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A spreadsheet model that is based on solving Manning equation for wide channel cross-section assumption has been developed. The model shows the variation of the water level in the cross-section. Mar 29, 2011 The equations below are those used, together with the Manning equation and Q = VA, in the partially full pipe flow calculator (Excel spreadsheet) for flow depth more than pipe radius, as shown below. Θ = 2 arccos (r – h)/r A = πr 2 – K = πr 2 – r 2 (θ – sinθ)/2. P = 2πr – S = 2πr – rθ. Equations are also given for calculating the Manning roughness coefficient, n, for a given depth of flow in a pipe of known diameter. Numerous worked examples illustrate the use of these equations together with the Manning equation for partially full pipe flow. A spreadsheet for making partially full pipe flow. May 13, 2011 Here is another freeware tool that I developed in Excel. With this workbook, you can calculate the discharge, the velocity, the Reynolds number, and the type of flow (laminar, transitional, turbulent) of an open channel with a trapezoidal cross-section. Manning’s equation is used for the calculations. The use of Excel spreadsheet formulas is a convenient way to make Manning equation calculations for uniform open channel flow. (For background information see 'Introduction to the Manning Equation for Open Channel Flow Calculations.'

Manning’s Equation for pipe flow (or Manning Formula for pipe flow) is an empirically derived formula used to calculate velocity and flow in any open channel, including a circular pipe not under surcharge conditions. Manning’s Equation is also included as an acceptable option in BS EN 752 and BS EN 16933-2 for analyzing flow in drainage pipes.

While the Manning Formula is much simpler to use than the Colebrook-White Equation, it is still simpler to use a Manning Formula chart if the calculation is to be done by hand. Many charts have been developed for Manning’s Formula, some examples are included below. Alternatively the simplicity of Manning’s Equation allows a simple nomograph to be used. Again there are many examples of Manning Equation nomographs, one of which is included below.

Manning’s Equation for Full Pipe Flow

Manning’s Equation calculates the velocity (V) of flow through a circular or non-circular cross section pipe running full (but not under pressure) using the below equation;

Hydraulic Radius (R) (m)

This is the flow cross sectional area divided by the wetted perimeter or the length of the cross section which is in contact with the flowing water. For circular pipes running full this can be taken as the pipe diameter/4. Click here for further details on how to calculate the Hydraulic Radius.

Hydraulic Gradient (S)

This is effectively the downward slope of pipe in m/m.

Manning’s Roughness Coefficient (n)

Manning’s Roughness Coefficient is an empirical coefficient used to allow for the frictional losses caused by the internal roughness of the pipe. Click here for further details on Manning’s Roughness Coefficient.

Manning’s Equation for Partially Full Pipe Flow

Similar to the Colebrook-White Equation, Manning’s Formula for full pipe flow can be used to calculate the discharge and velocity values for pipes running partially full by modifying the hydraulic radius. The CivilWeb pipe analysis spreadsheet includes a tool for calculating the flow and velocity at partial flows using Manning’s Equation. It also creates a graph so that the designer can ascertain many different values at a glance. Alternatively values for partially full pipe flow can be estimated from published charts such as the one below.

Design

The CivilWeb Pipe Flow Calculator spreadsheet package includes a Manning Formula Design spreadsheet which makes designing drainage pipes easy. The designer specifies the pipe roughness, required flow and max and min values for the velocity. The spreadsheet then calculates which standard pipe sizes and gradients would be suitable to suit the design conditions. The designer can then choose a pipe size and gradient and the spreadsheet calculates the pipes max flow capacity and velocities at full conditions and for the design flow.

Limitations

The Manning Formula was derived empirically from a limited data set, it does not have the theoretical credentials of the Colebrook-White Equation. While the Manning Formula is a good approximation of the Colebrook-White Equation over the original data set, it cannot accurately estimate flow outside these conditions. The Manning Formula for pipe flow has shown to be useful in the following conditions;

• The relative roughness (R/k) is between 7 and 130.
• The flow should be fully turbulent, ie vk/v > 807.

Studies have shown that Manning’s Equation is suitable for certain pipe sizes and pipe roughnesses, but should not be extrapolated beyond the data set. The below table shows the limits of the Manning Formula’s usefulness.

It should also be noted that for storm drainage pipes with a Colebrook Roughness Coefficient value of 0.6mm, the Manning Equation has been shown to overestimate the pipes capacity, so use of the Manning Equation for storm drainage is not recommended.

Runoff Calculator Spreadsheet

This spreadsheet calculates the design runoff flow for a site in accordance with the a number of different methods including the Wallingford Procedure.

Full Drainage Design Suite

Full drainage design suite (50% Discount) including 6 spreadsheet suites;

• Pipe Flow Calculator
• Manning Open Channel Design
• Linear Drainage Design
• Runoff Calculator
• Attenuation Design
• Soakaway Design

Where to find Excel Spreadsheets for Watershed Time of Concentration

To obtain an Excel spreadsheet for watershed time of concentration calculations, click here to visit our spreadsheet store. Obtain a convenient, easy to use spreadsheet for watershed time of concentration calculation at a reasonable price. Read on for information about Excel spreadsheets that can be used for watershed time of concentration calculations.

The time of concentration for a watershed is the time for rainfall that lands on the farthest point of the watershed to reach the outlet. The main reason for interest in the watershed time of concentration is for its use as the storm duration in finding the design rainfall intensity to use in Rational Method calculation of peak storm water runoff rate.

The reason that the watershed time of concentration is used as design storm duration is because it gives the largest peak storm water runoff rate for a given return period. This can be reasoned out as follows: If the storm duration is less than the time of concentration, then the storm will end before runoff from the entire watershed reaches the outlet. Thus flow from the entire watershed will never all be contributing to the outflow. If the storm duration is greater than the time of concentration, then the storm will continue longer than it takes for the entire watershed to contribute to the outflow, but the storm intensity will be less for a storm of longer duration than one of short duration for a given return period. Thus the maximum peak storm water runoff rate for a specified return period on a given watershed will be for a storm with duration equal to the time of concentration of that watershed.

We can now move on to a discussion of how to calculate values for the time of concentration of a given watershed.

Methods for Estimating Watershed Time of Concentration

There are several empirical equations that have been developed for calculating travel time/time of concentration for different types and conditions of watersheds. Some examples are the Kerby equation, the Izzard equation, the Manning Kinematic equation, the Bransby Williams equation, the National Resources Conservation Service (NCRS) method, and the Manning equation. The following three equations will be discussed in this article: 1) the Manning Kinematic equation for use with overland sheet flow, 2) the NRCS method for shallow concentrated flow, and 3) the Manning equation for channel flow. These three methods are recommended by the U.S. Soil Conservation Service (SCS) in ref #1 at the end of this article. The Iowa Stormwater Management Manual (ref #2) also recommends these three methods. Typically overland sheet flow will occur in the upper portion of the watershed, followed by shallow concentrated flow, with channel flow for the final portion of watershed before the outlet.

Calculations with the Manning Kinematic Equation

The boxes at the right show the Manning Kinematic equation for U.S. and for S.I. units. The parameters in the Manning Kinematic equation and their units are as follows:

• t₁ = overland sheet flow runoff travel time, min (NOTE: many places show the constant being 0.007 for U.S. units giving the time in hours. The equations in the boxes both give travel time in minutes.)
• n = Manning roughness coefficient, dimensionless*
• L = length of flow path, ft (S.I. – m)
• P = 2 year, 24 hr rainfall depth, in (S.I. – m)
• S = ground slope, ft/ft (S.I. m/m)

*See table of n values below.

The screenshot of an Excel spreadsheet template shown below will calculate overland sheet flow travel time with U.S. units using the Manning kinematic equation, based on the input values entered for the other parameters listed above. A tables with values of the Manning roughness coefficient for various overland flow conditions is also given below. This Excel spreadsheet and others for time of concentration calculations are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

Watershed Time of Concentration Calculations with the NRCS Method

The Manning Kinematic equation is recommended for travel length of no greater than 300 ft in ref #1 and for no greater than 100 ft in ref #2. Both of these references recommend use of the NCRS method for the shallow concentrated flow that normally develops within 100 to 300 ft into the watershed. The NCRS method calculates the velocity of the shallow concentrated flow first, based on the slope and the type of surface. The travel time is then calculated as travel length divided by velocity of flow. The equations used for the NRCS method are:

• t₂= L/(60V) ( for either U.S. or S.I. units )
• V = 16.1345 S^0.5 for U.S. units ( V = 4.9178 S^0.5 for S.I. units) for an unpaved surface
• V = 20.3282 S^0.5 for U.S. units ( V = 6.1960 S^0.5 for S.I. units) for a paved surface

An explanation of each of the parameters used in these equations follows:

• L is the length of the flow path in ft for U.S. or m for S.I. units
• V is the velocity of flow in ft/sec for U.S. or m/s for S.I. units
• S is the slope of the flow path, which is dimensionless for either U.S. or S.I. units
• t₂ is the travel time for shallow concentrated flow in minutes (for either U.S. or S.I. units)

The screenshot of an Excel spreadsheet template shown at the left will calculate shallow concentrated flow travel time with S.I. units using the NRCS method, based on the input values indicated. This Excel spreadsheet and others for time of concentration calculations are available in either U.S. or S.I. units at a very low cost at www.engineeringexceltemplates.com or in our spreadsheet store.

Calculation of Travel Time with the Manning Equation

The Manning equation is used for quite a variety of open channel flow calculations. It is recommended in ref#1 and ref #2 for any channel flow portion of the watershed runoff path. The following equations are used for Manning equation calculations:

• The Manning equation in U.S. units: Q = (1.49/n)A(R^2/3)(S^1/2)
• The Manning equation in S.I. units: Q = (1.0/n)A(R^2/3)(S^1/2)
• R = A/P
• V = Q/A
• t₃= L/(60V)

An explanation of the parameters in these equations and their U.S. and S.I. units follows:

• Q = channel flow rate in cfs for U.S. units or m³/s for S.I. units
• V = average velocity of flow in ft/sec for U.S. units or m/s for S.I. units
• R = hydraulic radius of the channel (= A/P) in ft for U.S. units or m for S.I. units
• A = channel cross-sectional area in ft² for U.S. units or m² for S.I. units
• P = wetted perimeter of channel in ft for U.S. units or m for S.I. units
• S = channel bottom slope, which is dimensioness for either set of units
• n = Manning roughness coefficient for channel
• L = length of flow path in ft for U.S. units or m for S.I. units
• t₃ = travel time for channel flow in min for either set of units

The screenshot of an Excel spreadsheet template shown at the right will calculate channel flow travel time with U.S. units using the NRCS method, based on the input values indicated. This Excel spreadsheet and others for time of concentration calculations are available in either U.S. or S.I. units at a very low cost at www.engineeringexceltemplates.com or in our spreadsheet store.

The overall time of concentration can now be calculated as the sum of t₁, t₂ and t₃.

References:

Manning Excel Sheet

1. U.S. Soil Conservation Service, Technical Note – Hydrology No N4, June 17, 1986.

Google Spreadsheet

2. Iowa Stormwater Management Manual, Section on Time of Concentration.

3. Knox County Tennessee Stormwater Management Manual, section on the Rational Method.

Free Excel Spreadsheet

4.Bengtson, Harlan H., Hydraulic Design of Storm Sewers, Including the Use of Excel, an online, continuing education course for PDH credit.

5. Bengtson, Harlan H., “Spreadsheets for Rational Method Hydrological Calculations,” an Amazon Kindle e-book.