(41) Bulk Cylindrical Tank

[David Hayden]

(10-10-2018 04:58 PM)Dieter Wrote:  The author distinguishes two cases if the liquid level is within the slanted bottom part of the tank: the measured level h may be less or greater than half of the height h₀ of the slanted part. So there are two formular 25-5 and 25-7. But as far as I can see they are equivalent since arcsin(x) = –arcsin(–x).
Dieter

I believe you're missing the fact that the sign changes for y*sqrt(r²-y²) also.

If anyone is like me, you struggled to figure out what y is in these equations. It's the radial distance from the center of the tank to the edge of the liquid. In the first side view showing liquid, it's r minus the length of the horizontal line that makes up part of the shaded area.

To derive equation 1, it was helpful (to me) to draw a top-down view of the partially filled slant section.

Thanks for posting this. Personally I love this sort of stuff because it gives me a chance to dust off my math skills.