Partial Cylinder Volume Calculator Gallons

Partial Cylinder Volume Formula:

\[ V = L \times (r^2 \times \arccos(\frac{r - h}{r}) - (r - h) \times \sqrt{2 \times r \times h - h^2}) \times 7.48052 \]

Volume (V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Partial Cylinder Volume Formula?

The partial cylinder volume formula calculates the volume of liquid in a partially filled horizontal cylindrical tank. This formula is essential for industries dealing with liquid storage and transportation, providing accurate volume measurements in gallons.

2. How Does the Calculator Work?

The calculator uses the partial cylinder volume formula:

\[ V = L \times (r^2 \times \arccos(\frac{r - h}{r}) - (r - h) \times \sqrt{2 \times r \times h - h^2}) \times 7.48052 \]

Where:

\( V \) — Volume in gallons
\( L \) — Length of the cylinder in feet
\( r \) — Radius of the cylinder in feet
\( h \) — Depth of liquid in feet
7.48052 — Conversion factor from cubic feet to gallons

Explanation: The formula calculates the cross-sectional area of the liquid segment and multiplies it by the length of the cylinder, then converts the result from cubic feet to gallons.

3. Applications of Partial Cylinder Volume Calculation

Details: This calculation is crucial for various industries including petroleum, chemical processing, water treatment, and agriculture where accurate measurement of liquid volumes in cylindrical tanks is necessary for inventory management, process control, and regulatory compliance.

4. Using the Calculator

Tips: Enter the length and radius of the cylinder in feet, and the depth of liquid in feet. All values must be positive numbers, and the depth must be between 0 and twice the radius value.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a conversion factor of 7.48052?
A: This factor converts cubic feet to US gallons (1 cubic foot = 7.48052 US gallons).

Q2: What if my tank is oriented vertically?
A: This formula is for horizontal cylinders. For vertical cylinders, use the standard cylinder volume formula: V = πr²h × 7.48052.

Q3: Can this calculator be used for metric units?
A: This specific calculator uses imperial units (feet and gallons). For metric units, different conversion factors would be needed.

Q4: What is the valid range for the depth value?
A: The depth (h) must be between 0 and 2r (twice the radius), representing an empty tank and a completely full tank respectively.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the inputs, but actual tank volumes may vary slightly due to construction tolerances, temperature effects, and other practical factors.