For a 90° medium-radius elbow and a 90° square (sharp) elbow in single-phase pipe flow, the typical equivalent lengths (in diameters) are approximately what values, respectively?

Introduction / Context:
Minor (local) losses in piping due to fittings are often represented using equivalent length, Le, expressed in pipe diameters, D. A 90° elbow causes additional head loss that can be approximated by Le/D values depending on geometry and radius.

Given Data / Assumptions:

• Single-phase, turbulent flow in a standard industrial pipe.
• Comparison between a medium-radius 90° elbow and a square (sharp) 90° elbow.

Concept / Approach:
Sharp elbows disturb the flow more strongly than swept elbows, producing larger separation and eddy formation. Therefore, their equivalent length is higher. Typical handbooks list Le/D for 90° elbows from roughly 20–30 for medium radius and about 50–60 for square elbows.

Step-by-Step Solution:
1) Identify the two fittings: medium-radius elbow vs sharp (square) elbow.2) Recall typical Le/D ranges: ~25 for medium radius, ~60 for square.3) Match the nearest option pair: 25 and 60.

Verification / Alternative check:
Using K-values, where K = f * (Le/D). If the pipe friction factor f is known, Le/D values that reproduce standard K data (e.g., K ≈ 0.9–1.5 for medium-radius elbows and ≈ 1.5–2.5 for sharp elbows) align with Le/D ≈ 25 and 60 in many practical cases.

Why Other Options Are Wrong:
3 and 5 are too small to represent typical 90° elbows.100 and 250, and 250 and 600 are unrealistically large for standard elbows and would massively overpredict minor loss.

Common Pitfalls:
Confusing K with Le/D; using laminar-flow correlations; ignoring fitting radius—sharper turns raise loss substantially.

Final Answer:
25 and 60