(41) Bulk Cylindrical Tank

[Albert Chan]

(10-13-2018 06:42 PM)Thomas Klemm Wrote:  Spherical Segment

\(V=\tfrac{1}{6}\pi h(3a^2+3b^2+h^2)\)

We know \(a=r\) and \(h=v\) but we have to calculate \(b\) ...

Solving for b, Spherical Segment Volume is actually very simple.

Let d be shortest distance from sphere center to dome bottom (call this hatch depth ?)

b² = R² - (d + h)² = (r² + d²) - (d² + 2 d h + h²) = r² - 2 d h - h²
V = Pi h/6 (3r² + 3r² - 6 d h - 3h² + h²)

V = Pi h (r² - d h - h²/3)

Example, same tank, but assumed Spherical Segment Dome Top:
Using above formula, with V_dome = 1943 gallon, calculated d = 21.78" (R = 75.22")
Graphical fitted R is still useful. Its longer length is easier to measure. d can be easily calculated.

Code:

level  h   Liquid Volume (gallon)
195"   3"  13322
198"   6"  13525 
220"  28"  14756