Height of liquid in a horizontal cylinder

• Bencr
In summary, the conversation discusses the difficulty of isolating the height of liquid in a cylinder when the volume and dimensions of the cylinder are known. It is determined that this is a complex problem, often requiring the use of calculus, and that it can be solved numerically by repeatedly adjusting the input height to get closer to the known volume.

Bencr

Hi

I am trying to calculate the height of liquid in a cylinder.

I know the dimensions of a cylinder and the volume of liquid.

I know how to calculate the volume for a given height, but i can't flip the equation to get the height.

volume = area * length;
area = r2(θ - Sin[θ])/2, where θ = 2ArcCos[(r-h)/r]

So that goes that

area = volume/length.

How can i isolate the height from the area calculation? I don't think it's possible because it relies on trig and calculating the dimensions of a triangle based on the height of liquid and the radius of the cylinder.

If it is not possible to isolate that height, is it possible to work it out another way without iterating over every possible height until i come to the actual volume specified.

My maths level is high school and that is 10 years ago so i don't remember ever calculating anything like this.

Thanks
Ben Crinion

Bencr said:
How can i isolate the height from the area calculation?
I don't think it's possible. Assuming the cylindrical tank is lying so that its axis is horizontal, the relationship between the height of a liquid in the tank and the volume of the liquid is fairly complex. Calculating the volume from a known liquid height and the dimensions of the tank typically requires the use of calculus, which only a small fraction of high school students study. Determining the height when the volume is known can by done numerically to as much precision as is required by plugging in a guessed value for the height and using it to calculate the volume. By adjusting the input height, you can get closer and closer to the known value of the volume.