Note: first and second stops will be reversed. Bring clothing and shoes suitable for walking on rough ground.

Transcription

1 Open Channel Page 1 Intro check on laboratory results Field Trip Note: first and second stops will be reversed Irrigation and Drainage Field Trip Bring clothing and shoes suitable for walking on rough ground. First stop: Go north from UTEP on Mesa. Turn left on Mesa Park Drive just before reaching Jaxons restaurant. Follow Mesa park drive to the end. Features: box culvert, blocks to slow flow and force jump, erosion Second Stop: Go to down Executive to the intersection with Paisano, Turn left

2 Open Channel Page 2 onto Paisano. Pull into the IBWC parking lot. Features: American Dam Third Stop: Follow Paisano to Racetrack then turn left on Doniphan and to to the end. Walk to view the Courchesne Bridge. Features: USGS gauging station

3 Fourth Stop: Follow Doniphan to Country Club and turn left. Go to Upper Valley Road and turn right. Stop off where the road bends left just past Villa Antigua Court (who makes up these names!) where the road crosses a canal. Features: canal, drain, sluice gate, wasteway Open Channel Page 3

4 Open Channel Page 4 Fifth Stop: Continue North on Upper Valley Road, jog right for a mile then left on Strahan Road to Canutillo. Go left a few meters then right on Bosque Road. Stop by the El Paso Water Utilities Well Field Assignment: Explain the hydraulic structures at each stop. Pasted from <

5 Monday, September 17, :28 PM Open Channel Page 5

6 Open Channel Page Determine the critical depth for 30 m 3 /s flowing in a rectangular channel with width 5 m. If the depth of flow is equal to 3 m, is the flow supercritical or subcritical? y c = (q 2 /g) = ((30/5) 2 /9.81) = (36/9.81) = 1.54 m since y> y c the flow is subcritical we could also calculate the Froude number Fr = V/Sqrt[g(A/T)] = (for rectangular channel) = V/Sqrt[g y w/ w] = V/Sqrt[gy] = (Q/A)/Sqrt[g y] = 0.37 which also says it is subcritical since Fr < 1

7 Screen clipping taken: 9/13/2006, 7:26 AM Open Channel Page 7

8 Open Channel Page 8 Tuesday, September 18, :07 AM Basic Hydraulic... Basic Hydraulic Principles John C. Walton Note: the concepts covered in these notes were taken from a variety of textbook and online sources and do not represent original work. Modified: September, 2007

9 Open Channel Page 9 p Aspects of Hydraulics: We will study 4 aspects of hydraulics: Surface hydrology, especially the relationship between rainfall and runoff. Example: storm runoff from a subdivision; one must size a culvert to hold the flow from the maximum storm. Example: It may not be economical to size the culvert for the maximum storm. Instead one might size a holding basin to hold the maximum 0-24 hour storm and the culvert for the, 24 hour storm. this has been done in El Paso and we will visit such a sight How will a system like this behave? What factors are important? time of concentration, drainage basin area, precipitation rate, surface slope and conditions Example: A town obtains its drinking water from a stream. How can you as the engineer ensure that sufficient water is available during a drought period? How can you ensure water quality is adequate. El Paso drinks from the Rio Grande in the summer but not in the winter. Why? Ground water hydrology many towns and cities including El Paso obtain most of their water from below the

10 Open Channel Page 10 surface of the ground, the ground water El Paso obtains water from the Mesilla bolson near Canutillo and from the Hueco bolson near the airport and elsewhere Where does ground water come from? - infiltration at the surface either in the recent or ancient past Open channel flow, or free surface flow - this is when the channel is open to the atmosphere, when there is a free surface Examples: irrigation canal, partially full culvert, partially full sewer pipe Pressure flow or closed conduit flow - when the water fills the pipe and is under pressure. Example: this is how water flows to your house. Engineers must design water supply systems that always have positive pressure and supply water. Otherwise we would have the Mexico City situation where every house and business has a water tank on the roof to store water when is does get there under positive pressure. A related problem is that when negative pressure occurs, contaminated water can be sucked into the water line. We will attempt to study all 4 areas in this class, that s a tall order and will limit our depth. We will combine learning the fundamentals with some computer work. Computer programs are what you will use on the job. The fundamentals are tested on the EIT and PE exams. Computer programs change every few years whereas the fundamentals will be as valid when you retire as they are today. Fundamental Principles All hydraulic equations are based upon three conservation laws. Conservation of mass (continuity), conservation of energy, and conservation of momentum. Continuity Continuity refers to conservation of mass. Since water is considered to be incompressible in most applications, mass and volume can be used interchangeably. = volumetric flow rate (m 3 /s) = flow area (m 2 ) V = average flow velocity (m/s) 1,2 = two locations Energy Energy is conserved. Conservation of energy is one of the most important concepts in hydraulics. In hydraulic applications, energy values are often converted to units of energy per unit weight, resulting in units of length - feet or meters. The energy equation is: where: H G = head gain, usually from a pump (m) = e/g H L = head loss in the system (m)

11 Open Channel Page 11 = pressure head, for the SI system p is in Pascals or Newtons/m 2, is the density of water (1000 kg/m 3 ), is the acceleration of gravity (9.8 m/s 2 ); for the English system pressure is generally converted to pounds force per square foot, = 62.4 pounds force per cubic foot = velocity head (m) = energy per unit mass (J/kg) Pressure is taken as gage pressure and as such is zero when the water pressure is equal to the atmospheric pressure - at a free surface. The final units for each term are either in units of length (meters or feet). Water always moves down gradient (i.e., from high to lower head) but may move uphill or from low to high pressure. As water moves through a pipe the three types of energy: pressure head, elevation head, velocity head may all change from one form to another. But the head only declines. The energy equation can also be expressed as energy per unit mass (J/kg) if we multiply by g: or energy per unit volume (J/m 3 = Pa) if we multiply the original equation by : Note that pressure is energy per unit volume. In hydraulics we typically use energy per unit weight because it is more convenient. Conservation of Momentum Conservation of momentum is used for some problems where energy conservation is difficult to measure. The best example is in a hydraulic jump. In a hydraulic jump a large amount of energy is lost as heat in the turbulence of the jump. Conservation of momentum is advantageous in this situation because momentum cannot be lost from internal friction, only through external forces on the water (e.g., friction on the bottom of the channel). = density of water (kg/m 3 ) P 1, P 2 = resultant pressure forces at sections 1 and 2 (N/m 2 ) W = weight of water between sections 1 and 2 (N) = channel slope F f = force of friction acting along the surface of contact between water and channel (N) Definition of Some Terms hydraulic grade line - is the sum of the pressure head and the elevation head.

12 Open Channel Page 12 for open channel flow this is the water surface elevation, at the free surface the pressure head is zero so the pressure head plus the elevation head equals the elevation head for a pressure pipe the hydraulic grade represents the height to which a water column would rise in a piezometer piezometer = a tube rising from the pipe that does not capture any of the velocity head energy grade line - is the sum of and is how far the water will rise in a pitot tube pitot tube = like a piezometer but captures all the velocity head Energy Gains and Losses. Energy losses in a system may be due to many things. The primary cause is usually friction between fluid particles and between the fluid and the walls. Secondary causes of energy loss are due to localized areas of increased turbulence and disruption of the streamlines such as at valves and fittings. The rate at which energy is lost in a pipe or channel in units of length/length = dimensionless is called the friction slope Generally energy is added to a flow by a pump Example 1-2: Energy Principles First apply the energy equation: Simplifications: no energy additions so H G drops out, V 1 =0 in the tank, p 1 is zero at the surface we know so we can solve for head loss by plug and chug, friction slope is just head loss divided by distance. Question: What happens to the answer if the pipe comes out of the top rather than the bottom of the tank? Show the trade off between elevation and pressure head. If this makes no difference in the energy equation, then why should the line come out of the bottom (to use the storage) Some Flow Parameters Area, Wetted Perimeter, and Hydraulic Radius area (A) is the cross-sectional area of the flow wetted perimeter (P) is the liquid/solid contact area, i.e., not counting the air/water interface

13 Open Channel Page 13 prismatic channel just means it has a consistent shape, slope, and roughness hydraulic radius (R) is the flow area divided by the wetted perimeter, it has units of length for a full flowing circular pipe it is: where r is the pipe radius and D is the pipe diameter. Other shapes are more complex. Since a circle has the lowest perimeter per unit area it has the least friction and the most efficient flow. Rectangular channel hydraulic radius: where the calculation of hydraulic radius is more complex for triangular and trapezoidal shapes Hydraulic Depth is the ratio of the flow area to the top width. Hydraulic depth is used to determine critical flow. Velocity Velocity varies across a pipe or stream channel. It is zero at the solid/liquid interface and increased from there. In a pipe it s at the center. The same is approximately true for an open channel. Generally we will deal with average velocity. Average velocity is more simple and is just the total flow divided by the flow area Steady Flow Flow often varies with time. In this class we will deal almost entirely with steady flow. For most hydraulic calculations this assumption is completely reasonable. For more complex situations computer codes can be used for transient analysis.

14 Open Channel Page 14 Laminar Flow, Turbulent Flow, Reynolds Number laminar flow is smooth, in this class we will consider laminar flow only in the case of ground water. Most flow of ground water is laminar. Reynolds number below 2,000 turbulent flow is rough and varies with time in a random or chaotic fashion. Most flow in pipes and channels is turbulent. Reynolds number above 4,000. the Reynolds number is calculated as: R = hydraulic radius = D/4 for pipe flow = kinematic viscosity in m 2 /s = = Friction Losses There are many methods for estimating friction losses associated with the flow of a liquid through a section of pipe, conduit, canal, or whatever. We will look at the common methods. Since they are all approximate, not all of them give the same answer. In practice some methods have been used for Open Channel Flow, Sewer Design, or Closed Conduit Flow. However by manipulation of the governing equations most of them can be used interchangeably. General Equation Format All the equations for friction losses have the format: V = average velocity (m/s) k = factor to account for empirical constants, unit conversions, and anything else required C = a flow resistance factor R = hydraulic radius (m) S = friction slope x,y = variable exponents The lining material of the flow channel or pipe usually determines the flow resistance (or roughness factor), C. Manning Equation The Manning equation is the most used equation for open channel flow such as irrigation canals. The roughness constant is represented by the Manning s n.

15 Open Channel Page 15 g p y g k = is 1.49 for US units of (ft, s) and 1.00 for SI units of (m, s) n = is obtained from tables and based upon roughness of the liner S = slope of the grade, since we have steady uniform flow the slope of the grade or channel is also the friction slope. The Manning equation in terms of total flow rate is: = section factor Chezy s (Kutter s) Equation This is used for sanitary sewer design.

16 Open Channel Page 16 where C can be calculated from Kutter s equation Hazen-Williams Equation The Hazen-Williams Equation is most frequently used in the design and analysis of pressure pipe systems. The coefficients are for water only in the normal temperature range for water supply. It should not be used, for example, for hot water. k = C = 1.32 for US Standard units, or 0.85 for SI units Hazen-Williams coefficient from a table Darcy-Weisbach (Colebrook-White) Equations This equation is most commonly used for pressure pipe systems. However it can be used for any liquid flow and/or for open channels. The equation is: f = the friction factor, this is generally looked up from the Moody diagram but it may also be calculated from the Colebrook equation A more typical format for the Darcy-Weisbach equation is in terms of the head loss. The head loss is just the friction slope times the distance traveled or length of the pipe. Replacing S by h L /L and hydraulic radius by D/4 gives: solving for h L gives: This is the form of the equation most familiar to students from fluid mechanics. The surface roughness coefficients for several methods are given in the table below. The specifics of estimating the friction factor are given in the chapter on closed conduit flow. Pressure Flow For pipes flowing full, many of the friction loss calculations are greatly simplified, since flow area, wetted perimeter, and hydraulic radius are all known functions of pipe radius or diameter.

17 Open Channel Page 17 Open Channel Flow Open channel flow is more complicated than pressure flow because the geometry is more variable. For example the hydraulic radius depends upon how full a channel is. The figure to the right is an agricultural drain in the Mesilla Valley. Uniform Flow Uniform flow is when the discharge, flow depth, area, hydraulic radius, etc. all constant along a section. This results when shear stress forces on the channel sides and bottom are equal and opposite to the forces of gravity. The gravity force is: the force of friction is releated to shear stress on the channel sides where: A = cross sectional area (m 2 ) K = empirically determined constant L = length of channel section (m) P = wetted perimeter (m) S = slope of channel V = velocity (m/s) = shear stress (N/m 2 ) The Chezy equation is derived by assuming that the shear stress is equal to a constant (K) times the velocity squared. For an open channel The depth of flow is constant so the hydraulic grade line and energy grade line must be parallel to the channel slope. This depth of flow is called the normal depth. in uniform flow the friction slope equals the slope of the channel in prismatic channels flow conditions will approach uniform flow if the channel is sufficiently long. the normal depth is the depth given by the Manning equation. It is a useful point of reference. When the channel changes the flow depth differs from the normal depth

18 Open Channel Page 18 Specific Energy and Critical Flow The energy in a channel section measured with respect to the channel bottom as the datum is known as the specific energy. The specific energy is defined as: where y is the depth of flow. The specific energy is used for open channel flow and is the sum of the elevation and velocity heads. Since we are in a open channel the pressure head at the surface is zero and the rest of the pressure distribution is approximately hydrostatic. Thus the total water depth is equal to the sum of the pressure and elevation heads at any point if the bottom of the channel is defined as datum. If a section is short and we assume friction losses are negligible then specific energy will be conserved. This is a useful concept. If the channel is rectangular then: This as a cubic equation. It has three solutions but only two have physical meaning. The figure to the right is a schematic example. The graph assumes a constant discharge. There are two possible values for the depth of flow, y for each value of E, the specific energy. At the same energy level the flow can be either fast shallow (called supercritical flow) or slow and deep (called subcritical flow). The two flow depths area called alternate depths. Since the energy level is the same, water can easily pop between these two states. The minimum specific energy for a particular flow rate is reached when the flow is critical. In the figure on the right the flow is subcritical prior to the sluice gate. The flow escaping under the sluice gate is supercritical flow. The specific energy is the same on each side of the sluice gate.

19 Open Channel Page 19 Critical depth and by analogy sub and supercritical flow can be determined by the Froude number. The Froude number is: where: D = hydraulic depth = A/T (m) A = cross sectional area of flow (m 2 ) T = top width of flow (m) where D is now the hydraulic depth of the channel defines as A/T where A is cross-sectional area and T is the top width of flow. When the Froude number is 1 the flow is critical, when it is < 1 the flow is subcritical when it is > 1 the flow is supercritical. For critical flow when Fr=1, and Q = V/A we can rearrange to get: where Q is volumetric flow rate, A is cross sectional area, and T is the top width of the flow. Now let s look at this for a rectangular channel where A = T y and A/T = y where: y = the depth of flow (m) allowing easy calculation of the critical depth of flow in the special case of a rectangular channel. q = flow rate per unit width = Q/w Again for rectangular shaped channels: When the thickness of the crest of a weir is more than 0.47 times the head, it is classified as a broad-crested weir. Critical flow occurs over the top of a broad crested weir. If the depth of flow can be measured then the flow rate over a broad crested weir can be calculated as:

20 Open Channel Page 20 or q = Q/w [=] m 2 /s w = width of the weir For high weirs the upstream velocity is almost zero. This and the assumption of constant specific energy can be used to give the flow rate in terms of the upstream elevation above the top of the weir:

21 Open Channel Page 21 p Channel Design Hydraulic Efficiency For a particular slope and surface roughness the discharge increases with an increase in the section factor,. For a given flow area, the section factor is highest for the least wetted perimeter. Minimization of the wetted perimeter for a given flow area maximizes the flow in that area, allowing smaller (presumably cheaper) channels to carry the most water. This is called the best hydraulic section. The results are: Trapezoidal channel: half a hexagon Rectangular channel: width is twice the depth (half a square) Triangular channel: side slopes are generally selected based upon other considerations, but a 45 degree slopes are most efficient Circular channel: semicircle The dimensions of a channel are not governed primarily by hydraulic efficiency. Other considers: Are the side slopes to steep to hold soil? Which design requries the least amount of space (expensive real estate)?, Which design has the lowest cost?, Would the flow velocity be erosive? How easy is it to construct? Will it be dangerous to people falling in?... are generally more important. Permissible Shear Stress and Velocity. During design the flow velocity relative to the maximum allowable shear stress for a particular material type must be considered. Table 1 provides typical examples of permissible shear stress for selected lining types. Lining performance relates to how well lining materials protect the underlying soil from shear stresses so these linings do not have permissible shear stresses independent of soil types. Permissible shear stress for gabion mattresses depends on rock size and mattress thickness. Typical Permissible Shear Stresses for Bare Soil and Stone Linings (Design of Roadside Channels with Flexible Linings Hydraulic Engineering Circular Number 15, Third Edition) Permissible Shear Stress Lining Category Lining Type N/m 2 lb/ft 2

22 Open Channel Page 22 Bare Soil Cohesive (PI=10)1 Clayey sands Inorganic silts Silty sands Bare Soil Cohesive (PI=20) Clayey sands Inorganic silts Silty sands Inorganic clays Bare Soil Non-cohesive2 (PI<10) Finer than coarse sand D75<1.3 mm (0.05 in) Fine gravel D75=7.5 mm (0.3 in) Gravel D75=15 mm (0.6 in) Gravel Mulch Coarse gravel D50=25 mm (1 in) Very coarse gravel D50=50 mm (2 in) Rock Riprap D50=0.15 m (0.5 ft) D50=0.30 m (1.0 ft) The maximum shear stress on a channel bottom in uniform flow can be estimated by: For nonuniform flow, such as rounding bends in the channel, the maximum shear stress may be significantly higher. Supercritical flow generally requires than channels be concrete lined. Hydraulic Jump A hydraulic jump occurs when water in an open channel is flowing supercritical and is slowed by a deepening of the channel or obstruction in the channel. The slowing causes the water to suddenly jump to the other specific energy state (slow, deep flow). To the right a hydraulic jump is shown forming downstream of a dam spillway. Hydraulic jumps release large amounts of energy and thus can lead to erosion problems where they occur. In the third figure a stilling basin has been designed below the dam to prevent erosion from the hydraulic jump.

23 Open Channel Page 23 y j p Specific energy is not conserved in a hydraulic jump since much energy is lost in the turbulence of the jump. In order to estimate the height of the water after a hydraulic jump we perform a momentum balance. Although significant energy losses occur in the jump, momentum can only be lost by friction on the walls, not through internal turbulence. Thus conservation of momentum is a better assumption than conservation of energy in this situation. In a rectangular channel the formula relating the upstream depth (y 1 ) and the downstream depth (y 2 ) is: where Flow Profiles Flow in uniform channels can be determined with the Manning equation and the Froude number. Depth of flow is first determined with the Manning (or other flow) equation. This is the normal depth (y n ), meaning the usual or expected depth of flow. If the slope is low, the normal depth (uniform flow depth, Manning equation depth) will be greater than the critical depth giving subcritical flow. If the channel slope is sufficiently steep the normal depth will be less than the critical depth giving supercritical flow. Horizontal and adverse slopes are special cases because a normal depth does not exist for these cases (i.e., water does not normally flow up slope).

24 When transitions in the channel are present (e.g., a change in slope of the channel) the usual flow patterns are perturbed in the transition region. The following classification system has been designed to describe the transition regions. The 1, 2, 3 designations indicate if the actual flow depth (y) is greater than normal and critical depths (Zone 1), between the normal and critical depths (Zone 2), or less than both the normal and critical depths (Zone 3). Zones 1 and 3 occur during backwater situations (e.g., where the channel slope decreases downstream. Zone 2 occurs in drawdown situations (e.g., where the channel slope increases). Open Channel Page 24

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26 Open Channel Page 26 Manning Equation Tuesday, September 18, :41 AM Screen clipping taken: 9/18/2007, 9:51 AM

27 Screen clipping taken: 9/18/2007, 9:52 AM Open Channel Page 27

28 Tuesday, September 18, :25 AM Open Channel Page 28

29 Open Channel Page 29 Man Ex Tuesday, September 18, :52 AM Screen clipping taken: 9/18/2007, 9:52 AM

30 Screen clipping taken: 9/18/2007, 9:53 AM Open Channel Page 30

31 Open Channel Page 31 Man Ex Tuesday, September 18, :53 AM Screen clipping taken: 9/18/2007, 9:53 AM

32 Screen clipping taken: 9/18/2007, 9:54 AM Open Channel Page 32

33 Open Channel Page 33 Screen clipping taken: 9/18/2007, 9:54 AM Screen clipping taken: 9/18/2007, 9:54 AM

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35 Open Channel Page 35 Critical Depth Tuesday, September 18, :54 AM Screen clipping taken: 9/18/2007, 9:57 AM

36 Open Channel Page 36 Screen clipping taken: 9/18/2007, 9:59 AM For rectangular channels ONLY: Screen clipping taken: 9/18/2007, 10:00 AM Screen clipping taken: 9/18/2007, 10:00 AM

37 Screen clipping taken: 9/18/2007, 10:01 AM Open Channel Page 37

38 Screen clipping taken: 9/18/2007, 10:01 AM Open Channel Page 38

39 Open Channel Page 39 Man Example Tuesday, September 18, :03 AM A Concrete sewer pipe 4 ft in diameter is laid so it has a drop in elevation of 1 ft per 1000 ft of length. If sewage (assume water properties) flows at a depth of 2 ft in the pipe, what will be the discharge? Screen clipping taken: 9/20/2007, 9:23 AM

40 Open Channel Page 40 Permissible Velocity Thursday, September 20, :26 AM A trapezoidal irrigation canal is to be excavated in soil and lined with coarse gravel. The canal is to be designed for a discharge of 200 cfs, and it will have a slope of What should be the magnitude of the cross sectional area and hydraulic radius for the canal if it is to be designed so that erosion of the canal will not occur? Choose a canal cross section that will satisfy the limitations.

41 Screen clipping taken: 9/20/2007, 9:26 AM Open Channel Page 41

42 Open Channel Page 42 Gradually Varied Flow Monday, September 24, :12 AM Gradually varied flow differs from uniform flow and rapidly varied flow (hydraulic jumps) in that the change in water depth in the channel takes place very gradually with distance. This is steady but nonuniform flow computers can solve this problem, we will study the general trends these can be categorized into a series of profiles (what we will do) one can also solve for the change in water depth over distance dd/dx = change in depth of water over distance = function of slope and discharge Channel properties are defined in terms of critical depth and normal depth, the normal depth is the depth given by the Manning Equation horizontal and adverse channels (obvious in name) steep is when normal depth is supercritical mild is when normal depth is subcritical critical is when normal depth is critical Steep, Critical, Mild, Horizontal, Adverse (SCMHA) Type I: dd/dx is positive, water is getting deeper, a backwater Type II: dd/dx is negative, water is getting shallower Type III: dd/dx is positive

43 Open Channel Page 43 where H is total energy head

44 Open Channel Page 44 Surface Profiles Tuesday, September 25, :12 AM

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46 Open Channel Page 46 Profiles Tuesday, September 25, :24 AM

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50 Open Channel Page Tuesday, October 02, :11 AM Quiz: a) b) c) A 3 m wide rectangular channel carries a discharge of 15 m 3 /s at a uniform depth of 1.7 m. the Manning's coefficient is n= Find: channel slope critical depth Froude number First Step: find the appropriate governing equations we're solving the Manning equation for the slope: SQRT(S) = n Q/(k A R 0.67 ) S = (n Q/(k A R 0.67 )) 2 n = 0.022, Q = 15, k=1, A = 1.73 = 5.1, P = = 6.4, R=A/P = 5.1/6.4 = S =

51 Open Channel Page 51 b) critical depth is when Froude number is equal to 1 Screen clipping taken: 10/4/2007, 9:11 AM for rectangular channels ONLY, this simplifies to:

52 Open Channel Page 52 plug and chug using Q and w gives yc = 1.37 m so the normal depth is > critical depth so (without calculating the Froude number is (>, <, =) 1?? What would we use to calculate critical depth for a nonrectangular channel? c) Fr = (rectangular channel) = Q/(yw (gy) 0.5 ) = 0.72 with y = yactual d) This is an Adverse, Horizontal, Mild, Steep channel?

53 Mild since the normal is > critical depth Open Channel Page 53

54 Open Channel Page 54 Flood Tuesday, October 02, :02 AM Where is the flow sub and supercritical? What is the Froude number? What profiles? note: profiles are complicated by changes in n as well as slope, not everything fits the ideal pattern, note change in Manning's n at end of concrete lining

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