Tag Archives: Darcy Weisbach equation

Partially Full Pipe Flow Viscous Liquid Spreadsheet

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Where to Find a Partially Full Pipe Flow Viscous Liquid Spreadsheet

To obtain a Partially Full Pipe Flow Viscous Liquid Spreadsheet, click here to visit our spreadsheet store.  This Excel spreadsheet is intended for calculating the flow rate. required diameter, depth of flow, or pipe slope for partially full flow of a viscous liquid in a circular pipe . You can buy a convenient partially full pipe flow viscous liquid spreadsheet for a very reasonable price.  It is available in either U.S. units or S.I. units.  Read on for background information about a partially full pipe flow viscous liquid spreadsheet

Background for a Partially Full Pipe Flow Viscous Liquid Spreadsheet

For information about making calculations for partially full flow of water in a circular pipe, see the post, Partially Full Pipe Flow Calculations Spreadsheet .   That post describes the use of the Manning Equation, which can only be used for the flow of water.  For flow of a liquid with viscosity and/or density different from water, the Darcy-Weisbach Equation should be used.  The parameters and equations for calculating them for partially full pipe flow are shown in the diagram below for flow at a depth greater than the pipe diameter.

Partially Full Pipe Flow Viscous Liquid Spreadsheet Diagram           Figure 1. Parameters and Equations for More Than Half Full Flow

The definition of hydraulic radius and the Darcy-Weisbach equation as applied to partially full pipe flow are shown below.

Partially Full Pipe Flow Viscous Liquid Spreadsheet Equations

 Example Partially Full Pipe Flow Viscous Liquid Spreadsheet

An example partially full pipe flow viscous liquid spreadsheet is partially shown in the image below.  .  This Excel spreadsheet can be used to calculate the pipe flow rate, required diameter, depth of flow or pipe slope for partially full pipe flow of a viscous liquid.   This Excel spreadsheet, as well as others for pipe flow and open channel flow calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Partially Full Pipe Flow Viscous Liquid Spreadsheet ScreenshotReferences

1. Bengtson, Harlan H.,  Uniform Open Channel Flow and The Manning Equation, an online, continuing education course for PDH credit.

2. Steel, E.W. & McGhee, T.J., Water Supply and Sewerage, 5th Ed., New York, McGraw-Hill Book Company, 1979

3. Bengtson, H.H., “Manning Equation Partially Filled Circular Pipes,”  An online blog article

4. Bengtson, H.H., “Partially Full Pipe Flow Calculations with Spreadsheets“, available as an Amazon Kindle e-book and as a paperback.

Flow Through Non Circular Ducts Spreadsheet

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Where to Find a Spreadsheet for Flow Through Non Circular Ducts

To obtain a spreadsheet for  flow through non circular ducts, click here to visit our spreadsheet store.  Intended for use in calculating flow rate or frictional head loss and frictional pressure drop, you can buy a convenient spreadsheet for  flow through non circular ducts calculations for a very reasonable price.  This spreadsheet makes calculations with the Hagen Poiseuille equation for laminar flow and with the Moody friction factor and the Darcy Weisbach equation for turbulent flow for flow through an annulus and for flow through a rectangular duct.  Turbulent flow calculations can be made for a general non-circular duct with known cross-sectional area and wetted perimeter.  It is available in either U.S. or S.I. units.  Read on for information about a spreadsheet for flow through a non circular duct calculations.

Turbulent Flow Through Non Circular Ducts

The Moody friction factor is used in the Darcy Weisbach equation for turbulent flow through non circular ducts.  The Darcy Weisbach equation is:

Flow Through Non Circular Ducts Equation

Where the hydraulic diameter is used for D in the Darcy Weisbach equation for flow through non circular ducts.  For further discussion of the Moody friction factor and its use in the Darcy Weisbach equation for pipe flow calculations, see the post, “Pipe Flow-Friction Factor Calculations with Excel Spreadsheets.”

Laminar Flow Through Non Circular Ducts

For laminar flow in an annulus or laminar flow in a rectangular duct, the Hagen Poiseuille equation should be used.  For flow through an annulus, it is:

Flow Through Non Circular Ducts Laminar Equations

Hagen Poiseiulle equations for laminar flow through an annulus

 

 Example Spreadsheet for Flow Through Non Circular Ducts

A spreadsheet for flow through non circular ducts calculations is partially shown in the image below.  This Excel spreadsheet can be used to calculate the frictional pressure drop and head loss or flow rate for flow through an annulus (laminar or turbulent flow), flow through a rectangular duct (laminar or turbulent flow) or flow through a general non circular duct (turbulent flow only).  This Excel spreadsheet, as well as others for pipe flow calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Flow Through Non Circular Ducts - Annulus

 Reference:

1. Bengtson, Harlan, “Pressure Drop in a Non Circular Duct”, an online blog article

Spreadsheets for Turbulent and Laminar Flow in Pipes

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Where to Find a Spreadsheet for Turbulent and Laminar Flow in Pipes

To obtain a spreadsheet for  Turbulent and Laminar flow in pipes, click here to visit our spreadsheet store.  Intended for use in calculating pipe flow rate, frictional head loss, or required pipe diameter, you can buy a convenient spreadsheet for turbulent or laminar flow in pipes calculations for a very reasonable price.  This spreadsheet makes calculations with the Hagen Poiseuille equation for laminar flow and with the Moody friction factor and the Darcy Weisbach equation for turbulent flow.  It is available in either U.S. or S.I. units.  Read on for information about a spreadsheet for turbulent and laminar flow in pipes calculations.

The Reynolds Number Criterion for Turbulent and Laminar Flow in Pipes

For flow in pipes, the Reynolds number is:  Re  =  DVρ/μ, for any consistent set of units for pipe diameter, D, flow velocity, V, fluid density, ρ, and fluid viscosity, μ.  Pipe flow will be turbulent if the Reynolds number is greater than 4000 and will be laminar if the Reynolds number for the flow is less than 2300.  If the Reynolds number is between 2300 and 4000, the flow may be either laminar or turbulent, depending on factors such as the type of pipe entrance and the roughness of the pipe wall.

Equations for Turbulent and Laminar Flow in Pipes

For discussion of the Moody friction factor and its use in the Darcy Weisbach equation for turbulent pipe flow calculations, see the post, “Pipe Flow-Friction Factor Calculations with Excel Spreadsheets.”  For laminar flow in pipes, the Hagen Poiseuille equation is as follows:             ΔP  =  8μLQ/(Πr4 ),  where  ΔP is the frictional pressure drop in lb/ft2, μ is the fluid viscosity in lb/ft-sec, L is the length of the pipe in ft, Q is the flow rate through the pipe in cfs, and r is the pipe radius in ft.  Note that the Hagen Poiseulle equation is identical with the Darcy Weisbach equation for pipe flow with the Moody friction factor equal to 64/Re.

 Example Spreadsheet for Turbulent and Laminar Flow in Pipes Calculations

A spreadsheet for Turbulent and Laminar Flow in Pipes calculations is partially shown in the image below.  This Excel spreadsheet can be used to calculate the frictional pressure drop and head loss for known pipe flow rate, diameter and length along with fluid density and viscosity and the pipe wall roughness.  It can also be used to calculate pipe flow rate or minimum required pipe diameter if the other parameters are known.  This Excel spreadsheet, as well as others for pipe flow calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

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. Darcy Weisbach equation history – http://biosystems.okstate.edu/darcy/DarcyWeisbach/Darcy-WeisbachHistory.htm

3. Bengtson, Harlan H.  Pipe Flow Calculations with the Darcy Weisbach Equation,  An online blog article.

4. Bengtson, H.H., Pipe Flow/Friction Factor Calculations with Excel, an online continuing education course for Professional Engineers.

5. Bengtson, Harlan, “Advantages of Spreadsheets for Pipe Flow/Friction Factor Calculations“, An Amazon Kindle e-book.

Natural Gas Pipeline Flow Calculation Spreadsheet

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Where to Find a Natural Gas Pipeline Flow Calculation Spreadsheet

To obtain a natural gas pipeline flow calculation spreadsheet , click here to visit our spreadsheet store.  Intended for use in making natural gas pipeline design calculations, you can buy a convenient natural gas pipeline flow calculation spreadsheet for a very reasonable price.  This spreadsheet makes calculations with the Weymouth equation, the Panhandle A equation, and the Panhandle B equation, and is available in either U.S. or S.I. units.  Read on for information about a natural gas pipeline flow calculation spreadsheet.

Choice of Equations for Natural Gas Pipeline Flow Calculations

Several different equations are used for natural gas pipeline flow calculations.  If the pressure drop across the pipe is less than 40 % of the average pipeline pressure, then the Darcy Weisbach equation is a possibility.  For longer pipelines with larger pressure drop, the three equations that are in most common use are the Weymouth equation, the Panhandle A equation, and the Panhandle B equation.  The choice among these three equations depends upon the pipeline diameter, the pipe length, and the average pipeline pressure.

The Weymouth Equation for Natural Gas Pipeline Flow Calculations

The Weymouth equation was the first of the three to be developed and was the first equation for natural gas pipeline flow calculations that didn’t require an iterative calculation to get a value for the friction factor.  The Weymouth equation is:

Where:

  • Q is the natural gas pipeline flow rate in SCFD
  • E is the pipeline efficiency
  • Tb is the base temperature in oR
  • Pb is the base pressure in psia
  • P1 is the inlet pressure in psia
  • P2 is the outlet pressure in psia
  • G is the specific gravity of the natural gas relative to air
  • Tf is the pipeline temperature of the flowing natural gas in oR
  • L is the pipeline length in miles
  • Le  is the effective pipeline length in  miles
  • ΔH is the height of the pipeline exit above the pipeline inlet in ft
  • Z is the compressibility factor of the natural gas at pipeline T & P
  • D is the pipeline diameter in inches.

Example Spreadsheet for Natural Gas Pipeline Flow Calculations

A spreadsheet for Natural Gas Pipeline Flow Calculations is partially shown in the image below.  It can be used to calculate the natural gas pipeline flow rate with the Weymouth equation, the Panhandle A equation and the Panhandle B equation.  This Excel spreadsheet, as well as others for pipe flow calculations, is available in either U.S. or S.I. units for a very reasonable price in our spreadsheet store.

Natural Gas Pipeline Flow Calculation

 

References for Further Information:

1. Crane Co.,  (1988),  “Flow of Fluids through Valves, Fittings and Pipes,  Technical Paper 401.

2.  GPSA  (Gas Processors Suppliers Association),  (1988),  Engineering Data Book, 11th Ed.

3. Bengtson, Harlan H., (2016), “Natural Gas Pipeline Flow Calculations,”  available as a paperback book or as an Amazon Kindle ebook.

4.  Bengtson, Harlan H.,  (2017),   “Pipe Flow/Friction Factor Calculations with Spreadsheets“,  available as a paperback book or as an Amazon kindle e-book.

5. Bengtson, Harlan H., (2014),  “Natural Gas Pipeline Flow Calculation Spreadsheet“, a blog article at www.EngineeringExcelTemplates.com.