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12-20-2018
03:56 PM

12-20-2018
03:56 PM

I am in school and trying to work through this example in the book. It all works out except the Theoretical Flow Rate which the book specifies as 15.3 GPM. From a little research I believe the issue is with how MathCad defines rpm but I can not figure it out.

Any help would be greatly appreciated,

Frank

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12-20-2018
06:10 PM

12-20-2018
06:10 PM

Don't divide by 231 - Mathcad knows units so it's going to do that on it's own, you're forcing it to do it twice.

Also, you have a unit of revolution in your input but none in your output. So, Mathcad is going to divide by 2*pi to get rid of it. Dealing with anything rpm related can be tricky.

So without the 231 and 2*pi factors you get the expected answer.

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12-20-2018
06:10 PM

12-20-2018
06:10 PM

Don't divide by 231 - Mathcad knows units so it's going to do that on it's own, you're forcing it to do it twice.

Also, you have a unit of revolution in your input but none in your output. So, Mathcad is going to divide by 2*pi to get rid of it. Dealing with anything rpm related can be tricky.

So without the 231 and 2*pi factors you get the expected answer.

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12-20-2018
07:56 PM

12-20-2018
07:56 PM

Re: Theoretical Flow Rate calculation

I greatly appreciate your answer. I was able to exchange the 231 with 2*pi and get the correct answer. I researched and now understand the 231 portion because that is converting in^3 to gallons which Mathcad does through its unit conversion but I must admit I still do not quite understand the rpm (2*pi)portion. Thanks again for the assistance!

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12-20-2018
11:25 PM

12-20-2018
11:25 PM

Re: Theoretical Flow Rate calculation

@FrankMozingo wrote:

I still do not quite understand the rpm (2*pi)portion. Thanks again for the assistance!

rpm should be considered "revolutions per minute", there are 2 pi radians per revolution, so you needed to correct for that

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12-21-2018
09:36 AM

12-21-2018
09:36 AM

Re: Theoretical Flow Rate calculation

Another way to do it is to make your displacement volume 4.712 in^3/rev (because that's what it truly is). That way the revolutions will cancel and you don't need the 2*pi. I would probably add it by making the stroke 0.5 in/rev.

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12-21-2018
10:51 AM

12-21-2018
10:51 AM

Re: Theoretical Flow Rate calculation

I used to work a lot with fourier transforms, the ones that deal with "samples per second" to compute the frequency vector. To allow understanding and graphics for upper management, I would define a new unit:

RPM := Hz/60. (note all caps!)

This allows a simple correlation between shaft speed and resolved data.