Tag Archives: hydraulic radius

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.

Critical Depth Open Channel Flow Spreadsheet

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Where to Find a Critical Depth Open Channel Flow Spreadsheet

To obtain a critical depth open channel flow spreadsheet for calculating critical depth and/or critical slope for open channel flow, click here to visit our spreadsheet store.  Read on for information about the use of a critical depth open channel flow spreadsheet for critical depth and critical slope calculations.

The Froude Number and Critical, Subcritical and Supercritical Flow

Any particular example of open channel flow will be critical, subcritical, or supercritical flow.  In general, supercritical flow is characterized by high liquid velocity and shallow flow, while subcritical flow is characterized by low liquid velocity and relatively deep flow.  Critical flow is the dividing line flow condition between subcritical and supercritical flow.

The Froude number is a dimensionless number for open channel flow that provides information on whether a given flow is subcritical, supercritical or critical flow.  The Froude number is defined to be:  Fr = V/(gL)1/2 , where V is the average velocity, g is the acceleration due to gravity, and L is a characteristic length for the particular type of open channel flow.  For flow in a rectangular channel:  Fr = V/(gy)1/2 ,   where y is the depth of flow.  For flow in an open channel with a shape other than rectangular:  Fr = V/[g(A/B)]1/2 , where A is the cross-sectional area of flow, and B is the surface width.

The value of the Froude number for a particular open channel flow situation gives the following information:

  • For Fr < 1, the flow is subcritical
  • For Fr = 1, the flow is critical
  • For Fr > 1, the flow is supercritical

Calculation of Critical Depth

It is sometimes necessary to know the critical depth for a particular open channel flow situation.  This type of calculation can be done using the fact that Fr = 1 for critical flow.  It is quite straightforward for flow in a rectangular channel and a bit more difficult, but still manageable for flow in a non-rectangular channel.

For flow in a rectangular channel (using subscript c for critical flow conditions), Fr = 1 becomes:   Vc/(gyc)1/2 = 1.  Substituting Vc =  Q/Ac =  Q/byc and  q = Q/b  (where b = the width of the rectangular channel), and solving for yc gives the following equation for critical depth: yc =  (q2/g)1/3.   Thus, the critical depth can be calculated for a specified flow rate and rectangular channel width.

For flow in a trapezoidal channel, Fr = 1 becomes:  Vc/[g(A/B)c]1/2 = 1.  Substituting the equation above for Vc together with Ac =  yc(b + zyc)    and   Bc =  b  +  zyc2 leads to the following equation, which can be solved by an iterative process to find the critical depth:

Critical Depth Open Channel Flow Spreadsheet Formula1

Calculation of Critical Slope

After the critical depth, yc ,  has been determined, the critical slope, Sc , can be calculate using the Manning equation if the Manning roughness coefficient, n, is known.  The Manning equation can be rearranged as follows for this calculation:

Critical Depth Open Channel Flow Spreadsheet Formula2Note that Rhc , the critical hydraulic radius, is given by:

Rhc =  Ac/Pc,  where Pc =  b  +  2yc(1 + z2)1/2

Note that calculation of the critical slope is the same for a rectangular channel or a trapezoidal channel, after the critical depth has been determined.  The Manning equation is a dimensional equation, in which the following units must be used:  Q is in cfs, Ac is in ft2, Rhc is in ft, and Sc and n are dimensionless.

Calculations in S.I. Units

The equations for calculation of critical depth are the same for either U.S. or S.I. units.  All of the equations are dimensionally consistent, so it is just necessary to be sure that an internally consistent set of units is used.  For calculation of the critical slope, the S.I. version of the Manning equation must be used, giving:

Critical Depth Open Channel Flow Spreadsheet Formula4In this equation, the following units must be used:  Q is in m3/s, Ac is in m2, Rhc is in m, and Sc and n are dimensionless.

A Critical Depth Open Channel Flow Spreadsheet Screenshot

The critical depth open channel flow spreadsheet template shown below can be used to calculate the critical depth and critical slope for a rectangular channel with specified flow rate, bottom width, and Manning roughness coefficient.  Why bother to make these calculations by hand?  This Excel spreadsheet and others with similar calculations for a trapezoidal channel are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

Critical Depth Open Channel Flow Spreadsheet Screenshot

References

1. Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

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

3. Bengtson, Harlan H. Open Channel Flow II – Hydraulic Jumps and Supercritical and Nonuniform Flow – An online, continuing education course for PDH credit.

 

 

 

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.