Tube Calculator

What is a Tube?

A tube, also known as a hollow cylinder or pipe, is a three-dimensional object with two concentric circular faces connected by two curved surfaces. It's characterized by its outer radius (r₁), inner radius (r₂), and height (h). Tubes are common in plumbing, construction, and industrial applications.

How to Calculate Tube Properties

To understand a tube fully, we need to calculate several key properties: its volume, surface area, and the relationship between inner and outer dimensions. Each of these properties is essential for engineering and design applications.

Formulas

Here are the essential formulas for a tube:

1. Volume (V):

\[ V = \pi h(r_1^2 - r_2^2) \]

2. Total Surface Area (A):

\[ A = 2\pi h(r_1 + r_2) + 2\pi(r_1^2 - r_2^2) \]

3. Wall Thickness (t):

\[ t = r_1 - r_2 \]

Where:

• \(r_1\) is the outer radius
• \(r_2\) is the inner radius
• \(h\) is the height
• \(t\) is the wall thickness
• \(\pi\) (pi) is approximately 3.14159

Calculation Steps

1. Determine the outer radius (r₁), inner radius (r₂), and height (h)
2. Calculate the volume using \(V = \pi h(r_1^2 - r_2^2)\)
3. Calculate the surface area using \(A = 2\pi h(r_1 + r_2) + 2\pi(r_1^2 - r_2^2)\)
4. Calculate the wall thickness using \(t = r_1 - r_2\)

Example and Visual Representation

Let's calculate the properties of a tube with:

• Outer radius (r₁) = 5 units
• Inner radius (r₂) = 3 units
• Height (h) = 10 units

1. Volume: \(V = \pi(10)(5^2 - 3^2) = 502.65\) cubic units
2. Surface Area: \(A = 2\pi(10)(5 + 3) + 2\pi(25 - 9) = 553.93\) square units
3. Wall Thickness: \(t = 5 - 3 = 2\) units

Visual representation of the example tube:

The diagram above shows a cross-sectional view of a tube, illustrating the outer radius (r₁), inner radius (r₂), and height (h). The shaded regions represent the solid material of the tube, while the hollow center shows the void space.