Partially Filled Horizontal Tank Calculator

Horizontal Tank 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 Tank Volume Formula?

The horizontal tank volume formula calculates the volume of liquid in a partially filled cylindrical tank positioned horizontally. This formula accounts for the circular segment created by the liquid level.

2. How Does the Calculator Work?

The calculator uses the horizontal tank 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 of liquid in the tank
\( L \) — Length of the tank
\( r \) — Radius of the tank
\( h \) — Depth of liquid (measured from bottom)
\( \arccos \) — Inverse cosine function
\( \sqrt{} \) — Square root function

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

3. Applications of Horizontal Tank Volume Calculation

Details: This calculation is essential in various industries including petroleum, chemical processing, water treatment, and agriculture for inventory management, process control, and capacity planning.

4. Using the Calculator

Tips: Enter the tank length, radius, and liquid depth. All values must be positive, and the depth cannot exceed twice the radius (the full diameter of the tank).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for measurements?
A: You can use any consistent unit system (meters, feet, inches, etc.). The result will be in cubic units of your input measurements.

Q2: What if my tank is completely full?
A: When depth equals the diameter (2 × radius), the formula simplifies to the standard cylinder volume formula: V = π × r² × L.

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

Q4: Does this formula work for elliptical tanks?
A: No, this formula is specifically for cylindrical horizontal tanks. Elliptical tanks require a different calculation.

Q5: How accurate is this calculation?
A: The formula is mathematically exact for perfect cylindrical tanks. Real-world accuracy depends on how well the tank matches a perfect cylinder.