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Manning Equation Open Channel Flow Calculator Excel Spreadsheets

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Where to Find a Manning Equation Open Channel Flow Calculator Spreadsheet

To obtain a Manning equation open channel flow calculator excel spreadsheet, click here to visit our spreadsheet store.  Why use online calculators or make open channel flow/Manning Equation calculations by hand when you can buy a variety of Manning equation open channel flow calculator excel spreadsheets or spreadsheet packages for prices ranging from $6.95 to $27.95?  Read on for information about Excel spreadsheets that can be used as a Manning equation open channel flow calculator.

picture for a Manning equation open channel flow calculatorAn excel spreadsheet can conveniently be used as a Manning equation open channel flow calculator.  The Manning equation can be used for water flow rate calculations in either natural or man made open channels.  Uniform open channel flow calculations with the Manning equation use the channel slope, hydraulic radius,  flow depth, flow rate, and Manning roughness coefficient.   Image Credit: geograph.org.uk

Uniform Flow for a Manning Equation Open Channel Flow Excel Spreadsheet

Diagram for a Manning Equation Open Channel Flow Calculator SpreadsheetOpen channel flow may be either uniform flow or nonuniform flow, as illustrated in the diagram at the left.  For uniform flow in an open channel, there is always a constant volumetric flow of liquid through a reach of channel with a constant bottom slope, surface roughness, and hydraulic radius (that is constant channel size and shape).  For the constant channel conditions described, the water will flow at a constant depth (usually called the normal depth) for the  particular volumetric flow rate and channel conditions. The diagram above shows a stretch of uniform open channel flow, followed by a change in bottom slope that causes non-uniform flow, followed by another reach of uniform open channel flow.  The Manning Equation, which will be discussed in the next section, can be used only for uniform open channel flow.

Equation and Parameters for a Manning Equation Open Channel Flow Calculator Excel Spreadsheet

The Manning Equation is:

Q = (1.49/n)A(R2/3)(S1/2) for the U.S. units shown below, and it is:

Q = (1.0/n)A(R2/3)(S1/2) for the S.I. units shown below.

  • Q is the volumetric water flow rate in the reach of channel (ft3/sec for U.S.) (m3/s for S.I.)
  • A is the cross-sectional area of flow  (ft2for U.S.) (m2for S.I.)
  • P is the wetted perimeter of the flow  (ft for U.S.)  (m for S.I.)
  • R is the hydraulic radius, which equalsA/P(ft for U.S.) (m for S.I.)
  • S is the bottom slope of the channel, (dimensionless or ft/ft -U.S. & m/m – S.I.)
  • n is the empirical Manning roughness coefficient, which is dimensionless

The equation V = Q/A, a definition for average flow velocity, can be used to express the Manning Equation in terms of average flow velocity,V, instead of flow rate,Q, as follows:

V = (1.49/n)(R2/3)(S1/2) for U.S. units with V expressed in ft/sec.

Or V = (1.0/n)(R2/3)(S1/2) for S.I. units with V expressed in m/s.

It should be noted that the Manning Equation is an empirical equation.  The U.S. units must be just as shown above for use in the equation with the constant 1.49 and the S.I. units must be just as shown above for use in the equation with the constant 1.0.

The Manning Roughness Coefficient for a Manning Equation Open Channel Flow Calculator Excel Spreadsheet

Manning Equation Open Channel Flow Calculator Manning Roughness CoefficientsAll calculations with the Manning equation (except for experimental determination of n) require a value for the Manning roughness coefficient, n, for the channel surface.  This coefficient, n, is an experimentally determined constant that depends upon the nature of the channel and its surface.  Smoother surfaces have generally lower Manning roughness coefficient values and rougher surfaces have higher values. Many handbooks, textbooks and online sources have tables that give values of n for different natural and man made channel types and surfaces. The table at the right gives values of the Manning roughness coefficient for several common open channel flow surfaces for use in a Manning equation open channel flow calculator excel spreadsheet.

Example Manning Equation Open Channel Flow Excel Spreadsheet

The Manning equation open channel flow calculator excel spreadsheet shown in the image below can be used to calculate flow rate and average velocity in a rectangular open channel with specified channel width, bottom slope, & Manning roughness, along with the flow rate through the channel.  This Excel spreadsheet and others for Manning equation open channel flow calculations for rectangular, trapezoidal or triangular channels, in either U.S. or S.I. units are available for very reasonable prices in our spreadsheet store.

Manning Equation Open Channel Flow Calculator Excel Spreadsheet

References

1. Bengtson, Harlan H., Open Channel Flow I – The Manning Equation and Uniform Flow, an online, continuing education course for PDH credit.

2. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual.

3. Chow, V. T., Open Channel Hydraulics, New York: McGraw-Hill, 1959.

4.  Bengtson, Harlan H., “Manning Equation Open Channel Flow Excel Spreadsheets,”  an online blog article, 2012.

5. Bengtson, Harlan H., “The Manning Equation for Open Channel Flow Calculations“, available as an Amazon Kindle e-book and as a paperback.

Watershed Time of Concentration Calculation with an Excel Spreadsheet

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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

Manning kinematic equation for watershed time of concentration calculationThe 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.

n values for watershed time of concentration calculation
watershed time of concentration spreadsheet

 

 

 

 

 

 

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 S0.5 for U.S. units ( V = 4.9178 S0.5 for S.I. units) for an unpaved surface
  • V = 20.3282 S0.5 for U.S. units ( V = 6.1960 S0.5 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)

spreadsheet for watershed time of concentrationThe 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(R2/3)(S1/2)
  • The Manning equation in S.I. units: Q = (1.0/n)A(R2/3)(S1/2)
  • 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

watershed time of concentration spreadsheet2The 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:

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

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

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

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.

Partially Full Pipe Flow Calculator with Excel Spreadsheets

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Where to Find Partially Full Pipe Flow Calculator Spreadsheets

To obtain Excel spreadsheets for partially full pipe flow calculations, click here to visit our spreadsheet store  for partially full pipe flow calculator spreadsheets. Read on for information about Excel spreadsheets that can be used as a partially full pipe flow calculator.

The Manning equation can be used for flow in a pipe that is partially full, because the flow will be due to gravity rather than pressure.  the Manning equation [Q = (1.49/n)A(R2/3)(S1/2) for (U.S. units) or Q = (1.0/n)A(R2/3)(S1/2) for (S.I. units)] applies if the flow is uniform flow  For background on the Manning equation and open channel flow and the conditions for uniform flow, see the article, “Manning Equation/Open Channel Flow Calculations with Excel Spreadsheets.”

Graph for use with a partially full pipe flow calculatorDirect use of the Manning equation as a partially full pipe flow calculator, isn’t easy, however, because of the rather complicated set of equations for the area of flow and wetted perimeter for partially full pipe flow.  There is no simple equation for hydraulic radius as a function of flow depth and pipe diameter.  As a result graphs of Q/Qfull and V/Vfull vs y/D, like the one shown at the left are commonly used for partially full pipe flow calculations.  The parameters, Q and V in this graph are flow rate an velocity at a flow depth of y in a pipe of diameter D.  Qfull and Vfull can be conveniently calculated using the Manning equation, because the hydraulic radius for a circular pipe flowing full is simply D/4.

With the use of Excel formulas in an Excel spreadsheet, however, the rather inconvenient equations for area and wetted perimeter in partially full pipe flow become much easier to work with.  The calculations are complicated a bit by the need to consider the Manning roughness coefficient to be variable with depth of flow as discussed in the next section.

Is the Manning Roughness Coefficient Variable for Partially Full Pipe Flow Calculations?

Using the geometric/trigonometric equations discussed in the next couple of sections, it is relatively easy to calculate the cross-sectional area, wetted perimeter, and hydraulic radius for partially full pipe flow  with any specified pipe diameter and depth of flow.  If the pipe slope and Manning roughness coefficient are known, then it should be easy to calculate flow rate and velocity for the given depth of flow using the Manning Equation                             [Q = (1.49/n)A(R2/3)(S1/2)], right?   No, wrong!  As long ago as the middle of the twentieth century, it had been observed that measured flow rates in partially full pipe flow aren’t the same as those calculated as just described.  In a 1946 journal article (ref #1 below), T. R. Camp presented a method for improving the agreement between measured and calculated values for partially full pipe flow.  The method developed by Camp consisted of using a variation in Manning roughness coefficient with depth of flow as shown in the graph above.

Although this variation in Manning roughness due to depth of flow doesn’t make sense intuitively, it does work.  It is well to keep in mind that the Manning equation is an empirical equation, derived by correlating experimental results, rather than being theoretically derived.  The Manning equation was developed for flow in open channels with rectangular, trapezoidal, and similar cross-sections.  It works very well for those applications using a constant value for the Manning roughness coefficient, n.  Better agreement with experimental measurements is obtained for partially full pipe flow, however, by using the variation in Manning roughness coefficient developed by Camp and shown in the diagram above.

The graph developed by Camp and shown above appears in several publications of the American Society of Civil Engineers, the Water Pollution Control Federation, and the Water Environment Federation from 1969 through 1992, as well as in many environmental engineering textbooks (see reference list at the end of this article).  You should beware, however that there are several online calculators and websites with equations for making partially full pipe flow calculations using the Manning equation with constant Manning roughness coefficient, n.  The equations and Excel spreadsheets presented and discussed in this article use the variation in n that was developed by T.R. Camp.

Excel Spreadsheet/Partially Full Pipe Flow Calculator for Pipe Less than Half Full

Diagram to for Partially Full Pipe Flow CalculatorThe parameters used in partially full pipe flow calculations with the pipe less than half full are shown in the diagram at the right.  K is the circular segment area; S is the circular segment arc length; h is the circular segment height; r is the radius of the pipe; and θ is the central angle.

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 less than pipe radius, as shown below.

  • h = y
  • θ = 2 arccos[ (r – h)/r ]
  • A = K = r2(θ – sinθ)/2
  • P = S = rθ

The equations to calculate n/nfull, in terms of y/D for y < D/2 are as follows

  • n/nfull = 1 + (y/D)(1/3) for 0 < y/D < 0.03
  • n/nfull = 1.1 + (y/D – 0.03)(12/7) for 0.03 < y/D < 0.1
  • n/nfull = 1.22 + (y/D – 0.1)(0.6) for 0.1 < y/D < 0.2
  • n/nfull = 1.29 for 0.2 < y/D < 0.3
  • n/nfull = 1.29 – (y/D – 0.3)(0.2) for 0.3 < y/D < 0.5

The Excel template shown below can be used as a partially full pipe flow calculator to calculate the pipe flow rate, Q, and velocity, V, for specified values of pipe diameter, D, flow depth, y, Manning roughness for full pipe flow, nfull; and bottom slope, S, for cases where the depth of flow is less than the pipe radius.  This Excel spreadsheet and others for partially full pipe flow calculations are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

screenshot of partially full pipe flow calculator spreadsheet

Excel Spreadsheet/Partially Full Pipe Flow Calculator for Pipe More than Half Full

The parameters used in partially full pipe flow calculations with the pipe more than half full are shown in the diagram at the right.  K is the circular segment area; S is the circular segment arc length; h is the circular segment height; r is the radius of the pipe; and θ is the central angle.

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.

  • h = 2r – y
  • θ = 2 arccos[ (r – h)/r ]
  • A = πr2 – K = πr2 – r2(θ – sinθ)/2
  • P = 2πr – S = 2πr – rθ

The equation used for n/nfull for 0.5 < y//D < 1 is: n/nfull = 1.25 – [(y/D – 0.5)/2]

An Excel spreadsheet like the one shown above for less than half full flow, and others for partially full pipe flow calculations, are available in either U.S. or S.I. units at a very low cost at www.engineeringexceltemplates.com.

References

1. Bengtson, Harlan H.,  Uniform Open Channel Flow and The Manning Equation, an online, continuing education course for PDH credit.

2. Camp, T.R., “Design of Sewers to Facilitate Flow,” Sewage Works Journal, 18 (3), 1946

3. Chow, V. T., Open Channel Hydraulics, New York: McGraw-Hill, 1959.

4. Steel, E.W. & McGhee, T.J., Water Supply and Sewerage, 5th Ed., New York, McGraw-Hill Book Company, 1979

5.  ASCE, 1969. Design and Construction of Sanitary and Storm Sewers, NY

6. Bengtson, H.H., “Manning Equation Partially Filled Circular Pipes,”  An online blog article

7. Bengtson, H.H., “Partially Full Pipe Flow Calculations with Spreadsheets“, available as an Amazon Kindle e-book and as a paperback.

 


 

 

 


Storm Sewer Hydraulic Design with Excel Spreadsheets

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Where to Find Storm Sewer Hydraulic Design Spreadsheets

For storm sewer hydraulic design spreadsheets, click here to visit our spreadsheet store.  Read on for information about the use of Excel spreadsheets for storm sewer hydraulic design calculations with the Manning Equation.

One part of storm sewer hydraulic design is determination of the design pipe diameter and sewer slope for the storm sewer pipe between adjacent manholes.  Although storm sewers are circular pipes, the storm water typically flows under gravity, rather than as pressure flow, so the Manning equation for open channel flow can be used for the calculations.  A storm sewer hydraulic design spreadsheet typically makes hydraulic calculations for full pipe flow.  For full pipe flow, the hydraulic radius becomes: R = A/P = (πD2/4)/(πD) = D/4.

The Manning Equation in a Storm Sewer Hydraulic Design Spreadsheet

The general form of the Manning equation in terms of velocity is: V = (1.49/n)(R2/3)(S1/2) for U.S. units and  V = (1.0/n)(R2/3)(S1/2) for S.I. units.  As noted above, R = D/4 for full pipe flow, so the Manning equation in U.S. units becomes  V = (1.49/n)[(D/4)2/3](S1/2) -U.S. units or V = (1.0/n)[(D/4)2/3](S1/2) – S.I units, for full pipe, gravity flow in a storm sewer pipe.  The parameters in the equations are as follows:

  • V is the flow velocity in the pipe (ft/sec – U.S. and m/s – S.I.).
  • n is the Manning roughness coefficient, an empirical, dimensionless constant.
  • D is the pipe diameter (ft -U.S. and m – S.I.).
  • S is the pipe slope, which is dimensionless.

The volumetric flow rate is related to the other parameters through the equation Q = VA or, for a circular pipe flowing full:  Q = (πD2/4)V, where Q will be in cfs for U.S. units or m3/s for S.I. units.

Calculation of Diameter and Slope with a Storm Sewer Hydraulic Design Spreadsheet

Diagram for Storm Sewer Hydraulic Design SpreadsheetThe required diameter and slope for the length of storm sewer between two manholes can be calculated with a storm hydraulic sewer design spreadsheet using the equations presented in the last section (Mannings equation and Q = VA) together with the typical design criteria that 1) the full pipe flow rate that the pipe can carry must be at least equal to the design peak storm water runoff rate to the inlet for that section of storm sewer and 2) the full pipe velocity must be equal to or greater than a specified minimum velocity.  The diagram above shows a sectional view of a storm sewer pipe between two manholes and the parameters being discussed here. The calculation procedure is illustrated by the example in the next section.

Example Storm Sewer Hydraulic Design Calculations

Problem Statement: For a section of storm sewer between two manholes, the design flowrate is: Qdes = 6.4 cfs. The required minimum full pipe storm water velocity is: V min= 3 ft/sec.  The Manning roughness coefficient (concrete pipe) is: n = 0.011.  Find a standard pipe diameter and sewer slope that will meet the two criteria: Qfull > Qdes and Vfull > Vmin for this section of storm sewer pipe.

Problem Solution: First the pipe diameter needed for a full pipe velocity of 3 ft/sec at design flow rate will be calculated using the equation: Q = VA.   Then the Manning equation will be used to calculate the sewer slope needed to give full pipe velocity equal to 3 ft/sec with the next larger standard pipe size.

Step 1:  The equation, Q = VA becomes: Qfull = Vfull(πD2/4). Substituting known values for Qfull and Vfull, the equation becomes: 6.4 = 3(πD2/4).  Solving for D gives: D = 1.65 ft = 19.8 in.  From the list of standard storm sewer pipe sizes in the next section it can be seen that the next standard size larger than 19.8 inches is 21 “, so that will be used for the diameter.

The Manning equation will then be used to calculate the slope for D = 21 in. = 1.75 ft, and V = 3 ft/sec. The Manning equation is: V = (1.49/n)[(D/4)2/3](S1/2).  Substituting values for V, D, and n gives:  3 = (1.49/0.011)[(1.75/4)2/3](S1/2).  Solving this equation for S gives: S = 0.00148.

Thus, the solution is: D = 21″, S = 0.00148. These values of D and S will give Qfull > 6.4 cfs, because Qfull = 6.4 cfs for Vfull = 3 ft/sec and D = 19.8″. With D = 21 ” and V = 3 ft/sec, Qfull must be greater than 6.4 cfs. The equation Q = (πD2/4)V can be used to check this.

Standard Pipe Sizes

Standard U.S. pipe sizes in inches for most types of pipe used as storm sewers:                          4, 6, 8, 10, 12, 14, 16, 18, 21, 24, 27, 30, 33, 36, 39, 42, 48, 54, 60

Standard S.I. pipe sizes in mm for most types of pipe used as storm sewers:                           100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050

Use of Excel Spreadsheets for Storm Sewer Design Calculations

For information on making storm sewer calculations with Excel spreadsheets, see the related article: “Excel Spreadsheets for Storm Sewer Hydraulic Design.”  For low cost, easy to use spreadsheets for several types of storm water calculations, including storm sewer hydraulic design, click here to visit our spreadsheet store.

References

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

2. McCuen, Richard H., Hydrologic Analysis and Design, 2nd Ed, Upper Saddle River, NJ, Prentice Hall, 1998.

3. Steele, E.W. and McGhee, T.J., Water Supply and Sewerage, New York, NY, McGraw-Hill Book Co, 1979.

4. Bengtson, Harlan H., Hydraulic Design of Storm Sewers with a Spreadsheet,” an Amazon Kindle ebook

5. Bengtson, Harlan H., “Hydraulic Design of Storm Sewers with Excel”  an online blog article.

 

 

Hydraulic Radius Open Channel Flow Excel Spreadsheets

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Where to Find Spreadsheets for Hydraulic Radius Open Channel Flow Calculations

For an Excel spreadsheet to use for hydraulic radius open channel flow calculations, click here to visit our spreadsheet store.  Read on for information about hydraulic radius open channel flow calculations.

The hydraulic radius is an important parameter for open channel flow calculations with the Manning Equation.  Excel spreadsheets can be set up to conveniently make hydraulic radius open channel flow calculations for flow through common open channel shapes like those for a rectangular, triangular or trapezoidal flume.  Parameters like trapezoid area and perimeter and triangle area and perimeter are needed to calculate the hydraulic radius as described in the rest of this article.

The hydraulic radius for open channel flow is defined to be the cross sectional area of flow divided by the wetted perimeter.  That is: R = A/P, where A is the cross sectional area of flow, P is the portion of the cross sectional perimeter that is wetted by the flow, and R is the hydraulic radius.  The next several sections will present the equations to calculate A, P, and R for some common open channel shapes, and then discuss the use of Excel spreadsheets for hydraulic radius open channel flow calculations.

Hydraulic Radius Open Channel Flow Calculation for Rectangular Channels

hydraulic radius open channel flow diagram for rectangular channelRectangular channels are widely used for open channel flow, and hydraulic radius open channel flow calculations are quite straightforward for a rectangular cross section. The diagram at the left shows the depth of flow represented by the symbol, y, and the channel bottom width represented by the symbol, b.  It is clear from the diagram that A = by and P = 2y + b.  Thus the equation for the hydraulic radius is: R = by/(2y + b) for open channel flow through a rectangular cross section.


Hydraulic Radius Open Channel Flow Trapezoidal Flume Calculations

hydraulic radius open channel flow diagram for trapezoidal flumeThe trapezoid is probably the most common shape for open channel flow. Many man-made open channels are trapezoidal flumes, including many urban storm water arroyos in the southwestern U.S.  Also, many natural channels are approximately trapezoidal in cross section. The parameters typically used for the size and shape of a trapezoidal flume in hydraulic radius open channel flow calculations are shown in the diagram at the right. Those parameters, which are used to calculate the trapezoid area and wetted perimeter, are as follows:

  • y is the liquid depth (ft for U.S. & m for S.I.)
  • b is the bottom width of the channel (ft for U.S. & m for S.I.)
  • B is the width of the liquid surface (ft for U.S. & m for S.I.)
  • λ is the wetted length measured along the sloped side (ft for U.S. & m for S.I.)
  • α is the angle of the sloped side from vertical. The side slope also often specified as horiz:vert = z:1.

The common formula for trapezoid area,  A = y(b + B)/2, is a good starting point for obtaining a useful equation for A.  It can be seen from the diagram that B = b + 2zy, so the trapezoid area can be expressed in terms y, b, and z:  A = (y/2)(b + b + 2zy)

Simplifying gives: A = by + zy2.

The wetted perimeter can be expressed as: P = b + 2λ.  The typically unknown sloped length, λ, can be eliminated using the Pythagoras Theorem:

λ2= y2+ (yz)2, or λ = [y2+ (yz)2]1/2 Thus the wetted perimeter is:

P = b + 2y(1 + z2)1/2,   and the hydraulic radius for a trapezoid can be calculated from:

R = (by + zy2)/[b + 2y(1 + z2)1/2]

Hydraulic Radius Open Channel Flow Triangular Flume Calculations

hydraulic radius open channel flow diagram for triangular channelAnother shape used in open channel flow is the triangular flume, as shown in the diagram at the right. The side slope is the same on both sides of the triangle in the diagram.  This is often the case.  The parameters used for hydraulic radius open channel flow calculations with a triangular flume are as follows:

  • B is the surface width of the liquid (ft for U.S. & m for S.I.)
  • λ is the sloped length of the triangle side (ft for U.S. & m for S.I.)
  • y is the liquid depth measured from the vertex of the triangle (ft for U.S. & m for S.I.)
  • z is the side slope specification in the form:  horiz:vert = z:1.

The common formula for triangle area is: A = By/2.  As shown in the figure, however,

B = 2yz, so the triangle area simplifies to: A = y2z.

The wetted perimeter is: P = 2λ , but as with the trapezoidal flume:  λ2= y2+ (yz)2.

This simplifies to the convenient equation: P = 2[y2(1 + z2)]1/2

The hydraulic radius is thus: RH= A/P = y2z/{2[y2(1 + z2)]1/2}

Excel Spreadsheets for Hydraulic Radius Open Channel Flow Calculations

With the equations given in the previous sections, the hydraulic radius can be calculated for a rectangular, triangular or trapezoidal flume if appropriate channel size/shape parameters are known along with the depth of flow.  An Excel spreadsheet like the one shown in the image below, however, can make the the calculations very conveniently.  Excel spreadsheets like the one shown below for use as hydraulic radius open channel flow calculators for rectangular, triangular, and trapezoidal flumes, as well as for partially full pipe flow, are available in our spreadsheet store.

screenshot of hydraulic radius open channel flow Excel spreadsheet

References:

1. Bengtson, Harlan H., Open Channel Flow I – The Manning Equation and Uniform Flow, an online, continuing education course for PDH credit.

2. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual.

3. Chow, V. T., Open Channel Hydraulics, New York: McGraw-Hill, 1959.

4. Bengtson, Harlan H., “The Manning Equation for Open Channel Flow Calculations,” available as an Amazon Kindle e-book and as a paperback.