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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.

 


 

 

 


Activated Sludge Aeration Tank Design with Excel Spreadsheets

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Where to Find Spreadsheets for Activated  Sludge Aeration Tank Design

For Excel spreadsheets to use for activated sludge aeration tank design or operation calculations, click here to visit our spreadsheet store.  Get an easy to use spreadsheet to make a variety of activated sludge aeration tank design calculations for a very reasonable price. Read on for information about activated sludge aeration tank design and operation calculations.

The activated sludge process is widely used for biological wastewater treatment all over the world.  This method of biological wastewater treatment was invented in England in about 1914.  An activated sludge wastewater treatment system always has an aeration tank and secondary clarifier, which function as a unit to remove biodegradable organic matter (biochemical oxygen demand or BOD) and suspended solids from the wastewater and keep the aerobic microorganisms that carry out the treatment in the system.  Most types of activated sludge processes also have a primary clarifier that removes settleable solids from the incoming wastewater before it goes to the aeration tank.  A flow diagram for a typical activated sludge wastewater treatment plant is shown in the diagram below.  The diagram shows the typical flow pattern through the primary clarifier, aeration tank and secondary clarifier mentioned above, plus initial preliminary treatment (screening, flow measurement and grit removal) and disinfection, which is usually the final step in wastewater treatment.

diagram for activated sludge aeration tank design

This article will emphasize the equations, parameters, and calculations for design and operation of the aeration tank/secondary clarifier of an activated sludge plant.

Parameters for Activated Sludge Aeration Tank Design Calculations

Activated Sludge Aeration Tank Design Flow DiagramThe diagram at the left shows a typical flow pattern for a conventional activated sludge aeration tank and secondary clarifier.  Some of the parameters that are typically used in activated sludge aeration tank design calculations are shown for the primary effluent, secondary effluent, waste activated sludge, and recycle activated sludge. The following list shows those parameters, along with some others that are used for activated sludge calculations, with their U.S. and S.I. units.

  • primary effluent flow rate, Qo,  (MGD – U.S. or m3/day – S.I.)
  • primary effluent biochemical oxygen demand (BOD) concentration, So, (mg/L – U.S. or g/m3 – S.I.)
  • primary effluent suspended solids conc., Xo, (mg/L – U.S. or g/m3 – S.I.)
  • aeration tank volume, V, (ft3 – U.S. or m3 – S.I.)
  • aeration tank MLSS (suspended solids conc.), X, (mg/L – U.S. or g/m3 – S.I.)
  • secondary effluent flow rate, Qe,  (MGD – U.S. or m3/day – S.I.)
  • secondary effluent susp.solids conc., Xe, (mg/L – U.S. or g/m3 – S.I.)
  • secondary effluent biochemical oxygen demand (BOD) concentration, Se, (mg/L – U.S. or g/m3 – S.I.)
  • waste activated sludge flow rate, Qw, (MGD – U.S. or m3/day – S.I.)
  • waste activated sludge biochemical oxygen demand (BOD) conc., Sw, (mg/L – U.S. or g/m3 – S.I.)
  • waste activated sludge susp. solids conc., Xw (mg/L – U.S. or g/m3 – S.I.)
  • recycle activated sludge flow rate, Qr, (MGD – U.S. or m3/day – S.I.)
  • Food to Microorganism ratio, F:M, (lb BOD/day/lb MLVSS – U.S. or kg BOD/day/kg MLVSS – S.I.)
  • Hydraulic retention time, HRT, (hours for U.S or S.I.)
  • Sludge retention time (also called sludge age), SRT, (days for U.S. or S.I.)
  • Volumetric loading, VL, (lb BOD/day/1000 ft3 – U.S. or kg BOD/day/m3 – S.I.)
  • % volatile solids in the aeration tank mixed liquor suspended solids, %Vol.

Activated Sludge Aeration Tank Design Calculations with Excel Spreadsheets

The table below shows the typical range of values for three commonly used activated sludge aeration tank design parameters: volumetric loading, hydraulic retention time, and food to microorganism ratio. The table includes design information for three activated sludge variations: conventional plug flow, complete mix, and extended aeration activated sludge plants.

Activated Sludge Aeration Tank Design Parameters Table

The spreadsheet image below uses Excel formulas to calculate the required aeration tank volume based on values provided for the input parameters shown in the spreadsheet: primary effluent flow rate, Qo; primary effluent biochemical oxygen demand (BOD), So; Aeration tank MLSS, X; design volumetric loading, VL; and % volatile solids in the aeration tank, %Vol.  The Excel spreadsheet uses the input data to calculate the design value of aeration tank volume, V, and values for two other design parameters that are sometimes used to size the aeration tank, hydraulic retention time in the aeration tank, HRT, and food to microorganism ratio, F:M, using the following equations.

  • V = [ (8.34*So*Qo)/VL ] (1000)
  • VMG = V*7.48/1,000,000
  • HRT = 24*VMG/Qo
  • F:M = (8.34*So*Qo)/(8.34*%Vol*X*VMG)  =  (So*Qo)/(%Vol*X*VMG)

For Excel spreadsheets to make a variety of activated sludge aeration tank design and operation calculations in either U.S. or S.I. units for a very reasonable price, click here to visit our spreadsheet store.

Activated Sludge Aeration Tank Design Calculations Spreadsheet

Activated Sludge Aeration Tank Operational Calculations with Excel Spreadsheets

The table below shows typical ranges for several commonly used operational activated sludge waste water treatment process parameters. Note that the values for all of these parameters remain the same for U.S. or S.I. units.  MLSS concentration will have the S.I. unit of g/m3, which is numerically equal to the U.S. units of mg/L. SRT will have units of days for either the U.S. or S.I. system.  F:M will have the S.I. unit of kg BOD/day/kg MLVSS, which is numerically equal to the U.S. unit of lb BOD/day/lb MLVSS. The % unit for Qr/Qo remains the same for U.S. or S.I. units.

Activated Sludge Aeration Tank Design Operational ParametersThe Excel spreadsheet image shown below uses the input values to calculate the activated sludge operational parameters shown.  The input parameters required are: primary effluent information (flow rate, Qo; BOD, So; and TSS, Xo); TSS in the waste and recycle activated sludge streams, Xw; the aeration tank volume, V; aeration tank MLSS, X; % volatile solids in the MLSS, %Vol; and sludge retention time, SRT.

The activated sludge operational parameters calculated by the Excel formulas in the spreadsheet are: recycle activated sludge flow rate, Qr; waste activated sludge flow rate, Qw, and aeration tank food to microorganism ratio, F:M. The equations used are as follows:

  • Qr = (X – Xo)/(Xw – X)
  • VMG = V*7.48/1,000,000
  • Qw = (8.34*VMG*X)/(8.34*SRT*Xw)  =  (VMG*X)/(SRT*Xw)
  • F:M = (8.34*So*Qo)/(8.34*%Vol*X*VMG)  =  (So*Qo)/(%Vol*X*VMG)

For Excel spreadsheets to make a variety of activated sludge aeration tank design and operation calculations in either U.S. or S.I. units at a very reasonable price, click here to visit our spreadsheet store.

Activated sludge aeration tank design and operations spreadsheet

References

References for Further Information:

1. Metcalf & Eddy, Inc, (revised by Tchobanoglous, G, Burton, F.L., Stensel, H.D., Wastewater Engineering Treatment and Reuse, 4th Edition, New York, NY, 2003.

2. Vesilind, P.A. and Morgan, S.M., Introduction to Environmental Engineering, 2nd Edition, Belmont, CA, Brooks/Cole, 2004.

3. Grady, C.P.L., Daigger, G.T., Lim, H.C., Biological Wastewater Treatment, 2nd Edition, New York, NY, Marcel Dekker, Inc., 1999.

4. Bengtson, Harlan H. “Biological Wastewater Treatment Process Design Calculations,” available as an Amazon Kindle e-book and as a paperback.

5. Bengtson, Harlan H., “Activated Sludge Calculations Spreadsheet: Aeration Tank Calculations,” an Amazon Kindle e-book.