Energy Loss in Pipe Flow – Entrance Loss for Sharp-Edged Inlet What is the head loss at the entrance of a pipe with a sharp-edged inlet (v is the average velocity in the pipe)?

Introduction:
Entrance loss is one of the standard minor losses in internal flows. Its magnitude depends on how the fluid is introduced into the pipe, especially the inlet geometry.

Given Data / Assumptions:

• Entrance is sharp-edged (square-edged).
• v is the uniform mean velocity inside the pipe.
• Discharge into the pipe from a large reservoir or plenum.

Concept / Approach:

The head loss due to entrance is expressed as h_e = K_e * v^2 / (2g). For a sharp-edged entrance, empirical data give K_e approximately 0.5. Streamline contraction and subsequent expansion to fill the pipe core create energy dissipation.

Step-by-Step Solution:

Verification / Alternative check:

Smoother bell-mouth inlets have much smaller K_e (approaching 0.04 to 0.1), while square-edged inlets have K_e close to 0.5. This range corroborates the selected value.

Why Other Options Are Wrong:

v^2 / (2g) and 2 * v^2 / (2g): Too large for a plain sharp edge; typical only for combinations of fittings or exits.1.5 * v^2 / (2g): No standard entrance configuration yields such a high coefficient.Approximately zero: Only for well-rounded bell-mouth entrances, not sharp-edged.

Common Pitfalls:

Memorizing a single coefficient for all entrances, or mixing entrance and exit losses. Always link the coefficient to the geometry.

Final Answer:

0.5 * v^2 / (2g)