Thanks Albert, but I think you misunderstand my confusion. I understand the formulas. It's the HP41C program at the end of the paper that I'm having trouble with.
(10-12-2018 10:34 PM)Albert Chan Wrote: (10-12-2018 08:34 PM)Dieter Wrote: For the record: with R = 90" the results are 13318 and 13509 gallons.
Assuming an elliptical dome top yields 13324 and 13532 gallons.
The numbers look good ...
To get the upper limit, assume cylindrical tank.
1" slice = Pi * 72² * 1 / 231 = 70.50 gallons
195" - 6" => 189 * 70.50 ~ 13325 gallons
198" - 6" => 192 * 70.50 ~ 13536 gallons
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Hi, David
I am guessing you have no problem with Eqn 25-13 first term.
It is just cyclindrical tank + slant bottom volume.
Volume of spherical cap = Pi h^2 (R - h/3), where h measured from top of cap.
So, volume of liquid in the cap
= volume of cap - volume of air
= Pi v0^2 (R - v0/3) - Pi h^2 (R - h/3)
We like to measure from the cap bottom. So, let v = v0 - h, we get h = v0 - v
Factor out the Pi, add unit conversion factor 231 in^3/gal ... you get the second term.
Using above R=90" example, and do the 198" level calculation:
First term = Pi * 72² * (180 + 12/2) = 3029199 in^3
h = 12 + 180 + 36 - 198 = 30 in
Volume of air = Pi h^2 (R - h/3) = Pi * 30² * (90 - 30/3) = 226195 in^3
Volume of cap = Pi v0^2 (R - v0/3) = Pi * 36² * (90 - 36/3) = 317577 in^3
Total volume = 3029199 + 317577 - 226195 = 3120581 in^3 = 13509 gallons
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