If you're curious about what's open channel flow or which is the most efficient cross-section for open channels, is it rectangular? or maybe trapezoidal? Then we recommend reading the text below to learn about this. The longitudinal slope of the channel is to be 0. It also provides equations to define the geometric A trapezoidal channel of most efficient section has side slopes of 1:1. A trapezoidal channel has Manning’s n=0. Overall, circular channels often showcase the highest efficiency when under optimal conditions. Question: Show that hydraulically most efficient trapezoidal section is half of a regular hexagon and its hydraulic radius is equal to half the depth of flow. This open channel flow calculator will help you find water flow velocity and volumetric flow rate through an open channel, given the channel's roughness coefficient, slope, and cross-sectional area. 5 m3/s of water. (b) A concrete-lined irrigation channel with Manning's n = 0. 1) The most efficient channel cross section is the one that maximizes the hydraulic radius (R), which occurs when the depth of flow (d) is half the width of the wetted perimeter. [3 marks) b. The concept of the most economical channel section is explained for rectangular and trapezoidal channel shapes. 2 m'/sec. For a 1:1 side slope (z=1), the relationship between the bottom width (b) and the depth (y) is: A trapezoidal channel has side slopes of 3 horizontal to 4 vertical and the slope of its bed is 1 in 2000. Semi-circular shape/circular shape are practical for concrete and steel pipes. 25 cumecs of water when 3⁄4 of vertical diameter is immersed. The channel is to be the most efficient one find whether the Aug 1, 2014 · Froehlich [9] determined cross-sectional dimensions of the most hydraulically efficient lined channels based on an analysis of a generalized trapezoidal shape that reduces to two standard sections with rounded bottom vertices as well as to the commonly used trapezoidal section with sharp bottom vertices. Jan 14, 2017 · “A trapezoidal section channel is most economical if when a semi-circle is drawn with its center, O, on the water surface and radius equal to the depth of flow, D, the three MOST ECONOMICAL RECTANGULAR AND TRAPEZOIDAL CHANNEL SECTIONS - OPEN CHANNEL FLOW The Classroom 914 subscribers Subscribed Explanation: The most efficient trapezoidal channel section is a half-hexagon (side slope of 1). For Chapter 2 Q2. Explanation: The most economical or most efficient or best section of the channel : A channel is said to be economical when it can pass a maximum discharge for a given cross-sectional area, resistance coefficient, and bottom slope. It shows that: 1) The most hydraulically efficient trapezoidal channel cross-section is half of a regular hexagon, with a side slope of 1/√3. The highest component of total construction cost is of lining & if the perimeter is kept minimum the cost of lining will be minimum, hence it will be the most economical section. 75 m3/sec of water with a bed slope (1 to 1000). Dec 16, 2022 · The calculations are done employing Manning's equation for flow in open channels. 014) is to be built to discharge water uniformly at a rate 200 ft/s. It examines rectangular, trapezoidal, triangular, and circular channel cross-sections. For trapezoidal channels, the most economical section is when the side slopes are at an angle of Mar 5, 2022 · Correct Answer - Option 2 : Half hexagon in the form of a trapezoid Explanation: A section is said to be most efficient, if, for a given cross-section area, the discharge carrying capacity is maximum. A rectangular flume is to be built to carry a discharge of 120 cfs on a slope of 0. Step 2: Apply Chezy's Equation to find the velocity The base of the most economical trapezoidal channel section is 6m and the side slope is 1H:2V, calculate the maximum discharge through the channel if the bed slope is 1 in 1000 and C = 50. . Manning coefficient is 0. Show also that if the side slopes can be varied the most efficient of all trapezoidal sections is a half-hexagon. Show that the most efficient trapezoidal channel section will have a hydraulic radius equal to one-half the depth. Rectangular, trapezoidal and circular sections are the usually adopted sections for channels. 6. If you understand this tutorial you don't need to search for any tutorial about the most efficient trapezoidal section or best trapezoidal hydraulic section Most Economical Trapezoidal channel Step 3: Deduce the Most Efficient Shape Based on the above comparison, the half hexagon (trapezoid) shape generally provides the highest hydraulic radius for a given cross-sectional area. 008 and a Mannings n efficient trapezoidal channel to carry a flow of 5. But in case of circular channels, the area of flow cannot be maintained constant. Trapezoidal Section For a trapezoidal channel with bottom width b, top width B, depth d, and side slope angle θ:= For a trapezoid with specific side slopes (e. May 16, 2021 · 2. ) HINTS: Q = 14864 Rasi for English units The most efficient trapezoidal section is equal to half of a regular hexagon The document discusses different channel cross-section shapes (rectangular, trapezoidal, triangular, and circular) and the conditions needed for each shape to be hydraulically efficient. [15 Marks APPENDIX 3 B Rectangle Trapezoid Circular (6-sing) A by P b+2y 6+21+ 24 B b b + 2xy sin R sin 5+2y (6 + x) b+ 2yx1 + x2 у D m 5+2. The exact shape depends on the channel type, but generally approaches a half-hexagon for trapezoidal channels and a half-circle for circular channels. In this calculator, you will learn how Manning's equation works and how to use it to determine water flow. 008 and Mannngs n = 0. 0015. 3K subscribers Subscribed The most efficient channel section, is semi-circular rectangular triangular half hexagon in the form of trapezoid. Apr 11, 2018 · Most economical trapezoidal channel Pavika fluid says Tawi 83. Determine the optimum dimensions of the channel if it is to carry water at 0. The width of the channel bottom, b = 6 m, and the side slope is 45°. For rectangular channels, the most economical section is when the base width is twice the flow depth. The channel has a trapezoidal section with bottom slope So = 0. Most of the man made (artificial) channels are prismatic channels over long stretches. . Jul 19, 2025 · The best trapezoidal channel section maximizes hydraulic efficiency by minimizing the wetted perimeter for a given area. The document discusses open channel design for both rigid boundary and erodible channels. A trapezoidal channel has side slopes of 3 horizontal to 4 vertical and the slope of its bed is 1 in 2000. ) A trapezoidal channel with unfinished concrete surfaces (n=0. From the equation of continuity it is Show that the most efficient trapezoidal channel section will have a hydraulic radius equal to one-half the depth. It combines the advantages of a trapezoidal shape and a half hexagon, promoting uniform flow distribution, minimizing flow separation, and reducing energy losses. What is the relation between hydraulic radius and depth for the most economical trapezoidal section? Sep 29, 2017 · The following points are worth noting: 1) The most economical section of a rectangular channel is one which has hydraulic radius equal to half the depth of flow. i. 3 y 4m 3 Determine the critical depth of the trapezoidal channel for a discharge of 15 m3/s. If the flume is constructed of The area A = Q/V = 100 m³/s / 2 m/s = 50 m². Dec 19, 2024 · Explanation: Half hexagon in the form of trapezoid Represents a well-proportioned trapezoidal section commonly used in canal design. 4. (4 marks) (b) A concrete lined irrigation channel with Manning's n=0. = 0. Though for some special reasons other #MostEconomicalTrapezoidalChannelNumericals #OpenChannelFlow #FluidMechanics #Hydraulics Most economical Trapezoidal channel numericals|| open channel flow|| Fluid Calculate the normal depth in a concrete trapezoidal channel with side slope of 1 to 3, a bed slope of 0. 002 . Semi-circular channels offer several For most efficient trapezoidal channel section with fixed side slope, a circle of radius y shall be inscribed in the trapezoidal section. 2 : For the most trapezoidal section, length of the sloping side should be half of the top width. Chapter 3 The area of cross-section of flow in a channel is 6 m2 . Additional Information Semicircular Theoretically most hydraulically efficient due to Calculating the most efficient trapezoidal section of a canal is crucial for optimizing water flow and minimizing the construction cost. , d n 2 + 1 = b + 2 n d 2 Hydraulic mean depth = Half of depth of flow i. For a channel cross-section to be efficient, it states that the wetted perimeter should be minimized while keeping the cross-sectional area constant. Our trapezoidal open channel calculator uses the most commonly used equation for analyzing rivers and streams - the Manning equation. Based on the options given, the answer would be All of the choices although circular channels are usually the most efficient 1 Answer Ideas for Solving the Problem Most Efficient Trapezoidal Channel: The most efficient trapezoidal channel has a hydraulic radius equal to half of the flow depth (R = y/2) and a side slope of 1:√3 (θ = 60°). 0009 and Manning Jan 29, 2019 · B = 2 Y 3 Additional Information A Trapezoidal channel will be most efficient if Length of sloping side = Half of top width i. Q-9: Find the proportions of a trapezoidal channel which will make the discharge a maximum for a given cross-sectional area of flow and given side slopes. Since a lined channel offers less resistance to flow than an unlined channel, the channel size required to convey a specified flow rate at a selected slope is smaller for a lined May 28, 2019 · This article derives the most efficient channel cross section using calculus of variations for the given flow area at the minimum wetting perimeter length, which is equivalent to the principle of Most fluid mechanics texts that include open channel flow include a derivation of optimal geometry for a trapezoidal channel. This occurs when the trapezoidal section is half of a regular hexagon. In trapezoidal channels, the ideal side slopes are at 60 degrees from horizontal, further impacting optimal flow characteristics and efficiency in water movement. 7m, H=2. Show that the head loss in a This document discusses the design of trapezoidal channels to maximize hydraulic efficiency. b) Storm water from a housing area is discharging 10. Geomorphology of natural channels concerns their shape and structure. Common cross-sections are triangular or trapezoidal with rounded This video explains about the derivation of condition for most economical trapezoidal channel section Sep 8, 2025 · For rectangular channels, the most efficient section features a hydraulic radius equal to half the flow depth. Which has the 13. In the context of open channel flows, the term best hydraulic cross section refers to the most efficient shape of an open channel. 72 m, Chezy coefficient is 75 and the longitudinal slope is 1 in 2500. One of the sloping sides (wetted length) = half of the top width 2. The most hydraulically-efficient channel shape varies, with triangular (45 degrees), circular (optimal when half full), and trapezoidal (60 degrees) channels being effective. 2) Practical channel designs modify the ideal shape for construction feasibility and costs. However, among the options provided, the semi-circular channel section is often considered the most efficient. 3. [5 marks] ii. Classification of Open Channel Flows channel in which the cross-sectional shape and size and also the bottom slope are constant is termed as a prismatic channel. The slope of the channel is 0. 1m 3/s of water at its full capacity? Show that the most efficient trapezoidal channel section will have a hydraulic radius equal to one-half the depth. There are some Download scientific diagram | Typical trapezoidal channel cross section from publication: Least-Cost and Most Efficient Channel Cross Sections | It has been a long-standing concern to decide if a Jun 24, 2020 · Most economical trapezoid channel section //open channel flow // Civil Engineer FBH 192K subscribers 868 What is the base of the most efficient trapezoidal concrete open channel if discharge is 100m3/s and velocity is 2m/s? different forms of channels. Considered the most efficient channel shape in practical applications. However, this formula is only valid for the most efficient section, and we are given a depth of 5m which may not correspond to the most efficient section. For minimum cross-section (most efficient trapezoidal section), the hydraulic radius is half the depth R = y/2). 012. 48 m. The formula for the bottom width (B) of a trapezoidal channel is given by: Geometric relationships like area, wetted perimeter and hydraulic diameter. This makes it the most efficient channel section. The most economical section of a triangular channel is one which has its sloping sides at an angle of 45 degree with the vertical. All natural channels generally have 1. 2. uhevc udjmr lib wplxb mbbwvjrq caqrw ecbbi jbb yinvr krxalx thzs gtai yjh sbcsu yxblt