Minor losses via fittings: using the equivalent-length method (Le/D), typical values for a 45° elbow and a 180° close return bend are approximately which pair?

Introduction / Context:
Pressure drop in pipelines arises from straight-run friction and additional “minor” losses due to fittings, valves, and bends. A common estimation tool is the equivalent-length method, which expresses a fitting’s loss as an equivalent length of straight pipe, Le, that would cause the same frictional loss as the fitting. Engineers often memorize or look up representative Le/D values to make quick calculations during preliminary design.

Given Data / Assumptions:

• Single-phase, incompressible flow in a standard industrial piping system.
• Typical commercial elbows and close return bends (not long-radius specialty items).
• Desire for order-of-magnitude design values rather than exact catalog numbers.

Concept / Approach:
Minor-loss coefficients (K) correlate to Le/D through Le/D = K / f, where f is the Darcy friction factor. Reference tables often provide average Le/D directly for common fittings based on typical Reynolds number ranges and surface roughness. Among choices given, a 45° elbow near Le/D ≈ 40–50 and a 180° close return bend near Le/D ≈ 70–80 are representative quick-estimate values for many water/utility services.

Step-by-Step Solution:

Verification / Alternative check:
Loss manuals (e.g., Crane-style compilations) show that return bends incur substantially larger losses than single elbows, consistent with the chosen pair. Exact values vary by radius and Reynolds number, but the pair (45, 75) reflects typical practice values.

Why Other Options Are Wrong:

• Very small values (5 and 10) underestimate losses for most standard fittings.
• Very large values (180–500) grossly overstate equivalent lengths for common sizes.

Common Pitfalls:
Using Le/D blindly without considering f; mixing K and Le/D data; ignoring fitting radius and entrance effects that can change losses.

Final Answer:
45 and 75