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Stor m Sewer Hydr au aul ic ic Cal cu cul at ati on ons with the Manni ng ng Eq Eq ua uati on on | En Eng in ineer in ing Ex Excel Spr ea eadsheets
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Storm Sewer Hydraulic Calculations with the Manning Equation Posted on March 5, 2011 by Harlan Bengts on
Introduction If you want to obtain an Excel spreadsheet to use for storm sewer hydraulic calculations, click here to visit our spreadsheet spreadshe et store store or or visit our companion site, www.enginee www.engineeringexceltemplates.com ringexceltemplates.com.. 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 between subsequent manholes. manholes. Although storm sewers 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 calculati calculations. ons. Storm sewer hydraulic hydraulic calculati ons are typically made for full pipe flow. flow. Under these conditions the hydraulic radius becomes: R = A/P = (πD (πD2 /4)/(πD) = D/4. The Manning Equation Applied to Full Pipe Flow The gene general ral form form of the Manning equation in terms terms of ve velo locity city is: V = (1.4 (1.49/n)( 9/n)(R R2/3 )(S1 /2 ) for for U.S. U.S. units and V = (1.0/n)( (1. 0/n)(R R2/3 )(S1/2 ) for for S.I. S.I. units. units. As noted noted above above,, R = D/4 D/4 for ful fulll pipe pipe flow, flow, so the Manning equation in U.S. U.S. units becomes V = (1.49/ (1.49/n)[ n)[(D/4) (D/4)2/3]( ](S S1 /2) -U.S. units or V or V = (1.0/n) (1.0/n)[(D [(D/4) /4)2/3](S1 /2) – S.I units, for full pipe, gravity flow in a storm sewer sewer pipe. The parameters in the equations are as follows follows:: V is 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 dimensionle dimensionless. ss. 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 /4)V )V , where Q will be in cfs for for U.S. units or m3/s for S.I. S.I. units. Calculation of Diameter and Slope for a Storm Sewer Pipe The required diameter di ameter and slope for 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 wat er runoff rate to the i nlet for that section of storm sewer and 2) the full pipe velocity must be equal to or greater than a specified specified minimum velocity. velocity. The diagram at the right shows a sectional view of a storm sewer pipe between two file:/ file:/// //Z:/ Z:/11 1110 10/4 /40 0 Calculat Calculation ions/4 s/40. 0.4 4 Mecha Mechanica nical/I l/Inf nfrast rastruct ructure ure Work Works/Re s/Refe feren rence ce/S /Sto torm rm Sew Sewer Hydra Hydraulic ulic Calculat Calculation ions s with the the Mannin Manning g Equa Equatio tion. n.ht htm m
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Stor m Sewer Hydr aul ic Cal cul ati ons with the Manni ng Eq uati on | Eng ineer ing Excel Spr eadsheets
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: Qdes = 6.4 cfs. The required minimum full pipe storm water velocity is: V mi n = 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: Qfull > Qdes and Vfu l l > Vmi n 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 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: Qfu l l = Vfu l l (πD2 /4). Substituting known values for Qfu ll and Vfu l l , 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 Qfu l l > 6.4 cfs, because Qfu l l = 6.4 cfs for Vfu ll = 3 ft/sec and D = 19.8″. With D = 21 ” and V = 3 ft/sec, Qfu l l 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 spreadsheet store or visit our companion site, www.engineeringexceltemplates.com. References 1. Bengtson, Harlan H., Hydraulic Design of Storm Sewers, Including the Use of Excel , an online, continuing education course for PDH credit. file:///Z:/1110/40 Calculations/40.4 Mechanical/Infrastructure Works/Reference/Storm Sewer Hydraulic Calculations with the Manning Equation.htm
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Stor m Sewer Hydr aul ic Cal cul ati ons with the Manni ng Eq uati on | Eng ineer ing Excel Spr eadsheets
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.
About Harlan Bengtson Dr. Bengtson has B.S. and M.S. degrees from Iowa State University and a PhD from the University of Colorado, all in Chemical Engineering. He is now retired after 30 years in engineering education, in teaching and administrative positions. His areas of expertise are environmental engineering, hydrology, engineering science and renewable energy. He is a licensed Professional Engineer in Missouri. He did consulting work while in academia and had prior industrial experie nce. Dr. Bengtson has authored numerous publications, presentations and technical reports. He is currently active as a technical writer. View all posts by Harlan Bengtson →
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