What is the percentage calculation of water in a waterbut.

Question

I'm having a senior moment and am unable to work out a simple formula for the volume of water in my water-but, question below:

I have a blue 120cm high water-but, it also has a ultrasonic sensor to measure where the water level is.

When the water-but is full the sensor shows there is 5cm between it and the water (this is 100% full).

When the water-but is empty the sensor shows there is 86cm between it and the water (this is 0% full).

So when the water-but is full and starts emptying what is the calculation to work out the percentage of water remaining?

Thanks in advance.

Answer 1

If the sensor is showing $s$ cm then the proportion full is $$\frac{86-s}{86-5}=\frac{86-s}{81}$$

Multiply by $100$ to get a percentage

Answer 2

Assuming that the lateral section always has the same area (like in a cylinder) or a cube, then the percentage is: $$ P = 100\% \times \frac{86 - h}{86 - 5} = 100\% \times \frac{86 - h}{81} $$

So, when the height is $h = 5$ cm, the percentage will be $100\%$ and when the height is $h = 86$ cm, the percentage will be $0\%$.

(Henry posted his answer while I was writing mine.)