Where to Find an Energy Grade Line and Hydraulic Grade Line Calculation Spreadsheet

To obtain an energy grade line and hydraulic grade line calculation spreadsheet, click here to visit our spreadsheet store.  Intended for use in calculating and plotting HGL and EGL for up to 10 points of stormwater flow along a storm sewer line, you can buy a convenient spreadsheet to make HGL and EGL calculations and plots for a very reasonable price.  This spreadsheet is available in either U.S. or S.I. units.  Read on for information about a spreadsheet for calculating and plotting storm sewer hydraulic grade line and energy grade line.

Equations for Hydraulic Grade Line and Energy Grade Line

The equations for the Hydraulic Grade Line and Energy Grade Line (EGL) are:

Where:    HGL

HGL = hydraulic grade line in ft                EGL = energy grade line in ft

P = pressure in psf                                        γ = specific weight in lb/ft³

h = elevation in ft                                         V = velocity in ft/sec

g = acceleration of gravity in ft/sec²

Example Energy Grade Line and Hydraulic Grade Line Calculation Spreadsheet

An Energy Grade Line and Hydraulic Grade Line calculation spreadsheet is partially shown in the image below.  This Excel spreadsheet can be used to calculate and plot the hydraulic grade line and energy grade line for up to ten points of stormwater flow through a storm sewer. This Excel spreadsheet, as well as others for stormwater management calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Reference: 

1. Bengtson, Harlan H., Hydraulic Grade Line and Energy Grade Line Spreadsheet, An informational blog article

 Where to Find a Chicago Storm Hyetograph Generation Spreadsheet

To obtain a Chicago Storm Hyetograph Generation excel spreadsheet, click here to visit our spreadsheet store.  For use in stormwater management calculation, you can buy a convenient Chicago Storm Hyetograph generation excel spreadsheet for a very reasonable price?  This spreadsheet will generate a design storm hyetograph using the Chicago storm model, a triangular storm model or the "alternating blocks" procedure in either U.S. or S.I. units.  Read on for information about Excel spreadsheets that can be used for Chicago storm hyetograph generation.

Models for Design Storm Hyetograph Generation

Models for Design Storm Hyetograph Generation

Several different hyetograph models can be used for design storm hyetograph generation, including the Chicago storm, triangular, or rectangular (constant intensity design storm) models or the "alternating blocks" procedure for constructing a design storm hyetograph.  An initial step typically needed is the generation of an equation for storm intensity as a function of storm duration at the design location, for the design recurrence interval.

The Chicago Storm Hyetograph

The Chicago Storm Hyetograph

For example, the Chicago storm hyetograph model uses the equation at the left for the portion of the hyetograph before the peak storm intensity.  A slightly different equation is used for the portion of the design storm hyetograph that is after the peak storm intensity.  The resulting hyetograph has the general shape shown in the diagram at the right.  A user specified parameter is r, which is the fraction of the hyetograph that is before the point of peak storm intensity.  The triangular hyetograph model is similar in shape, but the lines before and after the peak storm intensity are straight instead of curved.

Example Chicago Storm Hyetograph Generation Excel Spreadsheet

Example Chicago Storm Hyetograph Generation Excel Spreadsheet

The Design Storm hyetograph generation excel spreadsheet partially shown in the image below can be used to generate a triangular or Chicago storm hyetograph as discussed above.  The portion shown is for generating an equation for storm intensity as a function of storm duration.  This Excel spreadsheet, as well as others for stormwater management calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

References

1. American Iron and Steel Institute, Modern Sewer Design, 4th Edition, 1999.

2. Bengtson, Harlan H., "Design Storm Hyetograph Generation Spreadsheet," an online informational blog article.

Chicago Storm Hyetograph Generation Spreadsheet

Where to Find a Chicago Storm Hyetograph Generation Spreadsheet

Scroll down for the following blog articles in this category:

• Detention Pond Routing with an Excel Spreadsheet
• Storm Sewer Hydraulic Calculations with Excel
• Calculation of Time of Concentration with an Excel Spreadsheet
• Hydrographs and Baseflow Separation

 Introduction

To obtain an Excel spreadsheet for carrying out detention pond routing calculations and plotting inflow and outflow hydrographs, click here to go to our download page.  Read on for information about the use of an Excel spreadsheet for storm water detention pond routing.

Overview

Detention pond routing is used to project an outflow hydrograph from a stormwaterdetention pond based on a given inflow hydrograph, stage-storage information for the pond, and stage-outflow information based on the outflow control device.  An output from the routing process is typically a plot of the inflow and outflow hydrographs similar to that shown at the right.  The outflow is often controlled by a rectangular weir, an orifice, and/or a pipe.  In some cases two-stage control is used with perhaps an orifice to provide outflow control for small storms and a weir to control the outflow rate from larger storms.  The routing process should be set up so that changes can be made in outflow control parameters and effects on the outflow hydrograph can then be observed.

Input Information Needed

In addition to an inflow hydrograph like that shown above, stage-storage and stage-outflow information is needed.  The stage-storage information would typically be in the form of a table, graph, or equation showing the pond volume, V, as a function of the pond depth, h.  The stage-outflow information is typically in the form of an equation for outflow, O, as a function of pond depth, h, based on the type of outflow control device, as described in the next section.

Stage-Outflow Equations

A rectangular weir is one possible outflow control device, often in a riser as shown in the diagram at the left.  The equation for pond outflow  is:     O = C_dL(h – P)^1.5 where the parameters in the equation are as follow:

• O = pond outflow = discharge over the rectangular weir in cfs for U.S. units (m³/s for S.I. units)
• C_d = the discharge coefficient for the weir.  Typical value for U.S. units is 3.3 (1.84 for S.I. units)
• L = weir length in ft for U.S. units (m for S.I. units)
• h = stage (depth of water in pond) in ft for U.S. units (m for S.I. units)
• P = height of weir crest above pond bottom in ft for U.S. units (m for S.I. units)

Equations like this are also available for an orifice outlet, two stage outlet, and pipe outlet.  These equations are given and used in the Excel spreadsheets for pond routing from our download page.

The Storage Indication Routing Equation

In addition to the input information described above, a routing equation is needed.  A commonly used routing equation is the Storage Indication Equation:

0.5(I₁ + I₂ )Δt  +  (S₁ – 0.5O₁Δt)  =  (S₂ + 0.5O₂Δt) Where:

• Δt is the time interval used for the inflow and outflow hydrographs in minutes
• I₁ and I₂ are successive values of the inflow from the inflow hydrograph (cfs - U.S. or m³/s - S.I.)
• S₁ is the initial value of pond storage (pond volume at the beginning of the storm in cfs - U.S. or m³/s - S.I.)
• O₁ is the initial outflow rate at the beginning of the storm in ft³ - U.S. or m³ - S.I.)
• S₂ and O₂ are the pond storage and outflow respectively at time Δt after the beginning of the storm in the same units shown above.

For a given inflow hydrograph, I₁, I₂ , and all subsequent values of inflow for the duration of the storm are known.  Thus if the initial pond volume, S₁, and initial pond outflow, O₁, are known, then all of the parameters on the left hand side of the equation are known so the value of the right hand side of the equation (S₂ + 0.5O₂Δt) can be determined.

Now comes the elegant part of the storage indication routing procedure.  As described above S vs h and O vs h must be available, in the form of tables, graphs or equations.  Thus for any value of h, the parameter, S + 0.5OΔt can be determined and values of S and Ocan be determined for a known value of S + 0.5OΔt.  Thus, by stepwise calculations, the outflow hydrograph (O vs t) can be obtained.

An Excel Spreadsheet as a Pond Routing Calculator

The Excel spreadsheet template shown below can be used to carry out the pond routing procedure described above.   Why bother to make these calculations by hand?  This Excel spreadsheet can handle rectangular weir, orifice, two-stage (orifice/weir), pipe outflow control, and two-stage (pipe/weir), and is available in either U.S. or S.I. units at a very low cost from our download page.  These spreadsheets also generate a table and graph showing the inflow and outflow hydrographs for a given set of input parameters.

References

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

 Introduction

If you want to obtain an Excel spreadsheet to use for storm sewer hydraulic calculations, click here to visit our download page.  Read on for information about the use of storm sewer hydraulic calculations with the Manning Equation.

One part of storm sewer hydraulic design is determination of the design diameter and slope for the storm sewer pipe between subsequent 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.  Storm sewer hydraulic calculations are typically made for full pipe flow.  Under these conditions the hydraulic radius becomes: R = A/P = (πD²/4)/(πD) = D/4.

The Manning Equation Applied to Full Pipe Flow

The general form of the Manning equation in terms of velocity is: V = (1.49/n)(R^2/3)(S^1/2) for U.S. units and  V = (1.0/n)(R^2/3)(S^1/2) 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](S^1/2) -U.S. units or V = (1.0/n)[(D/4)^2/3](S^1/2) - 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 for a Storm Sewer Pipe

The required diameter and slope for the length of storm sewer between two manholes can be calculated 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 at the right 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 Calculation of Pipe Diameter and Slope

Problem Statement: For a section of storm sewer between two manholes, the design flowrate is: Q_des = 6.4 cfs. The required minimum full pipe storm water velocity is: V _min= 3 ft/sec.  The pipe roughness coefficient (concrete pipe) is: n = 0.011.  Find a standard pipe diameter and pipe slope that will meet the two criteria: Q_full > Q_des and V_full > V_minfor 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 pipe 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: Q_full = V_full(πD²/4). Substituting known values for Q_full and V_full, 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](S^1/2).  Substituting values for V, D, and n gives:  3 = (1.49/0.011)[(1.75/4)^2/3](S^1/2).  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 Q_full > 6.4 cfs, because Q_full = 6.4 cfs for V_full = 3 ft/sec and D = 19.8". With D = 21 " and V = 3 ft/sec, Q_full 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 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 download page.

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

 Introduction to the Time of Concentration

Introduction

Learn about hydrographs and their use in hyrdologic analysis.  This includes how to carry out baseflow separation, how to create a unit hydrograph from a storm hydrograph, and how to predict the runoff from a given storm based on a unit hydrograph for the drainage area.

Hydrograph Definition

A hydrograph, as used in hydrology, is a graph or table of values showing the changes in flow rate over time at a point on a river or some other point of hydrologic interest.  Such points of interest for a hydrograph, other than a point on a river or stream, include locations such as the entrance to a storm water detention system or a storm water drainage outlet from a drainage area.  Hydrographs are commonly used to show flow patterns following a storm, thus providing information about the storm water runoff rate at the point of interest.

A storm hydrograph for a point on a river will typically have a gradually decreasing flow rate prior to a storm.  Then after the storm starts, the flow rate will gradually increase as storm water runoff from more and more of the drainage area reaches the river.  The flow rate (discharge) will typically increase to a peak value and then gradually decrease to the pre-storm level again, as shown in sample hydrograph in the figure at the right.  For the flow at an outlet from a drainage area, where there is no non-storm water flow, the hydrograph will start at zero flow prior to the storm and go back down to zero flow.

 The Parts of a Hydrograph - Baseflow Separation

The portion of the hydrograph between the point where it starts to rise to the peak is called the rising limb and the portion to the right of the peak is called the receding limb.

The area under a hydrograph represents the volume of runoff.  It can be considered to be made up of two parts: i) the normal flow that would have been present even if the storm hadn't occurred, called baseflow, and ii) the flow due to the storm, called direct runoff.  The direct runoff due to a storm is often of interest, so the baseflow component must be separated from it.

The diagram at the right illustrates three baseflow separation methods: i) the constant discharge method, ii) the constant slope method, and iii) the concave method.  The constant discharge method consists of simply extending a horizontal line from the point where the hydrograph begins to rise to its intersection with the receding limb.  The intersection with the receding limb for both the constant slope and concave methods is at the inflection point (where the receding limb changes from convex to concave).  The time from the peak to the inflection point of the receding limb is often approximated by N = A^0.2, as shown on the diagram, where A is the watershed area in sq mi, and N is time in days.

Excel templates for baseflow separation by the concave method are available from the download page of EngineeringExcelTemplates.com.