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MathGroup Archive 2001

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Re: horizontal cylinder

  • To: mathgroup at
  • Subject: [mg26659] Re: horizontal cylinder
  • From: "Paul Lutus" <nospam at>
  • Date: Wed, 17 Jan 2001 00:47:15 -0500 (EST)
  • References: <93racv$>
  • Sender: owner-wri-mathgroup at

"Jessie" <jes_alarcos at> wrote in message
news:93racv$57j at
> 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.

Unfortunately, there is no "simple basic program" to solve this problem. It
is soluble in closed form, but not simply.

First, please tell us whether you intend to write this program using
Mathematica or a general-purpose programming language. If the former, here
is one approach.

In these equations, r = tank radius, h = water height in tank, z = tank

(* Provide the basic equation that relates the tank's width to a given
height *)

f[r_,h_] := Sqrt[1-h^2/r^2] 2 r

(* Integrate the above equation from bottom to (h) height, multiply by tank
length (z) *)

ff[r_,h_,z_] := z Integrate[f[r,x],{x,-r,h-r}]

(* Plot the basic equation to reveal why this approach works *)
(* (bottom of tank is at the left, top is at the right) *)


(* Example problem with numerical result *)

ff[4,6,9] // N


I strongly recommend that you not use this result until you understand why
it works. This will also allow you to detect any errors I may have made in
this quick solution.

Paul Lutus

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