Please help me solve this o-ring leak rate equation (Dimensional Analysis)

[WalkerSeattleRanger]

I have an equation I need help solving. This is a question about calculating o-ring leak rate. If possible could you walk me through the process to solve this because I want to learn how to do it and not just get an answer.

Here is the equation:

L = 0.7 x 0.000000134std. cc cm/cm^2 sec bar x 1.256in x 449lb/in^2 x 1.35 x 0.20

(L needs to be in std. cc/sec)

Here is the equation explained if you are interested to see what the equation is solving for:

http://www.engineersedge.com/fluid_flow/oring_leak_rate_13605.htm

Any help with this would be appreciated! Please let me know if you have any questions.

Walker

PS, I found this equation in the Parker handbook (3-21).

 

[rb1957]

so, the parameters are explained in the link.

some of the factors look "odd" ...
Q = 1.35 ?
(1-S)^2 = 0.2 ??

in the end I think the equation starts from basic science ... the leak is proportional to the pressure, the fluid, the diameter, the squeeze; and then a fudge factor (the 0.7 ?) to match to test results.

another day in paradise, or is paradise one day closer ?

 

[btrueblood]

So, the answer is: DON'T do dimensional analysis on this equation, the factors and values and units have been chosen to work to give the results in the units stated.

 

[rb1957]

well, you can if you're careful (and change "bar" to "psi") ... but it won't help understand the situation.

another day in paradise, or is paradise one day closer ?

 

[tbuelna]

That equation is from the Parker O-ring handbook. You can find more information in section 3.12.1.

 

[WalkerSeattleRanger]

Thanks for all the responses and help. I am aware that is from the Parker handbook, I just don't know the steps to do the dimensional analysis. If someone could do a sample problem for me so I could learn how to figure things out like this that would be a great help.

Thanks again.

 

[tbuelna]

This paragraph at the end of section 3.12.1 of the Parker handbook helps explain things: "For convenience, the formula contains mixed units. It was set up this way because in the United States O-ring diameters are usually given in inches, and pressures in pounds per square inch while permeability figures are usually shown in metric units. The 0.7 factor resolves these inconsistencies."

You should also remember that this approach for calculating leak rate is a rough approximation. From the Parker handbook: "This formula gives only a rough order of magnitude approximation because permeability varies between compounds in the same polymer, and because the assumptions on which it is based are not all exact." In fact, if you read the fine print below the graph for Q factor (fig 3-11) it states you should anticipate a variation of +/-50% from the predicted values shown.

 

[VEBill]

"I just don't know the steps to do the dimensional analysis."

It seems like you're asking how to do 'dimensional analysis'.

Essentially, you populate an equation with units (including the units of any constants) and ignore the values. It's done to ensure that the equation is 'balanced' (makes physical sense), or to determine a constant's actual units, or even to reveal a hidden unity constant (the units).

e.g. length x width = area; meters x meters = meters [sup]2[/sup]

Real world examples would be more complicated.

For details, there are plenty of explanations on the web. Just Google the phrase.

Was this what you're asking? If so...

Note that Eng-Tips isn't for 'coursework'. See red text just below.

Good luck.

 

[WalkerSeattleRanger]

Thanks again for the info and help. I assure you this is not course-work. I just don't know how to figure that problem out and was looking for someone to walk me through it.