(41) Bulk Cylindrical Tank

[Dieter]

(10-12-2018 10:41 PM)Thomas Klemm Wrote:  The slanted cylinder isn't a slanted cuboid. Top and bottom are not the same.
Thus we can't simply divide the whole volume by 2.

Instead this formula can be used:

\(V(x)=\left [ x(\pi-\cos^{-1}x)+\tfrac{1}{3}\sqrt{1-x^2}(2+x^2) \right ]Hr^2\)

So the formula in the paper is wrong. Thank you very much for checking and correcting this.
Edit: But I still don't understand why it's wrong. The liquid surface is a circle with a chopped of segment. If this area is known, why is the volume not area · h/2 ?

(10-12-2018 10:41 PM)Thomas Klemm Wrote:  This program for the HP-42S calculates the volume of the slanted cylinder:

You should add a RAD statement to make sure that radians mode is set.
Or modify the formula so that it works in any angular mode: pi – arccos(x) = pi·(1 – arccos(x)/arccos(–1)).

(10-12-2018 10:41 PM)Thomas Klemm Wrote:  Changed R to r to make it consistent with the paper.

Fine. Maybe you can finally post the complete formula in terms of the variables in the paper, i.e. with h and h₀ instead of x and H.
H = h₀/2 and x = 2h/h₀ – 1.

Dieter