Flow Through Non Circular Ducts Spreadsheet

Where to Find a Spreadsheet for Flow Through Non Circular Ducts

To obtain a spreadsheet for  flow through non circular ductsclick 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

A Spreadsheet for Choked Air Flow Calculation

Where to Find a Spreadsheet for Choked Air Flow Calculation

To obtain a spreadsheet for choked air flow calculations click here to visit our spreadsheet store.  Intended for use in making fanno flow calculations with adiabatic compressible flow of air, you can buy a convenient spreadsheet for choked air flow calculations for a very reasonable price.  This spreadsheet will also calculate the frictional pressure drop, and is available in either U.S. or S.I. units.  Read on for information about a choked air flow calculation spreadsheet for compressible pipe flow.

Conditions for Choked Air Flow Calculation with a Fanno Flow Excel Spreadsheet

For flow of air in a pipe with the frictional pressure drop less than 20% of the inlet air pressure, satisfactory results can be obtained using incompressible flow calculations with the Darcy-Weisbach equation.  For background information on that type of calculation, see the article, “Pipe Flow-Friction Factor Calculations with Excel Spreadsheets.”  If the frictional pressure drop is more than 20% of the incoming air pressure, then Fanno Flow equations should be used, as discussed here using a Fanno Flow Excel spreadsheet.

With adiabatic compressible flow conditions, the maximum air flow rate that can pass through a pipe is that which occurs when the exit Mach number is 1.0.  This is referred to as “choked flow.”

Equations for Choked Air Flow Calculations with a Fanno Flow Excel Spreadsheet

Shown below are the primary equations used in the fanno flow excel spreadsheet being discussed here for compressible flow of air in a pipe.  These equations are for compressible pipe flow with negligible heat transfer with the surroundings, but including effects of friction in the flow.

Fanno Flow Excel Spreadsheet EquationsThe parameters in these fanno flow equations are as follows:

  • f = Moody friction factor
  • L = pipe length
  • D = pipe diameter
  • k = adiabatic constant for the flowing air
  • M = mach number
  • T = air temperature
  • P = air pressure
  • ρ = air density

Parameters with an asterisk refer to conditions at the “choke point” in the pipe, where the Mach number is 1.

Screenshot for a Choked Air Flow Calculation Spreadsheet Using Fanno Flow Equations

The screenshot below shows part of a fanno flow excel spreadsheet for making compressible air flow calculations.  These calculations are for air flow in a pipe, in S.I. units. This Excel spreadsheet and others for compressible pipe flow calculations in a fanno flow excel spreadsheet are available in either U.S. or S.I. units at a very reasonable cost  in our spreadsheet store.Choked Air Flow Calculation Spreadsheet

Reference:

Bengtson, Harlan H.,  “Compressible Flow Pressure Drop Calculator Spreadsheet,” an online blog article

Pipe Flow-Friction Factor Calculator Excel Spreadsheet

Where to Find a Pipe Flow-Friction Factor Calculator Excel Spreadsheet

For a pipe flow-friction factor calculator Excel Spreadsheet, click here to visit our spreadsheet store.  Why read values from a Moody diagram, make iterative calculations to get friction factor, or use online calculators, when you can get a pipe flow-friction factor calculator Excel Spreadsheet for only $19.95?  Read on for information about the Darcy Weisbach equation and its use in an Excel spreadsheet as a friction factor/pipe flow calculator.

Excel spreadsheets are very convenient for Darcy Weisbach equation/pipe flow calculations, such as frictional pressure drop calculation or use of a friction factor calculator, at least in part because some of the calculations require iterative solutions.  The Darcy Weisbach equation is applicable to pressure flow in pipes, rather than gravity flow (as in sewer pipes), which is handled by open channel flow equations like the Manning equation.  The Darcy Weisbach equation provides the relationship among the following parameters: pipe diameter and length, pipe flow rate, and  frictional pressure drop or head loss.  Any one of these can be calculated if the others are known along with the density and viscosity of the fluid.

A Friction Factor Calculator and the Darcy Weisbach Equation

Moody diagram for pipe flow-friction factor calculator excel spreadsheetThe Darcy Weisbach equation  is hL= f(L/D)(V2/2g), with the parameters in the equation as follows: hLis the frictional head loss for flow of a fluid at average velocity, V, through a pipe of length,L, and diameter,D.  The Reynolds number for the flow (Re) and the relative roughness of the pipe (e/D) are needed to get a value for the friction factor,f.  The Moody Diagram at the right shows the nature of the dependence of the friction factor, f,  on Re and e/D.

Friction factor equations for pipe flow-friction factor calculator Excel spreadsheetEquations for f as a function of Re and e/D would be more convenient than a graph like the Moody Diagram for use with Excel spreadsheets making  pipe flow calculations with the Darcy Weisbach equation.  Such equations are shown in the box at the left, giving the relationships between Moody friction factor and Re & e/D for four different portions of the Moody diagram.  The four portions of the Moody diagram are:

  • laminar flow(Re < 2100 – the straight line at the left side of the Moody
  • smooth pipe turbulent flow(the dark curve labeled “smooth pipe” in the Moody diagram – f is a function of Re only in this region)Pipe Roughness Values for Pipe Flow-Friction Factor Calculator Excel Spreadsheet
  • completely turbulent region(the portion of the diagram above and to the right of the dashed line labeled “complete turbulence” – f is a function of e/D only in this region)
  • transition region(the portion of the diagram between the “smooth pipe” solid line and the “complete turbulence” dashed line – f is a function of both Re and e/D in this region and this is not an explicit equation for f)

The table above right gives pipe roughness values for several common pipe materials.  These can be used to calculate the pipe roughness ratio, e/D.

For a low cost Moody friction factor calculator download, that will calculate f for Reynolds number above 2100, see: www.engineeringexceltemplates.com

Frictional Head Loss and Frictional Pressure Drop Calculation

After using the Moody friction factor calculator to get a value for the friction factor, f, frictional head loss calculation is quite straightforward if the pipe length & diameter and average flow velocity are known.  You simply need to substitute values for L, D, V, and f into the Darcy Weisbach equation [hL= f(L/D)(V2/2g) ].  The Darcy Weisbach equation is a dimensionally consistent equation, so any consistent set of units can be used.  For U.S. units, hL, L, and D are typically in ft, V is in ft/sec, and g is 32.2 ft/sec2.  For S.I. units, hL, L and D are typically in m, V is in m/s, and g is 9.81 m/s2.  If volumetric flow rate, Q, is known rather than average velocity, V, then V can be calculated from:

equation to use with pipe flow-friction factor calculator Excel spreadsheet

Frictional pressure drop calculation from frictional head loss is done through the equation:

equations for use with pipe flow-friction factor calculator Excel spreadsheet

A Screenshot for a Pipe Flow-Friction Factor Calculator Excel Spreadsheet

The Excel spreadsheet screenshot below shows a pipe flow-friction factor calculator excel spreadsheet that is available as part of the “Pipe Flow-Friction Factor Calculation Package,”  at our spreadsheet store in either U.S. or S.I. units at a very low cost (only $16.95).  This spreadsheet package has three worksheets: one to calculate frictional head loss and pressure drop for known pipe diameter, length & material and flow rate; one to serve as a pipe flow rate calculator for known head loss/pressure drop, and pipe diameter, length & material; and one to calculate required pipe diameter for known head loss/pressure drop, flow rate, and pipe length & material.

spreadsheet screenshot for pipe flow friction factor calculator Excel spreadsheet
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. Source for pipe roughness values – http://www.efunda.com/formulae/fluids/roughness.cfm

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

5. Bengtson, Harlan H., “Pipe Flow Friction Factor Calculations with Spreadsheets,” available as an Amazon Kindle e-book and as a paperback.

6. Bengtson, Harlan H., “Pipe Flow Calculations with the Darcy Weisbach Equation“, an online blog article