# Math Help - Propane Tank measurement

1. ## Propane Tank measurement

I was not 100% sure where to post this but I needed some help with a real life application.

So I have a tank of liquid that is a cylinder in the middle with two hemisphere ends or two ellipsoid ends (instead of sphere being 4/3pi(r^2) it is (2/3pi(r^2)) for the ellipsoid. the Tank has to stay on its side so I use a So I have a plank that rises as the height of the liquid changes and reads off a percentage. Using Y for the height of the liquid i can use this formula.

06. Volume 2

and dividing the sphere part by two for the ellipsoid.

I can't see inside the tank in order to measure the height of the liquid. So i need a way to measure the height of the liquid based on how full the container is. I get a % reading for the tank of how full it is. So my measurement works converting everything from 0%,50%, and 100% but that is only because the height is 50% the way up at 50% the volume but changes because it is a cylinder on the side and not a straight side.

If I put this in the wrong section I'm sorry

2. ## Re: Propane Tank measurement

What are you trying to do? Find the height after knowing how full it is?

3. ## Re: Propane Tank measurement

Yes. So I have a either volume or % of how full the tank is. I need to figure out a way to convert this to height since the tank is one its side. I'm trying to put it into excel. I just need a formula of how to convert It. If it was a square or a cylinder upright, then when the tank is 11% full the height would be 11% and i would just do .11 times the height of the tank. But it is not, it is on its side. And since it is a hemisphere on both sides and a cylinder on it side I can't just assume that since it is 11% full the height is 11% the tank because it changes as the width of the tank changes.

4. ## Re: Propane Tank measurement

I can't see inside the tank so I can't measure the height or I would just do that. If you can tell me a reasoning behind the equation that would also be awesome, as I'm very interested in this.

5. ## Re: Propane Tank measurement

You said "I have a plank that rises as the height of the liquid changes". It may give you a % but the actual height is that % times the height of the entire tank.

6. ## Re: Propane Tank measurement

It's a booie in the tank the rises up as the tank level rises or lowers and causes the tank gauge gives a % of how full the tank is. not how heigh the liquid is in the tank. So I need to convert tank % of volume to height of that liquid inside that tank.

7. ## Re: Propane Tank measurement

The tank is sideways. So from 0-5% the height changes much more than from 45-50% because the tank is wider at 45-50% than at 0-5%

8. ## Re: Propane Tank measurement

If you have a cylinder on its side the volume is not porportinal to the area of a circle times it's height because the misty and height change at the same time as the cylinder gets wider. Am I thinking of this wrong? So I have a cylinder sideway with two hemispheres or ellipsoids on on it ends.

9. ## Re: Propane Tank measurement

Width* not misty

10. ## Re: Propane Tank measurement

Originally Posted by bustacap09
Yes. So I have a either volume or % of how full the tank is. I need to figure out a way to convert this to height since the tank is one its side. I'm trying to put it into excel. I just need a formula of how to convert It. If it was a square or a cylinder upright, then when the tank is 11% full the height would be 11% and i would just do .11 times the height of the tank. But it is not, it is on its side. And since it is a hemisphere on both sides and a cylinder on it side I can't just assume that since it is 11% full the height is 11% the tank because it changes as the width of the tank changes.
Find the full volume W of the tank.

At a particular % full find the volume of the liquid in it which is clearly the percentage times W.

Now put the volume of the liquid into the equation and find y.
You cannot solve the equation to get y in terms of V. You must use an iterative method such as Newton's method - Wikipedia, the free encyclopedia to find y