Velocity of approach for a sharp-crested weir A sharp-crested weir has effective crest length S. The upstream head above crest is H, and the measured discharge is Q m^3/s. What is the velocity of approach V_a (also written V_d) used for velocity-of-approach correction?

Introduction / Context:
In weir flow measurement, the approach velocity upstream adds kinetic head to the upstream energy level and slightly increases discharge beyond the ideal. Engineers therefore compute the velocity of approach and apply a correction to the head term when using standard weir formulas.

Given Data / Assumptions:

• Sharp-crested weir with effective crest length S (after end contractions).
• Upstream depth above crest = H (measured at an appropriate distance upstream to reduce drawdown error).
• Measured discharge Q through the weir.
• Approach channel of uniform width so that area upstream is S * H (for the velocity-of-approach estimate).

Concept / Approach:
Velocity of approach is the average upstream velocity associated with the approach cross-section. By continuity, V_a = Q / A_approach. For a sharp-crested weir, a practical estimate takes A_approach ≈ S * H, where S is effective crest length and H is head over the crest measured upstream.

Step-by-Step Solution:

Verification / Alternative check:
Units: Q (m^3/s) divided by S H (m * m) yields m/s, confirming a velocity. For wide channels, using the full upstream area provides a similar estimate.

Why Other Options Are Wrong:

• √(2 g H) and 2 g H belong to free-fall velocity or head relationships, not approach velocity from Q and area.
• Q / (S H^2) and Q / S have wrong dimensional forms.

Common Pitfalls:
Using crest length without adjusting for end contractions; measuring H too close to the crest; confusing jet velocity over the crest with the upstream approach velocity.

Final Answer:
V_a = Q / (S H)