Theoretical Flow Rate calculation

[FrankMozingo]

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 

[DJF · Accepted solution]

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.

[FrankMozingo]

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!

[Fred_Kohlhepp]

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@FrankMozingo wrote:

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

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

[DJF]

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.

[Fred_Kohlhepp]

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.