- #1
curtmorehouse
- 6
- 0
Homework Statement
I have a cylinder laid on it's side, a.k.a. a storage tank. I need to track the volume of liquid stored in said tank. I have a 'tank chart' that shows the volume of liquid in the tank for a specific 'depth' measurement. I think the measurements of the tank are wrong (and therefore the tank chart is wrong), but can not see the tank because it is in the ground.
I need to know the tank dimensions given a couple sets of known measurements for increases and decreases. The tank is said to be 80" diameter by 204" long.
For an increase of 6001 gallons of liquid, the depth changed from 12.5" to 80.375"
For a decrease of 207.2 gallons of liquid, the depth changed from 80.375" to 78.25"
I can provide more measurements like these if needed.
Homework Equations
$h = $tank_depth;
$d = $tank_diameter;
$r = $d / 2;
$l = $tank_length;
$x = pi() * $r * $r / 2;
$y = $r * $r * asin(1-$h / $r);
$z = ($r-$h)*sqrt($h*(2*$r-$h));
$area = $x - $y - $z;
$volume = $area * $l;
$volume = $volume / 231;
The Attempt at a Solution
MY attempts at a solution so far result in finding that increasing the size of the tank's length or diameter can make one set of depth/volume measurements work, but make other measurements fail.