Fluid mechanics loss coefficients: For a tee used as an elbow (flow enters the branch), how does its loss coefficient compare to that of a tee used as an elbow (flow enters the run)?

Introduction / Context:
Minor loss coefficients (K) in fittings quantify pressure drops due to flow separation and secondary motion. Tees configured as elbows are common in process piping, and the orientation of the entering leg (branch versus run) strongly influences K.

Given Data / Assumptions:

• Incompressible single-phase flow.
• Standard commercial tee fitting.
• K values referenced at turbulent Reynolds numbers typical of process services.

Concept / Approach:
When flow enters the branch and turns into the run, the geometry forces a sharper turn and stronger separation than the reverse case. The consequent energy dissipation is higher, so the loss coefficient is larger for entering-branch service than for entering-run service.

Step-by-Step Solution:

Verification / Alternative check:
Crane TP-410 and similar handbooks list tabulated K values showing higher coefficients for entering the branch versus entering the run, all else equal.

Why Other Options Are Wrong:

• Less than: contradicts standard data.
• Approximately 90: meaningless here; K is dimensionless and not fixed to 90.
• Both (b) and (c): includes an incorrect assertion.

Common Pitfalls:
Confusing branch and run nomenclature; reusing K values from straight-through tees for turned-flow cases; ignoring velocity head reference area consistency.

Final Answer:
More than that for tee used as elbow, entering run