Mesh Sizes, Size Classes & Representative Sizes

 

Understanding Figure 2.2: Mesh Sizes, Size Classes & Representative Sizes

Based on the provided text, here is a simple explanation of Figure 2.2 from Chapter 2.

What is Figure 2.2 Showing?

This figure shows how engineers convert a continuous range of particle sizes into neat, usable mathematical groups. It illustrates the link between Mesh Sizes, Size Classes, and Representative Sizes.

Imagine a long ruler measuring particle size from large (right) to small (left).

1. Mesh Sizes (D_i) — “The Fence Posts”

• Vertical lines labeled D₁, D₂, D₃… are the boundaries between size ranges.
• These correspond to physical sieves used in the lab.
• D₁ is the largest opening; D_N is the smallest.

Everything between two mesh-size lines belongs to one group.

2. Size Classes (1, 2, 3…) — “The Bins”

• The space between two mesh sizes is a Size Class.
• Example: Size Class 2 lies between D₁ and D₂.
• Any rock that passes D₁ but gets retained on D₂ belongs to this class.

3. Representative Sizes (d_pi) — “The Average Rock”

• Lines inside each class marked d_p2, d_p3, d_p4 represent a single “typical” size.
• Since we cannot calculate with a range (e.g., 10–20 mm), we choose one number to speak for the entire bin.
• This number is normally the geometric mean of the two mesh sizes:

d_pi = √( D_i−1 × D_i )

Summary Analogy

• Mesh Sizes (D) are the walls of a classroom.
• The Size Class is the room itself.
• The Representative Size (d_p) is the “average student” standing in the middle of the room.