Ellipse [Resolved]

[taxes]

Hi,

I need to be able to calculate the amount of liquid remaining in an oval tank at various levels, so that I can graduate a dipstick.

I have obtained some help as follows: (I have difficulty in copying some of the symbols and have explained them where relevent)


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let's say your ellipse has it's centre on the origin, and goes through the points

x=0,y=b; x=0,y=-b; x=a,y=0; x=-a,y=0

i.e. it has width 2a and height 2b. now the equation of the ellipse is given by

(x/a)^2 + (y/b)^2 = 1

i can prove this from something else if you want, but usually it is taken as the defenition of an ellipse.

now you want to find the area between the line y=k and the ellipse, k<b. to do this rearrange the equation:

x=a@(1 - (y/b)^2 ) ("@" should be a square root sign which I do not have on my keyboard)

and concentrate on y and x both greater than 0. now the area between the "top" of the ellipse and the line y=k is given by

y=b y=k a@(1 - (y/b)^2 ) dy. ("y=b" & "y=k" are interlined and preceded by a squiggle which looks like a vertically extended "S")

you should be able to do this integral with a simple substitution - let y = bsinq ("q" is the greek letter Theta which stands for an angle)"
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My problem is that my knowledge of Integration is virtually non-existent. Could someone please help me to interpret what I actually have to work out so that I can write a programme to do it.

For an example, assume an elipse 2.5 metres wide and 1.5 metres in height.

Obviously all I need to know is how to calculate the relative area of the ellipse and the finding the volume will be easy.