How to Work Out Water Tank Capacity
Measure the radius of the circle at the bottom of the cylinder., Find the area of the circle at the bottom of the cylinder., Calculate the total volume of a cylinder tank., Identify a circular sector and segment., Determine the area of your sector...
Step-by-Step Guide
-
Step 1: Measure the radius of the circle at the bottom of the cylinder.
The region enclosed by the circle at the bottom of the cylinder is your bottom base surface (B).
A radius is any line segment that runs from a circle’s center to its perimeter.
To find the radius, simply measure from the mid-point of the cylinder’s bottom to the outside of the circle.
A diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle’s perimeter.
For any circle, the diameter will be twice the radius.
Therefore, you can also find the radius of the circle at the bottom of the cylinder by measuring the complete radius and dividing that number in half. -
Step 2: Find the area of the circle at the bottom of the cylinder.
Once you know the radius of your bottom base surface (B), you can calculate the area.
To do so, use the formula B = πr2, using your radius as r and
3.14159 for π, which is a mathematical constant. , You can now determine the total volume of the tank by multiplying the area by the length of the tank.
The full formula for total volume of the tank is Vtank = πr2h. , If you imagine a circle cut into slices, like a pizza, each slice is a sector.
If a chord (a line segment that joins two points on a curve) cuts through that sector, it divides the sector into two parts: a triangle and a segment.
This segment is important because to calculate the filled volume of your cylinder, you’ll have to find the area of a segment (by finding the area of the whole sector and subtracting the area of the triangle) and multiply it by the length of the cylinder. , The sector is a fractional portion of the area of the whole circle.
To find its area, use the formula shown above. , Find the area of the triangle that was formed by the chord that cut through the sector.
Use the formula shown above. , Now that you have both the area of your sector and the area of your triangle, a subtraction will yield the area of your segment, D. , When you multiply the area of your segment by the height, the product is the filled volume of your tank.
The relevant formulas are shown above. , Your final step depends on if the height, d, is greater than or less than the radius, r.
If the height is less than the radius, use the volume created from the filled height Vfill.
So, If the height is greater than the radius, use the volume created by the empty portion, minus the total volume of the tank.
This will give you the filled volume: -
Step 3: Calculate the total volume of a cylinder tank.
-
Step 4: Identify a circular sector and segment.
-
Step 5: Determine the area of your sector.
-
Step 6: Get the area of the triangle.
-
Step 7: Subtract the area of the triangle from the area of the sector.
-
Step 8: Multiply the area of your segment by the height of your cylinder.
-
Step 9: Determine the fill height.
Detailed Guide
The region enclosed by the circle at the bottom of the cylinder is your bottom base surface (B).
A radius is any line segment that runs from a circle’s center to its perimeter.
To find the radius, simply measure from the mid-point of the cylinder’s bottom to the outside of the circle.
A diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle’s perimeter.
For any circle, the diameter will be twice the radius.
Therefore, you can also find the radius of the circle at the bottom of the cylinder by measuring the complete radius and dividing that number in half.
Once you know the radius of your bottom base surface (B), you can calculate the area.
To do so, use the formula B = πr2, using your radius as r and
3.14159 for π, which is a mathematical constant. , You can now determine the total volume of the tank by multiplying the area by the length of the tank.
The full formula for total volume of the tank is Vtank = πr2h. , If you imagine a circle cut into slices, like a pizza, each slice is a sector.
If a chord (a line segment that joins two points on a curve) cuts through that sector, it divides the sector into two parts: a triangle and a segment.
This segment is important because to calculate the filled volume of your cylinder, you’ll have to find the area of a segment (by finding the area of the whole sector and subtracting the area of the triangle) and multiply it by the length of the cylinder. , The sector is a fractional portion of the area of the whole circle.
To find its area, use the formula shown above. , Find the area of the triangle that was formed by the chord that cut through the sector.
Use the formula shown above. , Now that you have both the area of your sector and the area of your triangle, a subtraction will yield the area of your segment, D. , When you multiply the area of your segment by the height, the product is the filled volume of your tank.
The relevant formulas are shown above. , Your final step depends on if the height, d, is greater than or less than the radius, r.
If the height is less than the radius, use the volume created from the filled height Vfill.
So, If the height is greater than the radius, use the volume created by the empty portion, minus the total volume of the tank.
This will give you the filled volume:
About the Author
Kimberly Roberts
Creates helpful guides on DIY projects to inspire and educate readers.
Rate This Guide
How helpful was this guide? Click to rate: