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Central Angle and Depth Relation Calculus

how is the relationship between the central angle theta and the depth of an amount of liquid in a cylinder tank on its side h= r(1-cos(theta/2)?

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2 Answers

The picture might help:

cos(α/2) = (r-h)/r

r*cos(α/2) = r-h

h = r - r*cos(α/2) = r(1 - cos(α/2))

h = r(1 - cos(α/2))

Hopefully that helps.

Your formula h= r(1-cos(theta/2) is correct if the liquid level is below the center of the tank.

If the liquid level is above the center of the tank, the formula should be h= r(1+cos(theta/2)