Partially Filled Cylinder Volume Calculator

Partially Filled Cylinder Volume Formula:

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

Volume (V):

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1. What Is The Partially Filled Cylinder Volume Formula?

The partially filled cylinder volume formula calculates the volume of liquid in a cylindrical container when it's not completely full. This is particularly useful in engineering, chemistry, and various industrial applications where precise volume measurements are required.

2. How Does The Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of liquid in the cylinder
\( L \) — Length of the cylinder
\( r \) — Radius of the cylinder
\( h \) — Depth of the liquid

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. Importance Of Volume Calculation

Details: Accurate volume calculation is essential for inventory management, process control, and safety measurements in various industries including petroleum, chemical processing, and water treatment.

4. Using The Calculator

Tips: Enter the cylinder length, radius, and liquid depth in consistent units. All values must be positive numbers, with depth not exceeding the cylinder diameter (2r).

5. Frequently Asked Questions (FAQ)

Q1: What if the depth exceeds the cylinder radius?
A: The formula works for any depth from 0 to 2r (full cylinder). For h > r, the calculation automatically accounts for the larger segment.

Q2: What units should I use?
A: Use consistent units for all measurements (e.g., all in meters or all in inches). The result will be in cubic units of your input.

Q3: Can this be used for horizontal cylinders?
A: Yes, this formula is specifically designed for horizontal cylindrical tanks.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cylindrical shapes without accounting for tank ends or irregularities.

Q5: What about cylindrical tanks with different end types?
A: This formula calculates volume for a straight cylindrical section. For tanks with hemispherical or other end types, additional calculations are needed.