Answer to Question #21247 in Abstract Algebra for Hisham wadi

Question

Water tank cylinder with 1.8m diameter and 3.1 m length put on horizontal position I need formula to the volume of water at different heights
Regards

Answer 1

Let R - radius of the cylinder, h - the height of the liquid level, L - thelength of the cylinder.

Denote S - square circle segment occupied by water.Then the volume of fluidis V = S * L.It remains to calculate S.

1. if h is less than R

denote b = 1 - (h / R)and the half-angle of the segment occupied by thewater relative to the cylinder

a = arccos (b)Then S = R * R * (a-b * sqrt (1-b))

2. h if more R

denote H = 2R-h,then calculate the amount of the remainder without water Swt

denote b = 1 - (H / R)and the half-angle occupied by the remaining segmentsof the cylinder without water

a = arccos (b)Then Swt = R * R * (a-b * sqrt (1-b))and S = pi * R * R-Swt
Volume is V=S*L