Vertical Oval Tank Volume Calculation

To calculate the volume of an oval tank, you first need to determine the area, A, of the end, which has a stadium-like shape, and then multiply it by the length, l. The formula for the area A is:

A = πr² + 2ra

However, the definitions for r and a provided might not be accurate. Generally, for an oval tank with semicircular ends:

• r represents the radius of the semicircle (half the diameter of the circular end).
• a represents the straight sides of the stadium shape.

In correct terms:

• r = w / 2 (radius is half the width of the circular end).
• a is related to the height and width, though not directly equal to h - w.

For a typical oval tank design, a is often derived from the overall tank dimensions but should not be assumed as h - w without proper verification. In simplified cases, a can be approximated as the height minus the diameter of the semicircle (w), but this is not a universally standard definition.

Using the provided formula with these considerations:

V_tank = (πr² + 2ra)*l

Calculating the Fill Volume of a Vertical Oval Tank

It can help to visualize the tank as two semicircular ends connected by a rectangular section. To calculate the fill volume based on the fill height f, consider the following:

• When f < r: Use the circular segment method to calculate the fill volume, treating the filled portion as a vertical cylinder.
• When r ≤ f < (r + a): The filled volume includes the volume of the semicircle (up to r) and the rectangular section extending from r to f.
• When (r + a) ≤ f < h: At this point, the tank is mostly filled. The semicylindrical ends are completely filled, and the rectangular section is filled up to f. To calculate the remaining empty volume, subtract the filled volume from the total tank volume: V_{tank} - V_{filled}. Alternatively, the filled volume can be determined by calculating the circular segment volume of the top empty portion if needed.