hello everybody.
Please see attached sketch for horizontal storage vessel. There is horizontal tank used to store the chemical. We are providing the level guage on the side of the horizontal vessel. I want to calculate the height from top to locate nozzle for level guage.
Note that dish ends are elipsoidal. I am not furnishing the chemical data because i feel its not required here.
I just have a wage idea that there is some formulae used but i could not get it.
Please suggest.
Hi there,
A great site for maths is "Wolfram Mathworld".
You should separate your problem in two:
1. Finding the volume as a function of hight of the cylinder
2. finding the volume as a function of hight of the two semi-ellipsoids (one full ellipsoid)
For 1. Volume V is area of base x hight (length of vessel w/o the ellipses)
for the calculation of that area, try this (http://mathworld.wolfram.com/CircularSegment.html)
For 2. I guess it is the two of the three axis are equal, so will have to "rename" your ellipsoids to "Spheroids"; so try the following link (http://mathworld.wolfram.com/Spheroid.html). In the formula that is given with integrals, just set the limits accordingly: "a" is the radius of your spheroid (and the cylinder), "c" is the remaining radius of your ellipse. To calc as a function of h (liquid's hight) set the outer limmits (1st intergral) to lower "-c" & upper "h-c".
I hope I have helped.
Pacsal