The formula to calculate the gallons per inch (GPI) of a cylindrical tank is:
\[ GPI = \frac{\pi \left(\frac{D}{2}\right)^2 H}{231} \]
where \( GPI \) is the gallons per inch, \( D \) is the diameter of the tank (inches), and \( H \) is the height of the liquid in the tank (inches).
Gallons per inch is a measure of the volume of liquid that occupies a one-inch height in a cylindrical tank. It is a useful metric for determining the amount of liquid in a tank based on the liquid level’s height. This measurement is particularly important in industries where precise volume measurements are necessary, such as in chemical processing or water treatment facilities.
Let's assume we have the following values:
Step 1: Calculate the radius of the tank:
\[ \frac{D}{2} = \frac{24}{2} = 12 \text{ inches} \]
Step 2: Calculate the area of the base of the cylinder:
\[ \pi \left(\frac{D}{2}\right)^2 = \pi \times 12^2 = 144\pi \text{ square inches} \]
Step 3: Multiply the area by the height to get the volume in cubic inches:
\[ 144\pi \times 1 = 144\pi \text{ cubic inches} \]
Step 4: Convert the volume to gallons by dividing by 231:
\[ \frac{144\pi}{231} \approx 1.96 \text{ gallons} \]
Therefore, the gallons per inch (GPI) of the cylindrical tank is approximately \( 1.96 \) gallons.