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Re: horizontal cylinder

Well, I'm not very good either, but it should take no more than a little
elementary analytic geometry to conclude that, if the radius of the tank is
r, the height of the liquid (the tank is horizontal) is h, and the length of
the tank is t, then the volume of the liquid in the tank is given by the

 f[h_, r_, t_] :=
  t*((Pi*r^2)/2 - (r - h)*Sqrt[r^2 - (r - h)^2] - r^2*ArcSin[(r - h)/r])

 for 0 <= h <= 2 r (check this by plotting it with, say, r =1 and t = 1). I
expect you are a Mathematica user - in that case, simply paste the above
into your notebook and you're done (no programming needed). If you're not,
what can I say?

Tomas Garza
Mexico City

----- Original Message -----
From: "Jessie" <jes_alarcos at>
To: mathgroup at
Subject: [mg26683] [mg26652] horizontal cylinder

> Hi everyone,
> I am not really very good in mathematics and I am not a student.
> So I need help....
> I have tried to derived a general equation for finding the volume of a
> horizontal cylinder given length & diameter of the cylinder, and the
> of the liquid inside, all three terms as variables.
> I am planning to use the equation to make a simple basic program to
> calculate the volume of the horizontal cylindrical tank without the need
> look for a factor from table which uses ratio of diameter and height of
> liquid.
> Will please anyone help me out.

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