750.1 Open Channels - Revision history

Smithk: Updated website link for increased security

2021-10-25T14:22:32Z

Updated website link for increased security

← Older revision		Revision as of 09:22, 25 October 2021
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	==750.1.1 Types of Open Channel Flow==		==750.1.1 Types of Open Channel Flow==
	Open channel flow may be classified into several different types. Flow in an open channel is said to be steady if the discharge is constant with respect to time. If the discharge is increasing or decreasing with time, the flow is said to be unsteady. In general, all open channel flow encountered in highway drainage problems is unsteady. That is, the flow rate in these channels will vary with time. Design, however, must be based on the "worst" condition to be expected within a reasonable period of time. This worst condition is the peak flow rate produced by the [~~http~~://epg.modot.org/index.php?title=Category:749_Hydrologic_Analysis#749.2.1_Design_Frequency_Criteria selected design frequency]. Therefore, in design, the time dependent variations of open channel flow are ignored and the channel is assumed to be operating in a steady state.		Open channel flow may be classified into several different types. Flow in an open channel is said to be steady if the discharge is constant with respect to time. If the discharge is increasing or decreasing with time, the flow is said to be unsteady. In general, all open channel flow encountered in highway drainage problems is unsteady. That is, the flow rate in these channels will vary with time. Design, however, must be based on the "worst" condition to be expected within a reasonable period of time. This worst condition is the peak flow rate produced by the [https://epg.modot.org/index.php?title=Category:749_Hydrologic_Analysis#749.2.1_Design_Frequency_Criteria selected design frequency]. Therefore, in design, the time dependent variations of open channel flow are ignored and the channel is assumed to be operating in a steady state.

	Steady state flow may be divided into two subgroups; these are: uniform flow and varied flow. Steady state uniform flow is the primary type of flow considered in open channel hydraulics and is the only type of flow to be treated in depth in this guidance on open channel flow. Channel design is based on analysis assuming uniform open channel flow. Varied flow may be subdivided into two classes as gradually varied or rapidly varied. Rapidly varied flow may take the form of either a hydraulic drop or a hydraulic jump. The hydraulic jump has some applications in reducing the velocity of flow and will be discussed in [[750.6 Erosion Control and Energy Dissipation\|EPG 750.6 Erosion Control and Energy Dissipation]].		Steady state flow may be divided into two subgroups; these are: uniform flow and varied flow. Steady state uniform flow is the primary type of flow considered in open channel hydraulics and is the only type of flow to be treated in depth in this guidance on open channel flow. Channel design is based on analysis assuming uniform open channel flow. Varied flow may be subdivided into two classes as gradually varied or rapidly varied. Rapidly varied flow may take the form of either a hydraulic drop or a hydraulic jump. The hydraulic jump has some applications in reducing the velocity of flow and will be discussed in [[750.6 Erosion Control and Energy Dissipation\|EPG 750.6 Erosion Control and Energy Dissipation]].

Smithk: /* 750.1.5.1 General Considerations */

2021-06-02T13:18:18Z

750.1.5.1 General Considerations

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	===750.1.5.1 General Considerations===		===750.1.5.1 General Considerations===
	All non-erodible channels are to be designed on the basis of uniform open channel flow. The factors to be considered in design are the kind of material forming the channel lining; the "n" value of this material, the channel slope; the channel shape; and the freeboard. In addition to these hydraulic design factors, the designer must keep in mind other design limitations such as safety considerations. For example, the designer may be greatly restricted as to the channel shapes which he may ~~consider~~ inside a clear zone. In general, the object of design is to provide the least costly channel which has the required capacity and which will not scour. For non-erodible channels, this means selecting the smallest possible cross-section which will pass the design flow rate at the given channel slope. A factor of safety in channel design is introduced by addition of a freeboard to the computed depth of flow. For minimum freeboard to the top of the channel lining and to the top of the channel embankment, refer to [[748.3 Freeboard\|EPG 748.3 Freeboard]].		All non-erodible channels are to be designed on the basis of uniform open channel flow. The factors to be considered in design are the kind of material forming the channel lining; the "n" value of this material, the channel slope; the channel shape; and the freeboard. In addition to these hydraulic design factors, the designer must keep in mind other design limitations such as safety considerations. For example, the designer may be greatly restricted as to the channel shapes which may be considered inside a clear zone. In general, the object of design is to provide the least costly channel which has the required capacity and which will not scour. For non-erodible channels, this means selecting the smallest possible cross-section which will pass the design flow rate at the given channel slope. A factor of safety in channel design is introduced by addition of a freeboard to the computed depth of flow. For minimum freeboard to the top of the channel lining and to the top of the channel embankment, refer to [[748.3 Freeboard\|EPG 748.3 Freeboard]].

	In order to reduce the number of computations required to design non-erodible channels, a set of open channel flow charts have been developed and are presented below. Depths and velocities shown by these charts apply with accuracy only to channels in which uniform flow at normal depth has been established. These charts may be applied with sufficient accuracy for practical purposes, to channels of somewhat irregular cross section approximating that represented by the chart and to channels on an irregular bottom slope where the irregularities are sufficiently short that they may be represented by a continuous mean slope.		In order to reduce the number of computations required to design non-erodible channels, a set of open channel flow charts have been developed and are presented below. Depths and velocities shown by these charts apply with accuracy only to channels in which uniform flow at normal depth has been established. These charts may be applied with sufficient accuracy for practical purposes, to channels of somewhat irregular cross section approximating that represented by the chart and to channels on an irregular bottom slope where the irregularities are sufficiently short that they may be represented by a continuous mean slope.

EPGsysop: /* 750.1.4.3.2 Step-Backwater Analysis */

2017-04-07T19:33:24Z

750.1.4.3.2 Step-Backwater Analysis

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	====750.1.4.3.2 Step-Backwater Analysis====		====750.1.4.3.2 Step-Backwater Analysis====
	Step-backwater analysis is used for calculating water surface profiles for steady gradually varied flow conditions. Gradually varied water surface profiles are typically computed using the standard step method in which the stream reach of interest is divided into a number of subreaches by cross sections spaced ~~such~~ that the flow is gradually varied in each subreach. The energy equation is then solved in a step-wise fashion for the water surface elevation at one cross section based on the water surface elevation at the previous cross-section. Water surface profile computation therefore requires a beginning value of elevation or depth and proceeds upstream for subcritical flow and downstream for supercritical flow. In subcritical flow, uniform flow and normal depth at the most downstream cross section are ordinarily assumed as the boundary condition. In supercritical flow, critical depth is often the boundary condition at a control section.		Step-backwater analysis is used for calculating water surface profiles for steady gradually varied flow conditions. Gradually varied water surface profiles are typically computed using the standard step method in which the stream reach of interest is divided into a number of subreaches by cross sections spaced so that the flow is gradually varied in each subreach. The energy equation is then solved in a step-wise fashion for the water surface elevation at one cross section based on the water surface elevation at the previous cross-section. Water surface profile computation therefore requires a beginning value of elevation or depth and proceeds upstream for subcritical flow and downstream for supercritical flow. In subcritical flow, uniform flow and normal depth at the most downstream cross section are ordinarily assumed as the boundary condition. In supercritical flow, critical depth is often the boundary condition at a control section.

	The calculations involved in a step-backwater analysis are tedious and repetitive. It is recommended that a computer program such as the Corps of Engineers HEC-RAS be used for step-backwater calculations. See the documentation of the selected computer program for additional details on the step-backwater methodology used.		The calculations involved in a step-backwater analysis are tedious and repetitive. It is recommended that a computer program such as the Corps of Engineers HEC-RAS be used for step-backwater calculations. See the documentation of the selected computer program for additional details on the step-backwater methodology used.

	===750.1.4.4 Manning's Equation for Circular Pipes===		===750.1.4.4 Manning's Equation for Circular Pipes===

Smithk: /* 750.1.4.1.1 Manning's n */

2015-04-15T12:31:02Z

750.1.4.1.1 Manning's n

← Older revision		Revision as of 07:31, 15 April 2015
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	[[image:750.1.4.1.1 big Da.jpg\|left\|225px]]		[[image:750.1.4.1.1 big Da.jpg\|left\|225px]]





	:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.		:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.

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	[[image:750.1.4.1.1 small Da.jpg\|left\|275px]]		[[image:750.1.4.1.1 small Da.jpg\|left\|275px]]





	:::::::::: when 0.3 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 1.5.		:::::::::: when 0.3 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 1.5.

Smithk: /* 750.1.4.1.1 Manning's n */ updated formula due to wiki problem. No change in formula, just replaced formula with jpg of formula

2015-04-15T12:29:53Z

750.1.4.1.1 Manning's n: updated formula due to wiki problem. No change in formula, just replaced formula with jpg of formula

← Older revision		Revision as of 07:29, 15 April 2015
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	The n value to be used for calculating the velocity in rock or boulder lined channels may be calculated by the following formulae:		The n value to be used for calculating the velocity in rock or boulder lined channels may be calculated by the following formulae:

	:~~<math>n = \frac {α d_a^{\frac{~~1~~}{6}}}{2~~.~~25 + 5~~.~~23 log \Big(\frac{d_a}{D_{50}}\Big)}</math>~~		[[image:750.1.4.1.1 big Da.jpg\|left\|225px]]

	:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.		:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.

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	:~~<math>n = \frac {α d_a^{\frac{~~1~~}{6}}}{\sqrt{g} f(Fr) f(REG) f(CG)}</math>~~		[[image:750.1.4.1.1 small Da.jpg\|left\|275px]]
	:::::::::: when 0.3 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 1.5.		:::::::::: when 0.3 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 1.5.

Smithk: /* 750.1.4.1.1 Manning's n */

2015-04-15T12:17:17Z

750.1.4.1.1 Manning's n

← Older revision		Revision as of 07:17, 15 April 2015
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	The n value to be used for calculating the velocity in rock or boulder lined channels may be calculated by the following formulae:		The n value to be used for calculating the velocity in rock or boulder lined channels may be calculated by the following formulae:

			:<math>n = \frac {α d_a^{\frac{1}{6}}}{2.25 + 5.23 log \Big(\frac{d_a}{D_{50}}\Big)}</math>

	:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.		:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.

Smithk: /* 750.1.4.1.1 Manning's n */

2015-04-15T12:16:45Z

750.1.4.1.1 Manning's n

← Older revision		Revision as of 07:16, 15 April 2015
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	The n value to be used for calculating the velocity in rock or boulder lined channels may be calculated by the following formulae:		The n value to be used for calculating the velocity in rock or boulder lined channels may be calculated by the following formulae:

	~~:<math>n = \frac {α d_a^{\frac{1}{6}}}{2.25 + 5.23 log \Big(\frac{d_a}{D_{50}}\Big)}</math>~~
	:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.		:::::::::: when 1.5 ≤ d<sub>a</sub>/D<sub>50</sub> ≤ 185.

Smithk: /* 750.1.4.1.1 Manning's n */ minor clarification

2014-06-23T13:55:33Z

750.1.4.1.1 Manning's n: minor clarification

← Older revision		Revision as of 08:55, 23 June 2014
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	::n = Manning’s roughness coefficient		::n = Manning’s roughness coefficient
	::α = units correction constant, 0.213		::α = units correction constant, 0.213
	::𝜏<sub>o</sub> = mean boundary shear, lb/ft<sup>2</sup>		::<font size = 4.0> 𝜏<sub>o</sub></font size = 4.0> = mean boundary shear, lb/ft<sup>2</sup>
	::C<sub>n</sub> = roughness coefficient for SCS retardance class vegetation (see tables for [[#Classification of Vegetal Covers\|Classification of Vegetal Covers]] and [[#Coefficients for Roughness of Grass-Lined Channels\|Coefficients for Roughness of Grass-Lined Channels]])		::C<sub>n</sub> = roughness coefficient for SCS retardance class vegetation (see tables for [[#Classification of Vegetal Covers\|Classification of Vegetal Covers]] and [[#Coefficients for Roughness of Grass-Lined Channels\|Coefficients for Roughness of Grass-Lined Channels]])

			:::<font size = 3.0>''𝜏<sub>o</sub> = γRS<sub>o</sub>''</font size = 3.0>
	:::~~[[image:750.1.4.1~~.~~1 mean boundary shear~~.~~jpg\|left\|86px]]~~




	:::γ = unit weight of water, 62.4 lb/ft<sub>3</sub>		:::γ = unit weight of water, 62.4 lb/ft<sub>3</sub>

Smithk: /* 750.1.4.1.1 Manning's n */ minor clarifications, per Bridge

2014-06-23T13:25:51Z

750.1.4.1.1 Manning's n: minor clarifications, per Bridge

← Older revision		Revision as of 08:25, 23 June 2014
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	The roughness coefficient of grassed channels varies depending on grass properties as reflected in the C<sub>n</sub> parameter and the shear force exerted by the flow. This is because the applied shear on the grass stem causes the stem to bend, which reduces the stem height relative to the depth of flow and reducing the roughness. The following formulae may be used to estimate the n value for channels with grass linings, erosion control blankets or turf reinforcement mats.		The roughness coefficient of grassed channels varies depending on grass properties as reflected in the C<sub>n</sub> parameter and the shear force exerted by the flow. This is because the applied shear on the grass stem causes the stem to bend, which reduces the stem height relative to the depth of flow and reducing the roughness. The following formulae may be used to estimate the n value for channels with grass linings, erosion control blankets or turf reinforcement mats.

	:''n = ~~αC<sub>n</sub>𝜏<sub>o~~<~~/sub><sup~~>-0.4</~~sup~~>''		:''n'' = <math>\alpha C_n \tau_o^{-0.4}</math>

	::where:		::where:
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	:::S<sub>o</sub> = channel slope, ft/ft		:::S<sub>o</sub> = channel slope, ft/ft

	SCS Retardance Class C vegetation is appropriate for most seed mixtures used on MoDOT roadway projects and [[Media:750.1 Manning ~~Formula for Grassed Channels~~.pdf\|Manning Formula for Grassed Channels]] provides a solution for the above equation for Class C Vegetation. As an alternative to the above equation, the values given in [[#Roughness Coefficients for Various Materials\|Roughness Coefficients for Various Materials]] for grass-lined channels may be used as a conservative estimate for hand calculations.		SCS Retardance Class C vegetation is appropriate for most seed mixtures used on MoDOT roadway projects and [[Media:750.1.4.1.1 Manning.pdf\|Manning Formula for Grassed Channels]] provides a solution for the above equation for Class C Vegetation. As an alternative to the above equation, the values given in [[#Roughness Coefficients for Various Materials\|Roughness Coefficients for Various Materials]] for grass-lined channels may be used as a conservative estimate for hand calculations.

	<div id="Roughness Coefficients for Various Materials"></div>		<div id="Roughness Coefficients for Various Materials"></div>

Smithk: /* 750.1.4.1.1 Manning's n */

2014-06-23T13:00:10Z

750.1.4.1.1 Manning's n

← Older revision		Revision as of 08:00, 23 June 2014
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	::C<sub>n</sub> = roughness coefficient for SCS retardance class vegetation (see tables for [[#Classification of Vegetal Covers\|Classification of Vegetal Covers]] and [[#Coefficients for Roughness of Grass-Lined Channels\|Coefficients for Roughness of Grass-Lined Channels]])		::C<sub>n</sub> = roughness coefficient for SCS retardance class vegetation (see tables for [[#Classification of Vegetal Covers\|Classification of Vegetal Covers]] and [[#Coefficients for Roughness of Grass-Lined Channels\|Coefficients for Roughness of Grass-Lined Channels]])

	:::~~''𝜏<sub>o</sub> = γRS<sub>o</sub> ''~~
			:::[[image:750.1.4.1.1 mean boundary shear.jpg\|left\|86px]]




	:::γ = unit weight of water, 62.4 lb/ft<sub>3</sub>		:::γ = unit weight of water, 62.4 lb/ft<sub>3</sub>
	:::R = hydraulic radius, ft		:::R = hydraulic radius, ft
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	:n<sub>i</sub> = Manning’s n value for the material.		:n<sub>i</sub> = Manning’s n value for the material.
	:p = Total wetted perimeter, ft.		:p = Total wetted perimeter, ft.


	====750.1.4.1.2 Hydraulic Radius====		====750.1.4.1.2 Hydraulic Radius====