Pipe schedule number is a conventional index of wall thickness used in process piping. Which expression (using allowable internal working pressure P′ and allowable stress S, both in consistent units) defines the schedule number?

Introduction / Context:
Pipe “schedule” standardizes wall thickness across nominal sizes. Understanding its definition helps engineers relate design pressure and material allowable stress to expected wall thickness selection and mechanical robustness.

Given Data / Assumptions:

• P′: allowable working pressure (e.g., psi).
• S: allowable stress of pipe material (same unit basis).
• Schedule is a non-dimensional index used in ASME/ANSI standards.

Concept / Approach:

Historically, schedule number ≈ 1000 P′/S (with both P′ and S in psi). Larger schedule indicates thicker wall for a given nominal pipe size. The factor 1000 is conventional for scaling to convenient integers in catalogs (e.g., Sch 40, 80).

Step-by-Step Solution:

Verification / Alternative check:

Pipe tables and design references commonly cite the 1000 P′/S rule-of-thumb for schedule index derivation in legacy sizing frameworks.

Why Other Options Are Wrong:

100 P′/S or 10000 P′/S: Incorrect scaling. 1000 S/P′: Inverse trend (would imply thinner walls at higher pressure), which is illogical.

Common Pitfalls:

Assuming schedule directly gives thickness independent of diameter; actual wall thickness also depends on nominal size and schedule per tables.

Final Answer:

1000 P′ / S