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How to determine the darcy friction factor for irregular cross section ducts

  1. Sep 25, 2008 #1
    How to determine the darcy friction factor for irregular cross section tunnels

    hi, I needed to calculate the f value for tunnels with these cross section area but I am not sure what are method available to calculate these shapes. Two of those cross section areas are already provided as attachments. Any idea where to start? or what sort of methods could I use? And is there any published standards for such calculations for tunnels?

    Attached Files:

    Last edited: Sep 26, 2008
  2. jcsd
  3. Sep 26, 2008 #2
    it depends what flow region your in.

    Laminar - f=64/Re
    Turbulent - use the colebrook equation or swamee jain approximation.

    the one thing you need to find for your Re and for use in the colebrook equation is the hydraulic diameter. I'm not sure exactly how accurate this is, but in testing I found that the hydraulic diameter can usually be found by 4*A/p ie. 4 times the cross-sectional area divided by the wetted perimeter.
  4. Sep 26, 2008 #3
    The problem with the f=64/re solution is that it is limited to circular pipes. but the cross section of the tunnels are neither circular, square nor rectangular. Thus it made the f = 64/re relation invalid
  5. Sep 26, 2008 #4
    Is it really limited to circular pipes? I thought that it was true for all, but that you have to use the correct hydraulic diameter (can be calculated for many shapes as described above) in the Re equation (Characteristic length, L).

    Besides, are you in the turb or lam region?
  6. Sep 26, 2008 #5
    I am assuming laminar flow since the medium is air, though I haven't done the calculations yet as I wasn't given the air flow requirement yet so I just assumed laminar first.

    I've checked with one book of mine, McGraw Hill, it did list out different equations for different cross section profile, circular is 64/re. Rectangular, elipse and triangular ducts all have different formulae, mainly in the form of N/re. So I believe 64/re only applicable to circular ducts only.

    I just wonder whether hazen-williams equations would be applicable in this scenario. It's a very big tunnel as you can see from the pictures. The measurements are all in metre by the way.
  7. Sep 26, 2008 #6
    A quick note: after reaading through the hazen williams equations, I see no physical properties of the fluid. Is it perhaps only for water, I doubt it covers a wide range of fluids as their viscosity effects will obvious effect your pressure drop.
  8. Sep 26, 2008 #7
    Ah geez, thanks almost forgot about that fact. My boss asked me to look up for some Swiss standards for tunnels. I found something called SIA 197, Projecting of tunnels, Basic, I wonder anyone heard of it? It's in German and I don't really read Germans so anyone can tell me what is it about? Does it have the guideline to calculate friction loss in long tunnels?
  9. Sep 26, 2008 #8
    also, your reynold's number (after a few quick and dirty calcs) will be in the region of 245000*v. so depending on your air velocity, I think you'll probably be in the turbulent region.

    I worked ou the characteristic length (hydraulic diameter) of the second tunnel to be about 4.47m and then subbed that in to the Re equqtion and used 1 for air density and 18.27*10^6 for air viscosity at 18°C.

    I've been working a lot with fluids flowing through small pipes (a few mm diameter) so i'm not sure if everything that i know and use is applicable on such a large scale, such as your tunnels.
  10. Sep 26, 2008 #9
    yeah... you are right.. I've mistaken the concept. If it's turbulent I believe the literature of analysis would be different. I wonder the D in swamee jain or colebroke for that matter means hydraulic diameter or just diameter because I've only work on those equations on circular pipes and on tunnels such as the one I've posted. Thanks for your help btw.
  11. Sep 26, 2008 #10
    no problem. I've been using this stuff for a couple of months now and also spent lots of time on here asking about different elements, so I'd like to try and give some help back in return.
    The d in colebrook and swamee-jain is definitely hydraulic diameter, which can be substituted with normal diameter when working with circular cross sections, naturally.
    There was a pretty handy thread somewhere on the forum earlier that dealt with hydraulic diameters of different cross sections. I'll do a search and post the link.
  12. Sep 26, 2008 #11
  13. Sep 26, 2008 #12


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    Re: How to determine the darcy friction factor for irregular cross section tunnels

    Are these tunnels going to be completely full? If not, I would consider modeling them as an open channel flow.

  14. Sep 26, 2008 #13
    Re: How to determine the darcy friction factor for irregular cross section tunnels

    I believe he said they were going to be used for air, which would make them closed flow. Have you tried looking up any experimental data for this friction factor? The majority of everything in fluid mechanics is derived from experiment so I would think that there would be something out there.
  15. Sep 26, 2008 #14
    I've heard something about swiss SIA standard... SIA 197, but I can't find much information about it. Anyone got a copy of it and saw something I've mentioned in it?
  16. Sep 26, 2008 #15


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    Re: How to determine the darcy friction factor for irregular cross section tunnels

    Sorry, I didn't read that many posts down. I read wetted area and assumed it was liquid flow (plus the fact they are talking about the Darcy friction factor).

    To the OP, the Darcy equation is generally only valid for liquid flow. However, it may be used for gas/vapor flow with some restrictions. You can expect reasonably accurate results if your calculated pressure drop is less than 10% of the inlet pressure and the specific volume used is based on either the upstream or downstream conditions.

    Since air is your fluid, I would suggest using a more appropriate friction factor depending on your model constraints and assumptions (e.g. Weymouth, Panhandle).

    Last edited: Sep 26, 2008
  17. Sep 28, 2008 #16
    I am not the familiar with weymouth and panhandle. Would the colebrook equation or swamee and Jain estimate the friction factor for gas flow adequately acurate? Speaking of which, would the estimation of minor losses, mainly the K value differ between liquid and gas as well?
    Last edited: Sep 28, 2008
  18. Sep 29, 2008 #17


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    The Colebrook and Swamee-Jain equations are just estimations of the Darcy friction factor. The friction factor in the Darcy equation is typically the same as the Moody friction factor (i.e. the friction factor from a Moody diagram). Hence, the Colebrook and Swamee-Jain equations will only give you the Moody friction factor which isn’t usually all that good for gas flow.

    The K value (resistance coefficient) is generally considered as being independent of friction factor or Reynolds number, and may be treated as a constant for any given obstruction in a piping system under all conditions of flow. It is valid for gas or liquid phase.

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