Weirs with end contractions: compared to the channel width, how does the effective weir length (crest width) change?

Introduction / Context:
When a sharp-crested rectangular weir is placed in a channel and is not extended to the sidewalls, flow contracts at the ends. This phenomenon is known as end contraction and must be accounted for when determining effective weir length in discharge calculations.

Given Data / Assumptions:

• Sharp-crested rectangular weir set in a channel with clearances to the sidewalls (contracted weir).
• Free, ventilated nappe and standard approach conditions.
• Head measured at a prescribed distance upstream to minimize velocity head effects.

Concept / Approach:

End contractions reduce the effective length through which water passes. Empirical formulations correct the nominal crest length b by subtracting a quantity proportional to the head H, such as L_e = b − 0.1nH (with n the number of end contractions, often 2). Hence, the effective length is less than the channel width, and discharge is computed with L_e rather than the full channel width.

Step-by-Step Solution:

Verification / Alternative check:

Compare to a suppressed weir (crest flush with sidewalls): there, L_e equals the channel width and no end-contraction correction is required. The difference confirms that with end contractions, L_e is necessarily smaller.

Why Other Options Are Wrong:

(a) Holds only for fully suppressed weirs. (c) Half-width is arbitrary and generally incorrect. (d) Incorrect given standard practice. (e) Physically impossible with end contractions.

Common Pitfalls:

Neglecting to subtract contraction corrections; measuring head too close to the crest; not ventilating the nappe.

Final Answer:

It is less than the channel width due to end contractions.