Volume Calculator Horizontal Cylinder Formula

Horizontal Cylinder Volume Formula:

\[ V = L \times (r^2 \times \arccos((r - h)/r) - (r - h) \times \sqrt{2 r h - h^2}) \]

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 created by the liquid level and provides an accurate volume measurement based on the tank's dimensions and fill level.

2. How Does The Calculator Work?

The calculator uses the horizontal cylinder volume formula:

\[ V = L \times (r^2 \times \arccos((r - h)/r) - (r - h) \times \sqrt{2 r h - h^2}) \]

Where:

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

Explanation: The formula calculates the area of the circular segment created by the liquid level and multiplies it by the length of the cylinder to determine the total volume.

3. Applications Of Horizontal Cylinder Volume Calculation

Details: This calculation is essential in various industries including petroleum storage, chemical processing, water treatment, and any application involving horizontal cylindrical tanks for liquid storage.

4. Using The Calculator

Tips: Enter the cylinder length, radius, and liquid depth. All values must be positive, and the depth must be between 0 and 2 times the radius. Use consistent units for all measurements.

5. Frequently Asked Questions (FAQ)

Q1: What if my cylinder is completely full?
A: When depth equals 2×radius, the formula simplifies to the standard cylinder volume formula: V = π × r² × L.

Q2: What if my cylinder is completely empty?
A: When depth equals 0, the volume will be 0.

Q3: Can this formula be used for any unit system?
A: Yes, as long as all measurements use the same units (e.g., all in meters or all in feet).

Q4: What is the range of valid depth values?
A: Depth must be between 0 and 2 times the radius. Values outside this range are physically impossible.

Q5: How accurate is this calculation?
A: The formula provides a mathematically exact solution for ideal cylindrical tanks without considering factors like tank deformation or internal structures.