Horizontal Cylindrical Tank Calculator

What is a Horizontal Cylindrical Tank?

A horizontal cylindrical tank is a container shaped like a cylinder lying on its side. It's commonly used for storing liquids or gases in various industries, including agriculture, chemical processing, and water treatment. These tanks are efficient for storage and transportation due to their shape and orientation.

How to Calculate Horizontal Cylindrical Tank Properties

To fully understand a horizontal cylindrical tank, we need to calculate several key properties: its diameter, length, volume, surface area, and the volume of liquid at different fill levels. Each of these properties provides unique information about the tank's dimensions and capacity.

Formulas

Here are the essential formulas for a horizontal cylindrical tank:

1. Volume (V):

\[ V = \pi r^2 L \]

2. Surface Area (A):

\[ A = 2\pi r^2 + 2\pi r L \]

3. Volume of Liquid at Partial Fill (V_h):

\[ V_h = L \left( r^2 \arccos\left(\frac{r-h}{r}\right) - (r-h)\sqrt{2rh-h^2} \right) \]

Where:

• \(r\) is the radius of the tank
• \(L\) is the length of the tank
• \(h\) is the height of the liquid in the tank
• \(\pi\) is the mathematical constant pi (approximately 3.14159)

Calculation Steps

1. Determine the radius (r) and length (L) of the tank
2. Calculate the total volume using \(V = \pi r^2 L\)
3. Calculate the surface area using \(A = 2\pi r^2 + 2\pi r L\)
4. To find the volume at a specific fill level, measure the height (h) of the liquid
5. Calculate the partial volume using the formula for V_h

Example and Visual Representation

Let's calculate the properties of a horizontal cylindrical tank with a radius of 2 meters and a length of 6 meters:

1. Given: \(r = 2\) m, \(L = 6\) m
2. Total Volume: \(V = \pi r^2 L = \pi (2^2)(6) \approx 75.40\) cubic meters
3. Surface Area: \(A = 2\pi r^2 + 2\pi r L = 2\pi (2^2) + 2\pi (2)(6) \approx 100.53\) square meters
4. For a fill height of 1.5 m: \(V_h \approx 37.70\) cubic meters (50% full)

Here's a visual representation of this horizontal cylindrical tank:

In this diagram, you can see a 2D representation of our horizontal cylindrical tank with radius 2 meters and length 6 meters. The blue surface represents the liquid level at 1.5 meters (50% full). The red line shows the diameter, and the green line shows the length. The total volume (V), surface area (A), and partial volume (V_h) are labeled.