How much oil in the tank?

d2ww

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

Karoma

http://www.lmnoeng.com/Volume/CylConeSphere.htm

Calculator, equation, etc...

Hail 2 Da Chimp

Pepsi?

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!

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?

d2ww

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

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.

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.

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.