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How much oil in the tank?

  • 30-04-2008 12:42PM
    #1
    Closed Accounts Posts: 501 ✭✭✭


    Hi all,
    Hoping you can help me, looking for an equation for the volume of a partially filled cylinder on it's side.
    Thanks
    d2ww


Comments

  • Registered Users, Registered Users 2 Posts: 19,396 ✭✭✭✭Karoma




  • Registered Users, Registered Users 2 Posts: 7,589 ✭✭✭Hail 2 Da Chimp


    Pepsi?


  • Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    I think this is correct, not 100% sure though:

    If h is the height of the oil level above ground (h runs from 0 to 2r), and r is the radius of the tank, and L is the length of the tank, then the amount of oil in the tank is given by

    (PI*r^2)/2 - (r - h)*sqrt(2rh - h^2) - (r^2)*sin_inverse((r-h)/r)

    then multiply that by L

    I got that by taking the equation of a circle, x^2 + y^2 = r^2, solving for y

    y = sqrt(r^2 - x^2)

    and integrating from r-h to r.

    You need to double this result because it only gives you the area of the circle in the top-left quadrant. Multiplying by H then gives the volume you need.

    Edit: curse you karoma!
    That theta parameter in the calculation looks a bit strange. I don't see why you would need it.

    Pepsi?

    Partial credit!


  • Registered Users, Registered Users 2 Posts: 3,594 ✭✭✭Grudaire


    d2ww wrote: »
    Hi all,
    Hoping you can help me, looking for an equation for the volume of a partially filled cylinder on it's side.
    Thanks
    d2ww

    Eh isn't that just find the area filled if you look at it sideways- ie the arc +- a triangle, then multiply that by the length?


  • Closed Accounts Posts: 501 ✭✭✭d2ww


    Fremen, I'm unsure what you mean by 'a' in in your equation.


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  • Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    oops, a is the same thing as r
    I worked it out on paper in terms of a, then wrote it down in my post in terms of r, so I guess I got my wires crossed.

    It passes the three basic sanity checks, i.e. for h = 0, h = r and h = 2r, so I think it should be right.


  • Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    While you're at it, try to solve the related problem of finding the depth of oil in the tank corresponding to a given volume. i.e. try to calibrate, in litres, a dipstick for your oiltank.


  • Closed Accounts Posts: 501 ✭✭✭d2ww


    Thanks for that Fremen.
    MM, the thing is oil tanks are never perfect cylinders, the plastic one I have bulges out at both ends. I do however, have heights for 500 and 1000 liter deliveries, so can adjust the graph accordingly.


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