# Thread: How much fuel have I

1. ## 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)

2. 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.