Partial Cylinder Volume Calculator Cubic Feet

Partial Cylinder Volume Formula:

\[ V = L \times \left(r^2 \cdot \arccos\left(\frac{r - h}{r}\right) - (r - h) \cdot \sqrt{2 r h - h^2}\right) \times 0.037037 \]

Volume (V):

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1. What Is The Partial Cylinder Volume Formula?

The partial cylinder volume formula calculates the volume of a partially filled cylindrical container. This is particularly useful for determining liquid volumes in horizontal cylindrical tanks and containers.

2. How Does The Calculator Work?

The calculator uses the partial cylinder volume formula:

\[ V = L \times \left(r^2 \cdot \arccos\left(\frac{r - h}{r}\right) - (r - h) \cdot \sqrt{2 r h - h^2}\right) \times 0.037037 \]

Where:

\( V \) — Volume in cubic feet (ft³)
\( L \) — Length of the cylinder (ft)
\( r \) — Radius of the cylinder (ft)
\( h \) — Depth of the liquid (ft)
0.037037 — Conversion factor for proper unit handling

Explanation: The formula calculates the cross-sectional area of the liquid segment and multiplies it by the length of the cylinder to get the total volume.

3. Applications Of Partial Cylinder Volume Calculation

Details: This calculation is essential for various industries including petroleum, chemical processing, water treatment, and storage tank management where accurate volume measurements of partially filled cylindrical containers are required.

4. Using The Calculator

Tips: Enter the cylinder length and radius in feet, and the liquid depth in feet. Ensure the depth value does not exceed twice the radius (full cylinder height). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if the depth exceeds the radius?
A: The formula works for any depth from 0 to 2r (full cylinder). The calculation automatically adjusts for depths greater than the radius.

Q2: Why is there a conversion factor of 0.037037?
A: This factor ensures the result is in cubic feet when working with foot measurements, maintaining proper unit consistency.

Q3: Can this be used for vertical cylinders?
A: This formula is specifically for horizontal cylinders. For vertical cylinders, use the standard cylinder volume formula πr²h.

Q4: What precision should I use for measurements?
A: For accurate results, measure to at least three decimal places, especially for large tanks where small measurement errors can result in significant volume differences.

Q5: Are there limitations to this formula?
A: The formula assumes a perfect cylindrical shape with uniform dimensions. It may not be accurate for deformed or irregularly shaped containers.