Open-channel hydraulics (trapezoidal weirs): In a standard Cipolletti weir used for discharge measurement, what side slope is generally provided on each sloping face (horizontal : vertical)?

Introduction / Context:

A Cipolletti weir is a trapezoidal sharp-crested weir commonly used in irrigation and water-resources engineering to measure open-channel discharge. It is designed so that the contraction errors on the sides self-compensate, allowing a simple head–discharge relationship without side-contraction corrections.

Given Data / Assumptions:

• Weir is sharp-crested with trapezoidal opening.
• Standard Cipolletti proportioning is used for practical field measurements.
• Side slope is expressed as horizontal : vertical (H:V).
• Free overfall (ventilated nappe) conditions are assumed for correct calibration.

Concept / Approach:

For a trapezoidal weir, the side contractions reduce the effective width compared to a rectangular weir. Cipolletti specified a particular side slope that compensates for these side contractions so that the discharge formula resembles that of a rectangular weir without separate correction factors. The chosen slope balances geometry and hydraulics across typical heads.

Step-by-Step Solution:

Verification / Alternative check:

Textbook tables and field handbooks consistently cite 1:4 (H:V) as the Cipolletti slope; other slopes correspond to nonstandard trapezoidal weirs requiring separate calibration.

Why Other Options Are Wrong:

• 1:5, 1:3, 1:2, and 1:1 do not deliver the intended automatic compensation and are not the standard Cipolletti geometry.

Common Pitfalls:

• Confusing the notation (some authors write V:H; here the question uses H:V, i.e., 1:4).
• Applying side-slope data to suppressed rectangular weirs (which have vertical sides).

Final Answer:

1 : 4