Post by thread:[EE]:: Calculation of pneumatic resistance

I'm seeking to find a formula which will allow me to very approximately establish the pneumatic resistance of smooth walled ducts at modest flow rates. I know Gargoyle knows but I can't convince it to tell me. I'm sure more than one of the people receiving this also know. This is essentially a HVAC application. Flow rates are in the few litres per second range. Temperatures are in the 0 - 30 C range. Wall material will ultimately be something smooth which may be a metal on some or all faces. If replying to this on a list I'd be obliged if you'd also copy any useful answer to me directly as list servers sometimes swallow responses for a while. regards Russell McMahon Use whatever email address you already have for me, or else use. CHANGE Q'S TO R'S --> spam_OUTquvalTakeThisOuTpaqadise.net.nz <--- CHANGE Q'S TO R'S

Russell McMahon wrote: > I'm seeking to find a formula which will allow me to very approximately > establish the pneumatic resistance of smooth walled ducts at modest flow > rates. I know Gargoyle knows but I can't convince it to tell me. I'm > sure more than one of the people receiving this also know. > > This is essentially a HVAC application. Flow rates are in the few litres > per second range. Temperatures are in the 0 - 30 C range. Wall material > will ultimately be something smooth which may be a metal on some or all > faces. I have a paper source (the in Germany well-known Recknagel/Sprenger "Taschenbuch für Heizung+Klimatechnik"). It contains a few empirical diagrams, so for certain defined situations, I could look up the values. This may then enable you to extend it further, as long as only parameters change that have a known relationship (length, for example). Gerhard

Thanks for the offer - it may be a bit hard to model well and there are some variable variables :-) - but to give you an idea. There are two identical ducts in series with an essentially lossless section in between. . Per duct: Duct is a very wide and shallow rectangle (a slot in cross section ) - Duct length is (only) 400mm - Duct width is 350mm. - Air flow is about 10l / second Desired pressure is such that a fan rated in the 5 to 10 Watt range will maintain the given airflow with the smallest possible duct height (and therefore cross section). I'd guesstimate that 5000 to 1000 Pa range would be OK. (about 1/3 to 2/3 psi) In fact just about everything is potentially variable but that's a typical configuration. I think that a bit of playing is going to teach me much. An added factor to make it all more fun is that the air temperature drops or rises by around 20C across the length of each short duct :-). Odds are that's far too variable a set of variables to expect any useful results but you are most welcome to comment if appropriate. My friend Ken Mardle provided this reference http://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html which looks like it will be highly useful once I take the time to come to grips with its nuances. Russell I have a paper source (the in Germany well-known Recknagel/Sprenger "Taschenbuch für Heizung+Klimatechnik"). It contains a few empirical diagrams, so for certain defined situations, I could look up the values. This may then enable you to extend it further, as long as only parameters change that have a known relationship (length, for example). Gerhard

Dunno if Grainger catalogs exist in NZ but it contains useful discussion of just such in the appendices. regards, Jack ---- Russell McMahon <.....apptechKILLspam@spam@paradise.net.nz> wrote: {Quote hidden}> I'm seeking to find a formula which will allow me to very > approximately establish the pneumatic resistance of smooth walled > ducts at modest flow rates. I know Gargoyle knows but I can't convince > it to tell me. I'm sure more than one of the people receiving this > also know. > > This is essentially a HVAC application. > Flow rates are in the few litres per second range. > Temperatures are in the 0 - 30 C range. > Wall material will ultimately be something smooth which may be a metal > on some or all faces. > > If replying to this on a list I'd be obliged if you'd also copy any > useful answer to me directly as list servers sometimes swallow > responses for a while. > > > > regards > > Russell McMahon > Use whatever email address you already have for me, or else > use. > CHANGE Q'S TO R'S --> quvalKILLspampaqadise.net.nz <--- CHANGE Q'S > TO R'S > > > > > --

Hi Russell, I can't find something for air (in a quick search) but the equivalent plumbing term is "head loss per foot" in pipe. (Head is pressure in units of (vertical) feet of water, I think) This page has tables for copper and PVC tubing: http://www.plumbingsupply.com/pluminfo.html Sean On 5/19/07, Russell McMahon <.....apptechKILLspam.....paradise.net.nz> wrote: {Quote hidden}> I'm seeking to find a formula which will allow me to very > approximately establish the pneumatic resistance of smooth walled > ducts at modest flow rates. I know Gargoyle knows but I can't convince > it to tell me. I'm sure more than one of the people receiving this > also know. > > This is essentially a HVAC application. > Flow rates are in the few litres per second range. > Temperatures are in the 0 - 30 C range. > Wall material will ultimately be something smooth which may be a metal > on some or all faces. > > If replying to this on a list I'd be obliged if you'd also copy any > useful answer to me directly as list servers sometimes swallow > responses for a while. > > > > regards > > Russell McMahon > Use whatever email address you already have for me, or else > use. > CHANGE Q'S TO R'S --> EraseMEquvalspam_OUTTakeThisOuTpaqadise.net.nz <--- CHANGE Q'S > TO R'S > > > > > -

Russell McMahon wrote: > There are two identical ducts in series with an essentially lossless > section in between. . > > Per duct: > > Duct is a very wide and shallow rectangle (a slot in cross section ) > > - Duct length is (only) 400mm > - Duct width is 350mm. I think most formulas for duct resistance will fail here. If I understand fluid dynamics correctly, this is a length/width ratio that creates a flow situation that's quite different from the one that the normal resistance formulas assume (they assume much longer than wide). Normal formulas mostly assume a laminar flow profile, which can only be expected to start after a length of about 10 diameters. > - Air flow is about 10l / second Here is a formula for round pipes: (1) delta p = lambda * (l/d) * (rho/2) * w^2 delta p: pressure difference [N/m^2] lambda: friction coefficient [1] l, d: length, diameter [m] rho: specific mass [kg/m^3] w: flow speed [m/s] For rectangular ducts, an equivalent diameter can be calculated: (2) d equ = 2 * a * b / (a + b) d equ: equivalent diameter [m] a, b: sides of the rectangle [m] You now can express d in (1) in terms of a and b from (2), where a is constant and b is what you want. You have delta p and l given. rho is known (at least the range, depending on your temperature range). w can be expressed as a function of the volume flow (given) and cross section (composed of the given a and the result b). That leaves us lambda as only unknown. lambda (probably something like "friction coefficient" in English) depends on the flow profile (laminar, turbulent -- in your case the latter, given your short length), the smoothness of the inner surface and the Reynolds number. For turbulent flow and ideally smooth surfaces is (3) lambda = 0.3164 * Re^(-0.25) (If you want to go into more detail here and possibly take the surface smoothness into account, I have other formulas for this. But the principle remains the same; you'd only have one more variable in here and much more complex formulas.) The Reynolds number is (4) Re = w * d / nu w: flow speed [m/s] d: (equivalent) diameter [m] nu: "kinematische Zãhigkeit" (don't know the English name) [m^2/s] Now we can insert lambda from (3) in (1) and substitute Re with (4). In (4), we can substitute w and d like before (with a, b and the given volume flow), and nu is ~13 at 0°C, ~15 at 20°C, ~17 at 40°C (for air at 1 bar, in 10^-6 m^2/s). I didn't do all the substitutions, but you'll end up with a formula that you can solve for b (height of the duct), dependent on only known values. You'll get even a notion how much the various parameters influence the result; this could potentially be more interesting than the actual result itself. Gerhard