Author Archives: Harlan Bengtson

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 experience. Dr. Bengtson has authored numerous publications, presentations and technical reports. He is currently active as a technical writer.

Spreadsheets for Lime Soda Water Softening Calculations

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Where to Find Spreadsheets for Lime Soda Water Softening Calculations

For Excel spreadsheets to make lime soda water softening calculations, click here to visit our spreadsheet store.  Obtain convenient, easy to use spreadsheets for lime soda water softening calculations at reasonable prices. Read on for information about the use of Excel spreadsheets for this application.

Water Hardness Background for Lime Soda Water Softening

Hardness in water is caused by divalent cations, primarily Ca++ and Mg++.  Water hardness is sometimes classified in terms of the cation as calcium hardness or magnesium hardness.  The sum of the two is typically referred to as total hardness or simply hardness.  For lime soda water softening chemistry it is also necessary to have knowledge about the anions in the water.  Hardness due to Ca++ or Mg++ together with carbonate (CO3=) or bicarbonate (HCO3–) is called carbonate hardness.  At typical drinking water pH, the anion for carbonate hardness is almost completely bicarbonate.  Hardness due to Ca++ or Mg++ together with any anion other than carbonate/bicarbonate is called noncarbonate hardness.

The two most widely used methods for softening water (reducing hardness to an acceptable level) are lime soda water softening and ion exchange softening.  Ion exchange softening is typically used for groundwater softening and for home water softeners, while lime soda water softening is the usual method of choice for a surface water source.  This article is about lime soda water softening.

Lime Soda Water Softening Background

Lime soda softening uses addition of lime and soda ash to remove Ca++ and Mg++ ions, bringing their concentration down to an acceptable level.  The lime may be in the form of quicklime (CaO) or hydrated lime (Ca(OH)2), also called slaked lime.  Soda Ash is Na2CO3.  Calcium ions are removed be bringing the pH level up enough to convert Ca(HCO3)2 to CaCO3, which is relatively insoluble in water and precipitates out down to a residual level of about 30 to 40 mg/L.  Magnesium is precipitated out as Mg(OH)2.  Some lime soda softening processes require addition of carbon dioxide (recarbonation) at one or more points in the process to reduce the pH.

Lime Soda Water Softening Process Alternatives

Three common alternative processes for lime soda water softening are i) two-stage, excess lime treatment, ii) single-stage, selective calcium removal, and iii) split treatment.  Flow diagrams and a brief description of each follows.

Flow diagram for lime soda water softening with excess lime

The two-stage, excess lime softening process provides the most complete softening.  It is capable of removing calcium and magnesium carbonate and noncarbonate hardness, down to the solubility limits of about 30 to 40 mg/L of calcium hardness and about 10 mg/L of magnesium hardness.

Flow diagram for lime soda water softening with selective calcium removal

The single-stage, selective calcium removal process is suitable for water sources with 40 mg/L or less of magnesium hardness.  As indicated by its name, this process removes only calcium hardness and has no effect on magnesium hardness.  A suitably softened water should have less than 40 mg/L of magnesium hardness, so this is the limiting factor for use of this simpler process, which requires less chemicals.

Flow diagram for lime soda water softening with split treatment

The split treatment softening process illustrated in the diagram above is another alternative for water sources with more than 40 mg/L of magnesium hardness.  It is a two –stage process, but typically requires less chemicals than the excess lime process, and typically doesn’t require recarbonation.

Spreadsheets for Lime Soda Water Softening Calculations

There are logical choices (e.g. Is Alkalinity > Hardness or is Hardness > Alkalinity) in calculating the types of hardness in a water supply source.  Also there are logical choices and numerous equations used in calculating chemical dosages for lime soda water softening.  This makes a spreadsheet a very good vehicle for making lime soda water softening calculations.  The first spreadsheet screenshot below shows the type of spreadsheet calculations that can be made for identifying the types of hardness in a source water.  The second screenshot shows dosage calculations for a selective calcium removal softening process.  For low cost, easy to use spreadsheets to make these calculations as well as similar calculations for the excess lime and split treatment lime soda processes, in S.I. or U.S. units, click here to visit our spreadsheet store.

screenshot of lime soda water softening spreadsheetScreenshot - lime soda water softening spreadsheet

References

1.  Viessman, Warren., Jr & Hammer, Mark J., Water Supply and Pollution Control, 6th Ed., Addison Wesley, Menlo Park, CA, 1998

2. Bengtson, Harlan H., “Lime Soda Softening Process Calculations,” an Amazon Kindle ebook.

3. Bengtson, Harlan H., “Lime Soda Water Softening Calculations,”  an online, self-study, continuing education PDH course for Professional Engineers.

ISO 5167 Venturi Meter Calculations with Spreadsheets

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Where to Find ISO 5167 Venturi Meter Spreadsheets

For Excel spreadsheets to make ISO 5167 venturi meter calculations, click here to visit our spreadsheet store.  Obtain convenient, easy to use spreadsheets for ISO 5167 venturi meter calculations at reasonable prices. Read on for information about the use of Excel spreadsheets for venturi meter calculations.

How a Venturi Meter Works

Diagram for ISO 5167 Venturi meter calculationsVenturi meters function by sending pipe flow through a constricted area (the venturi throat), as shown in the diagram at the right.  Due to the increased fluid velocity passing through the constriction, there will be a decreased pressure at that location.   The pipe flow rate can then be calculated from the measured pressure difference between the undisturbed pipe flow and the flow through the constriction.

equation for ISO 5167 venturi meter calculationsA general equation for calculating flow rate through a venturi meter is shown at the left.  The parameters in the equation and their units are as shown below:

 

  • Q is the flow rate through the pipe and through the meter  (cfs – U.S. or m3/s – S.I.)
  • C is the discharge coefficient, which is dimensionless
  • A2 is the constricted area perpendicular to flow (calculated from the venturi throat diameter)  (ft2 – U.S. or m2 – S.I.)
  • P1 is the undisturbed upstream pressure in the pipe  (lb/ft2 – U.S. or N/m2 – S.I.)
  • P2 is the pressure in the pipe at the constricted area, Ao (lb/ft2 – U.S. or N/m2 – S.I.)
  • β = d/D = (diam. at A2/pipe diam.), which is dimensionless
  • ρ is the fluid density (slugs/ft3 – U.S. or kg/m3 – S.I.)

ISO 5167 Venturi Meter Guidelines

ISO 5167-4: 2003 provides discharge coefficient values for three venturi meter variations, subject to the venturi meeting a set of specifications and guidelines given in the publication.  The three venturi meter variations are i) “as cast” convergent section, ii) “machined” convergent section, and iii) “rough welded sheet iron” convergent section.  For each of these three variations, ISO 5167-4:2003 specifies a range for pipe diameter, diameter ratio (d/D), and Reynolds number in the pipe.

A Spreadsheet Screenshot for ISO 5167 Venturi Meter Calculations

The image below shows part of an Excel spreadsheet that can be used for ISO 5167 venturi meter calculations, such as flow rate calculation, discharge coefficient, pressure difference, or venturi throat diameter.  For this spreadsheet and other low cost, easy to use spreadsheets for gas flow or liquid flow ISO 5167 venturi meter calculations in S.I. or U.S. units, click here to visit our spreadsheet store.

screenshot of spreadsheet for ISO 5167 venturi meter calculations

 

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. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual, available for on-line use or download at: http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/index.htm

3. International Organization of Standards -Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full. Part 4, Reference number: ISO 5167-4:2003

4. Bengtson, Harlan H., “Orifice or Venturi Pipe Flow Meters: for Liquid Flow or Gas Flow,” an Amazon Kindle ebook.

5. Bengtson, Harlan H., “Flow Measurement in Pipes and Ducts,” an online, self-study, continuing education course for Professional Engineers at www.CEDengineering.com.

6. Bengtson, Harlan H., “Orifice and Venturi Meters Pipe Flow Meters – for Liquid and Gas Flow,” an online, self-study, continuing education course for Professional Engineers at www.suncam.com.

Activated Sludge Calculations in a Solids Mass Balance Spreadsheet

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Where to Find a Solids Mass Balance Spreadsheet for Activated Sludge Calculations

For Excel solids mass balance spreadsheets to make activated sludge calculations calculations, click here to visit our spreadsheet store.  Obtain a convenient, easy to use spreadsheet for solids mass balance activated sludge calculations for only $22.95. Read on for information about the use of an Excel spreadsheet for estimating the effect of recycle flow, BOD and TSS through solids mass balance activated sludge calculations.

Solids Mass Balance Background for Activated Sludge Calculations

Several streams from sludge treatment processes are typically recycled back into the wastewater treatment plant inflow.  Examples are sludge thickener overflow, anaerobic digester supernatant, aerobic digester supernatant, centrate from centrifuge dewatering, and filtrate from filtration dewatering.  The liquid flow, BOD load, and TSS load in these recycled streams contribute to the wastewater flow to be handled by the mainstream wastewater treatment processes.

An iterative solids mass balance is an organized procedure for estimating the total flow rate, BOD load, and TSS load in the recycled flows from sludge treatment and handling processes.  This type of calculation is illustrated in an eight page example in Metcalf and Eddy (Reference #1).  The flow diagram below shows a typical set of sludge treatment processes and recycle flows for an activated sludge plant.

Solids Flow Diagram for Activated Sludge Calculations


Activated Sludge Calculations Influent and Effluent Inputs for Spreadsheet

General information about the wastewater influent flow and characteristics will need to be input to the spreadsheet along with information about target effluent characteristics.  The screenshot below shows typical influent and effluent inputs needed.

Activated Sludge Calculations Solids Mass Balance Spreadsheet

Solids Mass Balance Activated Sludge Calculations for Each Treatment Process

The next step is solids mass balance calculations for each of the treatment processes, leading to estimates of the recycle flow rate, BOD load and TSS load for each recycle stream.  For a wastewater treatment plant with the flow diagram shown above, there would need to be solids mass balance calculations for the primary clarifier, the aeration tank/secondary clarifier, the sludge thickener, the anaerobic digester, and the sludge dewatering process.  The screenshot below shows typical inputs and outputs for a solids mass balance over a sludge thickener.

Screenshot thickener calculations - Activated Sludge Calculations

Similar calculations would be made for each of the wastewater treatment and sludge treatment/management processes, leading to information about recycle flow rate, BOD load, and TSS load, for each recycle stream as shown in the summary tables in the next section.  After completion of the first iteration, the recycle flowrate, BOD load and TSS load are added to values for those parameters for the incoming wastewater and all of the solids mass balance calculations are repeated in a second iteration.

Summary Tables

The screenshot below shows a set of tables summarizing the results of the calculated recycles flows from the first three iterations of the activated sludge calculations.   Spreadsheets are available to make this type of solids mass balance calculations in either U.S. or S.I. units at a very low cost (only $22.95) in our spreadsheet store.  These spreadsheets are set up to make the solids mass balance calculations for four iterations.

Summary Tables for Activated Sludge Calculations Solids Mass Balance

References

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. Bengtson, Harlan H.,  “Activated Sludge Solids Mass Balance Spreadsheet,”  an online blog article.

 

 

Hydraulic Jump Calculator Excel Spreadsheets

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Where to Find Hydraulic Jump Calculator Excel Spreadsheets

For an Excel spreadsheets to use as an open channel flow, hydraulic jump calculator, click here to visit our spreadsheet store.  Obtain a convenient, easy to use rectangular channel hydraulic jump calculator spreadsheet for only $14.95. Read on for information about the use of an Excel spreadsheet as a horizontal, rectangular channel hydraulic jump calculator.

Background for Hydraulic Jump Calculator

In order to discuss hydraulic jumps it’s necessary to talk about subcritical and supercritical flow.  In general subcritical flow takes place at low velocities and high flow depths, while supercritical flow occurs at high velocities and low flow depths.  For more details about critical, subcritical, and supercritical flow, see the article, “Open Channel Flow Spreadsheets – Critical Depth and Critical Slope.”  The diagram above shows supercritical flow on a steep slope, changing to subcritical flow on a mild slope.  As shown, the transition from supercritical flow to subcritical flow takes place with a hydraulic jump.  Whenever supercritical flow takes place on a slope that isn’t steep enough to maintain supercritical flow, the transition to subcritical flow will take place through the mechanism of a hydraulic jump as illustrated in the diagram.

Hydraulic Jump Calculator Parameters

Hydraulic jump calculations center on relationships among the supercritical conditions before the jump (upstream or initial conditions) and the subcritical conditions after the jump (downstream or sequent conditions).  The diagram at the left shows initial supercritical parameters and sequent subcritical parameters for a hydraulic jump.  The parameters and their typical units are summarized below:

  • y1 = the initial (upstream) depth of flow in ft for U.S. or m for S.I. units
  • V1 = the initial (upstream) liquid velocity in ft/sec for U.S. or m/s for S.I. units
  • E1 = the initial (upstream) head in ft for U.S. or m for S.I. units
  • y2 = the sequent (downstream) depth of flow in ft for U.S. or m for S.I. units
  • V2 = the sequent (downstream) liquid velocity in ft/sec for U.S. or m/s for S.I. units
  • E2 = the sequent (downstream) head in ft for U.S. or m for S.I. units
  • Q = the flow rate through the hydraulic jump in cfs for U.S. or m3/s for S.I. units
  • ΔE = the head loss across the hydraulic jump in ft for U.S. or m for S.I. units

An Excel Spreadsheet as a Hydraulic Jump Calculator

The Excel spreadsheet template shown below can be used to carry out hydraulic jump calculations.   Why bother to make these calculations by hand?  This Excel spreadsheet can calculate the sequent depth, sequent velocity, jump length, head loss across the jump, and hydraulic jump efficiency for specified initial depth, flow rate and channel width.  These spreadsheets are available in either U.S. or S.I. units at a very low cost (only $14.95 in our spreadsheet store.  These spreadsheets also have a tab for calculation of flow rate under a sluice gate and all of the equations used in the spreadsheet calculations are shown on the spreadsheets.

Note that some of the equations used in the spreadsheet calculations apply only for rectangular, horizontal channels, so the spreadsheets should be used only for channels that are at least approximately rectangular in cross-section and have a zero or very small slope.

References

1. Harlan H. Bengtson, “Hydraulic Jumps and Supercritical and Nonuniform Open Channel Flow,”  an online continuing education course for Professional Engineers.

2.  U.S. Department of Transportation, FHWA, Hydraulic Design of Energy Dissipators for Culverts and Channels, Hydraulic Engineering Circular No. 14, 3rd Ed, Chapter 6: Hydraulic Jump.

Activated Sludge Secondary Clarifier Design Spreadsheets

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Where to Find Activated Sludge Secondary Clarifier Design Spreadsheets

For an Excel spreadsheet for activated sludge secondary clarifier design calculations, click here to visit our spreadsheet store.  Obtain a convenient, easy to use primary and secondary clarifier design spreadsheets for only $11.95.  Read on for information about the use of an Excel spreadsheet for activated sludge secondary clarifier design calculations.

Activated Sludge Secondary Clarifier Design Parameters

Flow Diagram for Activated Sludge Secondary Clarifier DesignThe parameters typically used for activated sludge secondary clarifier design are the surface overflow rate (SOR), solids loading rate (SLR), and weir overflow rate (WOR).  Activated sludge parameters are shown in the flow diagram at the right.  The equations defining these three parameters are:

SOR = Qo/A,  SLR = (Qo + Qr)X/A, and  WOR = Qo/L,  where:

  • Qo = primary effluent flow rate in MGD (U.S.) or m3/d (S.I.)
  • A = total surface area for secondary clarifier(s) in ft2 (U.S.) or m2 (S.I.)
  • Qr = recycle activated sludge flow rate in MGD (U.S.) or m3/d (S.I.)
  • X = mixed liquor activated sludge solids concentration in mg/L (U.S. or S.I.)
  • L = length of secondary clarifier effluent weir in ft (U.S.) or m (S.I.)

Typical values of surface overflow rate and solids overflow rate for activated sludge secondary clarifier design are shown in the tables below:

Design Parameters for Activated Sludge Secondary Clarifier Design

Activated Sludge Secondary Clarifier Design Parameters

Calculation of Activated Sludge Secondary Clarifier Surface Area

The equation for calculating the needed activated sludge secondary clarifier surface area from a design SOR value with units as shown above is:  A = Qo*106/SOR

The formula for calculating activated sludge secondary clarifier surface area from a design value of SLR with parameter units as shown above is:  A = (Qo + Qr)*8.34*X/SLR

An Excel Spreadsheet as an Activated Sludge Secondary Clarifier Design Calculator

The Excel spreadsheet template shown below can be used to carry out the activated sludge secondary clarifier design calculations described above.   Why bother to make these calculations by hand?  This Excel spreadsheet can handle primary and secondary clarifier surface area calculations and determine diameter for circular clarifier(s) or length and width for rectangular clarifier(s) and is available in either U.S. or S.I. units at a very low cost (only $11.95)  in our spreadsheet store.  These spreadsheets also make weir overflow calculations to aid in effluent weir design.

screenshot of activated sludge secondary clarifier design spreadsheet

Reference

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.


Detention Pond Routing Spreadsheet Calculations

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Where to Find a Detention Pond Routing Spreadsheet

For detention pond routing spreadsheet to carry out routing calculations and plot inflow and outflow hydrographs, click here to visit our spreadsheet store.  Read on for information about the use of a storm water detention pond routing spreadsheet.


Overview Detention Pond Routing with a Spreadsheet

A detention pond routing spreadsheet is used to project an outflow hydrograph from a stormwater Inflow and Outflow Hydrographs from a Detention Pond Routing Spreadsheetdetention 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 for a Detention Pond Routing Spreadsheet

In addition to an inflow hydrograph like that shown above, stage-storage and stage-outflow information is needed for a detention pond routing spreadsheet.  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 for a detention pond routing spreadsheet

Detention Pond Routing Spreadsheet Weir Outlet DiagramA 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 = CdL(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)
  • Cd = 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 detention pond routing spreadsheet in either S.I. units or U.S. units in  our spreadsheet store.

The Storage Indication Routing Equation for Detention Pond Routing Spreadsheet Calculations

In addition to the input information described above, a routing equation is needed for a detention pond routing spreadsheet.  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 O can be determined for a known value of S + 0.5OΔt.  Thus, by stepwise calculations in a detention pond routing spreadsheet, the outflow hydrograph (O vs t) can be obtained.

An Excel Spreadsheet as a Pond Routing Calculator

The template shown below is a  detention pond routing spreadsheet to carry out the 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 in our spreadsheet store.  These spreadsheets also generates a table and graph showing the inflow and outflow hydrographs for a given set of input parameters.

screenshot of a detention pond routing spreadsheet

References

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

 

Minimum Pipe Wall Thickness Calculator Excel Spreadsheet

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Where to Find a Minimum Pipe Wall Thickness Calculator Spreadsheet

For an Excel spreadsheet to use as a minimum pipe wall thickness calculator, click here to visit our spreadsheet store.  Read on for information about the use of an Excel spreadsheet as a minimum pipe wall thickness calculator.

The Barlow Formula for a Minimum Pipe Wall Thickness Calculator

The classic Barlow formula for calculating bursting pressure for a pipe is:

P = 2S*T/Do where:

  • Do is the outside diameter of the pipe with units of inches (U.S.) or mm (S.I.)
  • S is the strength of the pipe material with units of psi (U.S.) or N/mm2 (S.I.)
  • T is the wall thickness with units of inches (U.S.) or mm (S.I.)
  • P is the fluid pressure in the pipe with units of psi (U.S.) or MPa (S.I.)

If the ultimate tensile strength of the pipe material is used for S, then P will be the bursting pressure, while P will be the pressure at which permanent deformation of the pipe begins if S is the yield strength of the material.

The Barlow formula can be rearranged to: T = /Do*P/2S to use in a minimum pipe wall thickness calculator for the pipe wall thickness for a given bursting pressure or deformation pressure.

Calculation of Maximum Pipe Operating Pressure

The Barlow formula can be modified to calculate the maximum fluid operating pressure for a given pipe wall thickness and pipe diameter, by incorporation of a safety factor and corrosion allowance as follows:

P = 2S*(T – Tc)/SF*Do

where  SF is a safety factor (dimensionless) and Tc is a corrosion allowance in inches (U.S.) or mm (S.I.).  This equation uses the outside pipe diameter in the calculations, which is convenient, because the outside pipe diameter remains the same for all of the schedules (wall thicknesses) for a given nominal pipe size.  The calculation can be done using the outside pipe diameter (Do) in an equation based on the inside pipe diameter, by using the relationship,  Di =  Do –  2T , to give the equation:

P = 2S*(T – Tc)/SF*(Do –  2T)

Use of Equations in a Minimum Pipe Wall Thickness Calculator

The last equation in the previous section can be rearranged to give a pipe wall thickness formula as follows:

T = (P* SF*Do + 2S*Tc)/(2S + 2P*SF)

An Excel Spreadsheet as a Minimum Pipe Wall Thickness Calculator

The Excel spreadsheet template shown below can be used as a minimum pipe wall thickness calculator or to calculate the maximum operating pressure in a pipe if the necessary other parameters are known/specified.   Why bother to make these calculations by hand?  This Excel spreadsheet and others for pipe flow calculations are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

Minimum Pipe Wall Thickness Calculator Spreadsheet


Spreadsheets for ISO 5167 Orifice Plate Flow Meter Calculations

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Where to Find Spreadsheets for ISO 5167 Orifice Plate Flow Meter Calculations

For Excel spreadsheets to make ISO 5167 orifice plate flow meter calculations, click here to visit our spreadsheet store.  Why use online calculators or try to use the incredibly long ISO 5167 equations for hand calculations when you can buy a spreadsheet for gas flow or liquid flow, large bore or small bore ISO 5167 orifice plate flow meter calculations for only $15.95 each. Read on for information about the use of an Excel spreadsheet for large bore and small bore orifice meter/gas flow rate or liquid flow rate calculations.


Orifice Meter Background for ISO 5167 Orifice Plate Flow Meter Calculations

ISO 5167 Orifice Plate Flow Meter DiagramFor background on orifice meters and the orifice meter coefficient, see the articles, “Excel Spreadsheets for Orifice and Venturi Flow Meter Calculations” and “Calculate an Orifice Coefficient with ISO 5167.”  The diagram at the left shows the general orifice meter configuration and some of the parameters used in calculations.  Equations from ISO 5167-2:2003 are presented in the next section.

Equations for ISO 5167 Orifice Plate Flow Meter Large Bore Calculations

Equation for ISO 5167 Orifice Plate Flow Meter Spreadsheet CalculationsThe equations for pipes with diameter between 2 in. and 40 in (50 mm to 1000 mm) are given in Reference #1 at the end of this article, ISO 5167-2:2003.  The equations are summarized here.  The commonly used equation for compressible fluid (gas) flow rate is shown at the right, where the parameters are defined as follows:

  • Q = flow rate through pipe and meter, cfs (m3/s for S.I. units)
  • Co = orifice discharge coefficient, dimensionless
  • Ao = orifice  area, ft2 (m2 for S.I. units)
  • P1 = upstream absolute pressure in the pipe, lb/ft2 (kN/m2 for S.I. units)
  • P2 = pressure at the downstream pressure tap, lb/ft2 (kN/m2 for S.I. units)
  • β = Do/D1 = orifice diam./pipe diam., dimensionless
  • Z = compressibility factor of the gas at P1, T1
  • R = Ideal Gas Law Constant = 345.23 psia-ft3/slugmole-oR                                         ( or 8.3145 kN-m/kgmole-oK for S.I. units)
  • MW = molecular weight of the gas
  • T1 = upstream absolute temperature in the pipe, oR (oK for S.I. units)
  • Y = Expansion Factor – see equation for Y below

Y  =  1  –  (0.351  +  0.265 β4 +  0.93 β8)[ 1 – (P2/P1)1/k ]

where:  k is the Specific Heat Ratio (Cp/Cv) of the flowing gas

The orifice coefficient, Co, can be calculated from the following equations:

Where Re is the Reynolds number in the pipe  ( Re  =  DVρ/μ )

An Excel Spreadsheet as an Orifice Meter/Gas Flow Calculator

The Excel spreadsheet template shown below can be used to calculate gas flow rate, required orifice diameter, or pressure difference across the orifice, if the other two are known.  This spreadsheet is for large bore pipes (2 in. to 40 in diameter) and uses S.I. units.   The image shows just the first page of the worksheet to calculate gas flow rate.  Why bother to make these calculations by hand?  This Excel spreadsheet and others with similar calculations for ISO 5167 orifice plate flow meter calculations are available in either U.S. or S.I. units at a very low cost (only $14.95 each) in our spreadsheet store.  There are also spreadsheets for large bore orifice meter calculations for liquid flow and for small bore orifice meter calculations (gas flow or liquid flow).  The small bore spreadsheets are for pipes with diameter between 1/2 inch and 1 1/2 inches (12 mm to 40 mm), and use slightly different equations from ASME MFC-14M:2001.

Screenshot of ISO 5167 Orifice Plate Flow Meter Excel Spreadsheet

References:

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

2. International Organization of Standards – Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full. Reference number: ISO 5167-2:2003.

4. Bengtson, Harlan H., “Orifice or Venturi Pipe Flow Meters: for Liquid Flow or Gas Flow,” an Amazon Kindle ebook.

5. Bengtson, Harlan H., “Flow Measurement in Pipes and Ducts,” an online, self-study, continuing education course for Professional Engineers at www.CEDengineering.com.

6. Bengtson, Harlan H., “Orifice and Venturi Meters Pipe Flow Meters – for Liquid and Gas Flow,” an online, self-study, continuing education course for Professional Engineers at www.suncam.com.

7. Bengtson, Harlan H. “Orifice Gas Flow Calculation Excel Spreadsheets,” an online blog article.


 

 

 

 

 

 

 

 

 

Storm Water Drain Inlet Calculations Spreadsheet

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Introduction

For a storm water drain inlet calculations spreadsheet, click here to visit our spreadsheet store.  Read on for information about storm water inlet design and Excel spreadsheets to do the calculations.

Design of storm water drain inlets is basically determining the size opening needed to handle the design peak storm water runoff rate, for the particular type of inlet opening.  The links above also have spreadsheets for calculating the peak storm water runoff rate with the Rational Method equation.

Types of Pavement Drain Inlets

stormwater drain inlet calculations spreadsheet curb inlet figureThe types of pavement drain inlets in common use include curb inlets, gutter inlets and combination inlets.  A curb inlet is just an opening in the curb as shown in the image at the stormwater drain inlet calculations spreadsheet gutter inlet figureleft.  A combination inlet has both a curb opening and a grate opening in the bottom of the gutter as shown in the image at the right.  Gutter inlets typically have a grate over the opening, while curb inlets are storm water drain inlet calculations spreadsheet depressed gutter inlettypically open without a grate, as shown in the pictures.  A sketch of a depressed gutter inlet is shown at the bottom left.

Curb Inlet Image Credit: Lone Star Manhole and Structures

Combination Inlet Image Credit: Robert Lawton – Wikimedia Commons

Depressed Gutter Inlet Image Credit:  H. H. Bengtson

The Weir Model for Sizing Storm Water Drain Inlets

The openings for storm water drains can be modeled as a weir if the opening isn’t completely submerged at the design storm water runoff flow rate.  For a curb opening this would be the case if the depth of storm water at the opening is less than the height of the opening.  For a gutter opening it would occur if the design flow rate of storm water runoff enters the grate around the edges, without completely submerging the opening.

The equation used to size storm drains with unsubmerged openings is theC sharp crested weir equation:  Q = CwLd1.5, where:

  • Q = the design storm water runoff rate that must flow through the inlet in cfs for U.S. or m3/s for S.I. units.
  • Cw = a weir coefficient, which is a dimensionless constant.  Typical values are 2.3 for U.S. units and 1.27 for S.I. units.
  • L = the length of the curb opening (or the length of the the gutter opening in the direction of the storm water flow), in ft for U.S. or m for S.I. units.
  • d = the depth of storm water above the bottom of the curb opening or its depth above the gutter inlet opening in ft for U.S. or m for S.I. units.

The Orifice Model for Sizing Storm Water Drain Inlets

The storm water drain opening can be modeled as an orifice if it will be completely submerged at design flow of storm water runoff.  This would be the case for a curb opening if the water depth is more than the height of the curb opening at design storm water flow.  A gutter opening could be modeled as a weir if the gutter opening is completely submerged at the design storm water runoff rate.  The equation used for sizing storm water inlets with the orifice model is:

Q = Co A(2gde)1/2 ,  where:

  • Q = the design storm water runoff rate that must flow through the inlet in cfs for U.S. or m3/s for S.I. units.
  • Co = the orifice coefficient, which is dimensionless.  The value typically used for storm water inlet design is 0.67.
  • A = the area of the inlet opening in ft2 for U.S. or m2 for S.I. units.
  • g = the acceleration due to gravity (32.2 ft/sec2 for U.S. or 9.82 m/s2 for S.I units).
  • de = the height of storm water above the centroid of the opening in ft for U.S. or m for S.I. units.

Note that de = d – h/2, for a curb opening, where d is the depth of storm water above the bottom of the opening and h is the height of the curb opening.  For a gutter opening,  de = d, where d is the height of storm water above the gutter opening at design storm water flow.

An Excel Spreadsheet as a Storm Water Drain Inlet Design Calculator

The Excel spreadsheet template shown below can be used to calculate the required size of a curb inlet for storm water drainage, based on specified information about the design storm water runoff rate, height of the curb opening, and the height of the storm water above the bottom of the opening.  Why bother to make these calculations by hand?  This Excel spreadsheet and others with similar calculations for a gutter opening are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

storm water inlet calculations spreadsheet

References:

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

2. ASCE. 1992. Design and Construction of Urban Stormwater Management Systems. The Urban Water Resources Research Council of the American Society of Civil Engineers (ASCE) and the Water Environment Federation. American Society of Civil Engineers, New York, NY.

3. Texas Department of Transportation/Online Hydraulic Design Manual/Storm Drain Inlets.

 


Heat Exchanger Thermal Design Calculations Spreadsheet

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Where to Find a Heat Exchanger Thermal Design Calculations Spreadsheet

For a double pipe heat exchanger thermal design calculations spreadsheet, click here to visit our spreadsheet store.  Read on for information about the use of a heat exchanger design thermal design calculations spreadsheet for a double pipe heat exchanger.

The Basic Equation for a Heat Exchanger Thermal Design Calculations Spreadsheet

The basic heat exchanger design equation is:  Q = U A ΔTlm,    where:

  • Q = the rate of heat transfer between the two fluids in the heat exchanger in But/hr (kJ/hr for S.I. units)
  • U is the overall heat transfer coefficient in Btu/hr-ft2–oF  (kJ/hr-m2-K for S.I. units)
  • A is the heat transfer surface area in ft2 (m2 for S.I. units)
  • ΔTlm is the log mean temperature difference in oF,  (K for S.I units)  calculated from the inlet and outlet temperatures of both fluids.

For a heat exchanger thermal design calculations spreadsheet, the heat exchanger equation can be used to calculate the required heat exchanger area for known or estimated values of the other three parameters, Q, U, and ΔTlm.  Each of those parameters will be discussed briefly in the next three sections.

The Log Mean Temperature Difference, ΔTlm , for a Heat Exchanger Design Spreadsheet

Equation for heat exchanger thermal design calculations spreadsheetThe driving force for a heat transfer process is always a temperature difference. For heat exchangers, there are always two fluids involved, and the temperatures of both are changing as they pass through the heat exchanger.  Thus some type of average temperature difference is needed.  Many heat transfer textbooks (e.g. ref #1 below) show double pipe heat exchanger diagram for heat exchanger thermal design calculations spreadsheetthat the log mean temperature difference is the appropriate average temperature difference to use for heat exchanger design calculations.  The definition of the log mean temperature difference is shown in the figure above.  The meanings of the four temperatures in the log mean temperature difference equation are rather self explanatory as shown in the diagram of a counterflow double pipe heat exchanger at the right.

The Heat Transfer Rate, Q, for a Heat Exchanger Thermal Design Calculations Spreadsheet

In order to use the heat exchanger design equation to calculate a required heat transfer area,  a value is needed for the heat transfer rate, Q.  This rate of heat flow can be calculated if the flow rate of one of the fluids is known along with its specific heat and the required temperature change for that fluid. The equation to be used is shown below for both the hot fluid and the cold fluid:

Q = mH CpH (THin – THout) = mC CpC (TCout – TCin), where

  • mH is the mass flow rate of the hot fluid in slugs/hr (kg/hr for S.I. units).
  • CpH is the specific heat of the hot fluid in Btu/slug-oF (kJ/kg-K for S.I. units).
  • mC is the mass flow rate of cold fluid in slugs/hr (kg/hr for S.I. units).
  • CpC is the specific heat of the cold fluid in Btu/slug-oF (kJ/kg-K for S.I. units).
  • The temperatures (THin, THout, TCout, & TCin) are the hot and cold fluid temperatures going in and out of the heat exchanger, as shown in the diagram above.  They should be in oF for U.S. or K for S.I. units.

The heat transfer rate, Q, can be calculated in a preliminary heat exchanger design spreadsheet if the flow rate, heat capacity and temperature change are known for either the hot fluid or the cold fluid. Then one unknown parameter can be calculated for the other fluid.  (e.g. the flow rate, the inlet temperature, or the outlet temperature.)

The Overall Heat Transfer Coefficient, U, for a Heat Exchanger Design Spreadsheet

The overall heat transfer coefficient, U, depends on the convection coefficient inside the pipe or tube, the convection coefficient on the outside of the pipe or tube, and the thermal conductivity of the pipe wall.  See the article, Forced Convection Heat Transfer Coefficient Calculations, for information about calculating the heat transfer coefficients and click here to visit our spreadsheet store, for spreadsheets to calculate the inside and outside convection coefficients and to calculate the overall heat transfer coefficient.

A Heat Exchanger Thermal Design Calculations Spreadsheet

The screenshot below shows a heat exchanger thermal design calculations spreadsheet that can be used to carry out thermal design of a double pipe heat exchanger.  The image shows only the beginning of the calculations.  The rest of the spreadsheet will calculate the length of pipe needed, the length of each pass for a selected number of 180 degree bends, and the pressure drop through the inside of the pipe.  Why bother to make these calculations by hand?  This Excel spreadsheet is available in either U.S. or S.I. units at a very low cost at in our spreadsheet store.

Heat Exchanger Thermal Design Calculations Spreadsheet

References

1. Kuppan, T., Heat Exchanger Design Handbook, CRC Press, 2000.

2. Kakac, S. and Liu, H., Heat Exchangers: Selection, Rating and Thermal Design, CRC Press, 2002.

3. Bengtson, H., Fundamentals of Heat Exchangers, an online, continuing education course for PDH credit.

4. Bengtson, H., Thermal Design of a Double Pipe Heat Exchanger, and online blog article.