Mesh number represents the number of openings per linear inch of a screen.
If mesh number increases, the number of openings per inch increases.
This means each opening becomes smaller.
So, as mesh number increases from \(3\) mesh to \(10\) mesh, the screen becomes finer.
A finer screen has smaller clear opening.
Therefore:
\[
\text{mesh number increases} \Rightarrow \text{clear opening decreases}
\]
Thus, the correct answer is:
\[
\text{Clear opening decreases}
\]