Inverted siphon head loss components (canal works): In Unwin’s formula for head loss through an inverted siphon barrel, the named factor primarily represents which type of head loss?

Introduction / Context:

Inverted siphons (also called depressed culverts) convey canal discharge under obstructions. Estimating total head loss through the siphon barrel is essential for fixing water surface profiles and ensuring adequate capacity. Empirical expressions like Unwin’s formula split the loss into recognizable parts—friction and local (entry/exit/bends) losses.

Given Data / Assumptions:

• Pressurized barrel flow through an inverted siphon.
• Use of Unwin’s empirical form for head loss.
• Losses include friction and local disturbances.

Concept / Approach:

Unwin’s approach represents total head loss as a sum of (i) a friction term proportional to length/diameter and velocity head and (ii) coefficients for local (minor) losses at entry, exit, and bends. The specific ‘‘factor’’ typically cited in the formula refers to the friction component governing the distributed loss along the barrel.

Step-by-Step Solution:

Verification / Alternative check:

Entry/exit losses are handled with separate coefficients (K_e, K_ex). The friction factor dominates for long barrels and is the key ‘‘factor’’ engineers adjust via diameter and lining roughness.

Why Other Options Are Wrong:

• Entry / exit only: These are minor (local) losses treated with separate coefficients.
• Gradient: Barrel slope minimally affects pressurized loss compared to friction/local coefficients.

Common Pitfalls:

• Ignoring local losses at transitions; they can be significant in short siphons.
• Using open-channel formulations instead of pressurized pipe loss expressions for barrels.

Final Answer:

friction loss along the barrel