Weir Crest Width Explained

In fluid mechanics and hydraulic engineering, a weir is a structure built across an open channel, like a river or canal, to measure or control the flow of water. The crest is the top edge of the weir over which the water flows.

Defining Narrow-Crested Weirs

Weirs are often classified based on the width of their crest. A key distinction is made between narrow-crested and broad-crested weirs.

• A weir is classified as narrow-crested when the width of its crest is relatively small compared to the height of the water flowing over it.
• Specifically, for a weir to be considered narrow-crested, the width of the crest ($w$) must be less than the head of water ($H$) above the crest. Mathematically, this condition is represented as:

  $w < H$

Understanding the Crest Width Condition

When the crest width ($w$) is less than the water head ($H$), the water flowing over the crest accelerates significantly. The velocity of the water along the crest is high, and the pressure distribution on the crest is not uniform. This contrasts with broad-crested weirs, where the crest is wide enough ($w \ge 15H$, a common rule of thumb, though the exact definition can vary) to establish a more hydrostatic pressure distribution across the crest, and the velocity is lower.

Analyzing the Options

Based on the definition:

• Option 1: equal to H - This condition does not define a narrow-crested weir.
• Option 2: more than H - This is generally characteristic of broad-crested weirs, not narrow-crested ones.
• Option 3: less than H - This is the defining characteristic of a narrow-crested weir. The crest is narrow relative to the water depth flowing over it.
• Option 4: None of the above - Since Option 3 is correct, this option is incorrect.

Therefore, a weir is considered narrow-crested if the width of its crest is less than the height of the water above the crest.