Volume Calculator Horizontal Cylinder Height

Horizontal 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 Horizontal Cylinder Volume Formula?

The horizontal cylinder volume formula calculates the volume of liquid in a partially filled horizontal cylindrical tank. It accounts for the circular segment area based on the fluid depth and multiplies by the cylinder length.

2. How Does the Calculator Work?

The calculator uses the horizontal cylinder volume formula:

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

Where:

\( V \) — Volume (cubic units)
\( L \) — Length of the cylinder (units)
\( r \) — Radius of the cylinder (units)
\( h \) — Depth of fluid (units)

Explanation: The formula calculates the area of the circular segment occupied by the fluid and multiplies it by the cylinder length to get the total volume.

3. Importance of Volume Calculation

Details: Accurate volume calculation is essential for tank capacity planning, fluid storage management, industrial processes, and various engineering applications involving cylindrical containers.

4. Using the Calculator

Tips: Enter length, radius, and depth in consistent units. Depth must be between 0 and 2×radius. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use consistent units for all measurements (e.g., all in meters or all in feet). The result will be in cubic units of your input.

Q2: What if my cylinder is completely full?
A: When depth equals 2×radius, the formula simplifies to the standard cylinder volume formula: V = πr²L.

Q3: What if my cylinder is completely empty?
A: When depth equals 0, the volume will be 0.

Q4: Are there limitations to this formula?
A: This formula assumes a perfect cylindrical shape with uniform dimensions. It may not account for internal components or irregular shapes.

Q5: Can this be used for inclined cylinders?
A: No, this formula is specifically for horizontal cylinders. Inclined cylinders require more complex calculations.