# Level of liquid in the cylindrical tank, AKA Quarter-Tank Problem

This online calculator finds the height above the bottom of a horizontal cylinder (such as a cylindrical gas tank) to which the it must be filled for it to be full at specified percentage (for example, one quarter full amounts)

Level of liquid in the cylindrical tank, AKA Quarter-Tank Problem

This online calculator finds the height above the bottom of a horizontal cylinder (such as a cylindrical gas tank) to which it must be filled to a specified percentage (for example, one-quarter full)

The Quarter-Tank Problem can be formulated like this:

Finding the height above the bottom of a horizontal cylinder (such as a cylindrical gas tank) to which it must be filled for it to be one-quarter full.

This calculator solves the more general problem; it finds the height above the bottom of a horizontal cylinder to which it must be filled to a specified percentage.

This task is the exact opposite of the task solved in Cylindrical tank volume calculator.

Here is the equation which connects level of liquid and volume of liquid in the tank:

$\pi R^2 p = R^2 acos((R - h) / R) - (R - h)\sqrt{(2Rh - h^2)}$

where p is needed fraction, i.e., 0.25 for one-quarter full, R is the radius of the cylinder, and h is the liquid's height.

This equation does not have an analytical solution for h. However, it can be solved by numerical methods, like Secant method, which is indeed used in this calculator.

Also, it is worth noting that this is quite a simple case. However, we also have calculators for tilted cylinder case - Liquid level in the tilted cylinder and Tilted cylindrical tank volume

#### Level of liquid in the cylindrical tank, AKA Quarter-Tank Problem

Digits after the decimal point: 4
Liquid level

URL copied to clipboard
PLANETCALC, Level of liquid in the cylindrical tank, AKA Quarter-Tank Problem