Water tanks are huge water storage tanks. They are found commercially in a variety of shapes, including horizontal cylinders, vertical cylinders, and rectangles. The appropriate method for determining tank capacity depends on the shape of the tank. Remember, though, that the results will only be rough estimates, because the calculations determine the volume of the tank assuming it has the shape of a perfect geometric solid.
Steps
Method 1 of 3: Calculate the Capacity of a Horizontal Cylindrical Tank
Step 1. Measure the radius of the base circle of the cylinder
The region bounded by the base circumference of the cylinder is the surface of the lower base (B). A radius is any linear segment that connects the center of a circle with its circumference. To find the radius, simply measure the distance between the central point of the base of the cylinder and any point on the circumference.
A diameter is any straight linear segment that passes through the center of the circle and has its ends on the circumference of the circle. In each circle, the diameter equals twice the radius. Therefore, you can find the radius of the base circle of the cylinder also by measuring the diameter and dividing it in half
Step 2. Find the area of the base circle of the cylinder
Once you know the radius of the lower base (B), you can calculate the area. To do this, use the formula B = πr2, denoting the radius with r and 3.14159 with π, which is a mathematical constant.
Step 3. Calculate the total volume of a cylindrical tank
Now you can determine the total volume of the tank by multiplying the area by the length of the tank. The complete formula for the total volume of the tank is Vs tank = πr2h.
Step 4. Find a circular sector and a segment
Imagine cutting a circle into slices, like a pizza: each slice is a sector. If a chord (a linear segment that joins two points on a curve) crosses that sector, it splits it into two parts: a triangle and a segment. This segment is important because, to calculate the volume of the portion of the cylinder full of water (i.e. the volume of water contained in the tank), the area of the segment must be found (by calculating the area of the whole sector and subtracting the area of the triangle) and multiply it by the length of the cylinder.
Step 5. Calculate the area of the sector
The sector is a fractional portion of the surface of the entire circle. To determine its area, use the formula given above.
Step 6. Calculate the area of the triangle
Determine the area of the triangle formed by the chord that crosses the sector. Use the formula above.
Step 7. Subtract the area of the triangle from the sector area
Now that you have both the area of the sector and the area of the triangle, doing the subtraction will give you the area of segment D.
Step 8. Multiply the area of the segment by the height of the cylinder
If you multiply the area of the segment by the height, the product you get is the volume of the portion of the tank filled with water. Relative formulas are shown above.
Step 9. Determine the fill height
The final step depends on whether the height d is greater or less than the radius r.
- If the height is less than the radius, use the volume created by the filling height VFull. Or,
- If the height is greater than the radius, it uses the volume created by the empty portion, minus the total volume of the tank. This way you will get the volume of the water-filled portion.
Method 2 of 3: Calculate the Capacity of a Vertical Cylindrical Tank
Step 1. Measure the radius of the base circle of the cylinder
The region bounded by the base circumference of the cylinder is the surface of the lower base (B). A radius is any linear segment that connects the center of a circle with its circumference. To find the radius, simply measure the distance between the central point of the base of the cylinder and any point on the circumference.
A diameter is any straight linear segment that passes through the center of the circle and has its ends on the circumference of the circle. In each circle, the diameter equals twice the radius. Therefore, you can find the radius of the base circle of the cylinder also by measuring the diameter and dividing it in half
Step 2. Find the area of the base circle of the cylinder
Once you know the radius of the lower base (B), you can calculate the area. To do this, use the formula B = πr2, denoting the radius with r and 3.14159 with π, which is a mathematical constant.
Step 3. Calculate the total volume of a cylindrical tank
Now you can determine the total volume of the tank by multiplying the area by the length of the tank. The complete formula for the total volume of the tank is Vs tank = πr2h.
Step 4. Determine the volume of the water-filled portion
This portion is nothing more than a cylinder smaller than the entire tank, with the same radius but with a different height: the filling height d. Therefore: ? = π? 2h.
Method 3 of 3: Calculate the Capacity of a Rectangular Tank
Step 1. Calculate the volume of the tank
To determine the volume of a rectangular tank, multiply the length (l) by the depth (p) by the height (h). Depth is the horizontal distance from side to side, length is the longest dimension, and height is the vertical length from top to bottom.
Step 2. Calculate the volume of the water-filled portion
In rectangular tanks the filling portion has the same length and depth as the full tank but a lower height. The new height is the fill height, d. Therefore, the volume of the water-filled portion equals length times depth times fill height.
Advice
- To determine the volume of the cylinder you can use the calculators available online, but only if you already know the measurements of the radius, length and height.
- Remember that these measurements will only give you approximate results, as they assume that the tanks have perfect geometric shapes, when in reality they are more or less irregular.
