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*To*: quattro@coimbra.ans.net*Subject*: re: untightened sparkplugs vs. Poiseuille's Law*From*: Phil Rose <pjrose@servtech.com>*Date*: Sun, 7 Jun 1998 00:16:35 -0500*Sender*: owner-quattro@coimbra.ans.net

Back-of-the-envelope time. How much leakage past a loose sparkplug is not enough to notice the effects--or is too much to endure? Can a plug be pretty damn loose, yet offer considerable resistance to leakage? Thinking about my recently posted concern about engine performance vis-a-vis untorqued sparkplugs, I recalled something called Poiseuille's Law. This bit of physics permits one to estimate the volumetric flow or "leak" rate (U) for any fluid with viscosity (n) passing though a capillary tube of radius (r) and length (L) while under uniform pressure (P). Air qualifies as a fluid, as has been discussed in many posts of some months ago. I approximated the path offered by loose sparkplug threads as being equivalent to a capillary tube (hey, remember this is the Qlist, not the Society of Automotive Engineers). So, according to Monsieur Poiseuille, U= (¼)(P)(r^4)/(8)(n)(L). At the end of the compression stroke, the 3B engine develops approx. 11 atmospheres of pressure in each cylinder. A leakage path of cylinder gases is assumed to be along the "loose" sparkplug threads, and I approximate that path as having a radius of, oh say from about 0.01 to 0.03 cm--really a wild guess. The pathlength L around the threads is fairly close to 50 cm. The viscosity of compressed air at 400 degrees K is about 225 x 10^-6 dyne sec/cm^2. The pressure of 11 atmospheres is expressed as 1.114 x 10^7 dynes/cm^2. Plugging all this into Poiseuille's equation (for several guessed values of the capillary radius) gives the following results: capillary radius., r 0.01 cm 0.02 cm 0.03 cm calc'd leak rate 3.9 cc/sec 62 cc/sec 314 cc/sec compress. loss @3000 rpm 0.1% 1.6% 7.5% @1000 rpm 0.3% 4.8% 22% Note that there is a very large (4th power) dependence of the leak rate on the diameter of the capillary ("open" thread path). To arrive at the 3rd and 4th rows of results, there are two _additional_ factors to consider: (1) Cylinder volume-->2300 cc divided by 5 and then divided again by compression of 11-fold yields a compressed cylinder volume of about 40 cc. So compression loss (%) can be calculated based on this number. (2) At 3000 rpm, there is one engine rev every 0.02 seconds. This gives the entire compression stroke about a 0.01 second duration (10 milliseconds). Hence, I estimate for the _worst_ case (the huge 0.03 cm capillary radius--or over 1/2 millimeter) that the total volume of cylinder gases lost by the plug is (0.01 x 314) about 3 cc, making about 7% loss of compression. Heck, this is within compression specs, isn't it? But at 1000 rpm it's a pretty big loss (22%). Clearly, the narrower leak paths reduce the leakage (and compression loss) to pretty negligible values (in my inexpert opinion). I don't know of an untorqued sparkplug would offer a pathway equivalent to a 0.3 mm radius; it seems big, but maybe possible. Does someone have tables of tapped thread dimensions that would be applicable for Audi engines? While a few percent loss may not be significant for compression, _any_ leakage translates directly to a loss of fuel, which surely becomes measurable at the level of a few percent. Since the absolute amount of plug leakage will be inversely proportional to engine speed, owing to the increased duration per stroke, I suspect that increased fuel consumption at very low rpm (e.g., idle speed) may turn out to be the main problem from moderately loose plugs. Obviously, having plugs with lots of fine threads helps to retard these losses. But nothing beats remembering to tighten them correctly. There could be important secondary effects on leak rate from heating/expansion that can't easily be calculated. Now, back to driving. Phil Phil Rose Rochester, NY '89 100 '91 200q pjrose@servtech.com

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