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Math Help - How much fuel have I

  1. #1
    samleigh
    Guest

    Question How much fuel have I

    I have a large Diesel Fuel tank (7.5m long and 2.9m in diameter) with a clear pipe up the center to show the level in the tank. My problem is how to calculate the volume for any given height on the guage??
    (If the tank was vertical I know it would be Pi*r squared*height, but yes you guessed it the tank is horizontal)
    Last edited by ThePerfectHacker; November 11th 2007 at 08:04 PM.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    You want to see the computations, or just the answer?

    If you are into Calculus, integration, already, the volume in terms of the depth, h, of the fuel is

    The origin (0,0) is at the bottom of the circle, so that the depth of the fuel is h always.
    The center of the circle is at (0,1.45).
    The radius of the cirle is 2.9/2 = 1.45 m
    The equation of the circle is x^2 +(y-1.45)^2 = (1.45)^2
    So, x = sqrt[(1.45)^2 -(y-1.45)^2]

    dV = (2x)(dy)(7.5)
    dV = 15(x)dy
    dV = 15sqrt[(1.45)^2 -(y-1.45)^2]dy
    Integration is from y=0 to y=h

    V = (15)INT.(0 --> h)[sqrt[(1.45)^2 -(y-1.45)^2]dy

    V = 15{(1/2)(y-1.45)sqrt[(1.45)^2 -(y-1.45)^2] +(1/2)(1.45)^2 *arcsin[(y-1.45)/1.45]} |(0-->h)

    V = (7.5){(h-1.45)sqrt[(1.45)^2 -(h-1.45)^2] +[(1.45)^2]*arcsin[(h-1.45)/1.45]}

    That is it.
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