Question

Tyler series sieves used for grading of food grains should have consecutive sieves having screen opening sizes \(D_1\) and \(D_2\) so that

• A. \(D_1/D_2 = 2.0\)
• B. \(D_1/D_2 = (2)^{1/2}\)
• C. \(D_1/D_2 = (2)^{1/8}\)
• D. \(D_1/D_2 = (2)^{1/4}\)

Hint:

Remember the standard Tyler screen ratios:
- Standard Series: \(\sqrt{2}\) (or \(2^{1/2} \approx 1.414\)) ratio of openings.
- Close-sizing Series: \(\sqrt[4]{2}\) (or \(2^{1/4} \approx 1.189\)) ratio of openings.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Standard screen/sieve series are designed so that the openings of consecutive sieves vary in a systematic, mathematically defined ratio.
This ensures uniform and logarithmic classification of particle sizes during sieve analysis.

Step 2: Detailed Explanation:
The standard Tyler Mesh Series is based on a reference screen of 200 mesh (having a wire diameter of \(0.0021\text{ inches}\) and an opening of \(0.0029\text{ inches}\) or \(0.074\text{ mm}\)).
In this series, the area of the openings of any consecutive sieve doubles from one sieve to the next.
Since the area of the square opening is \(A = D^2\), doubling the area means the linear opening size (\(D\)) must vary by a ratio of \(\sqrt{2}\):
\[ \frac{D_1}{D_2} = \sqrt{2} = (2)^{1/2} \approx 1.414 \]
For closer sizing, intermediate sieves are inserted, giving a ratio of \(\sqrt[4]{2}\) or \((2)^{1/4}\).

Step 3: Final Answer:
The ratio for the standard consecutive sieves is \((2)^{1/2}\), which corresponds to option (B).