Cipolletti Weir Discharge Formula

A Cipolletti weir is a type of trapezoidal weir used to measure discharge in open channels. It has specific side slopes (1 horizontal to 4 vertical) which eliminate the need for end contractions, simplifying the discharge calculation compared to standard rectangular weirs.

Discharge Calculation

The discharge ($Q$) over a weir is typically calculated using a formula that includes the coefficient of discharge ($C_d$), the length of the weir crest ($L$), the acceleration due to gravity ($g$), and the head ($H$) over the crest.

When the velocity of approach (the velocity at which water approaches the weir) is considered negligible, the formula for discharge simplifies. For a Cipolletti weir under this condition, the discharge formula is:

This formula represents the flow rate, where:

• $Q$ is the discharge (e.g., in m³/s or cfs)
• $C_d$ is the coefficient of discharge (dimensionless)
• $L$ is the length of the weir crest (e.g., in m or ft)
• $g$ is the acceleration due to gravity (approx. 9.81 m/s² or 32.2 ft/s²)
• $H$ is the head over the weir crest (e.g., in m or ft)

This equation matches the standard form for a suppressed rectangular weir when velocity of approach is ignored, and it applies directly to the Cipolletti weir due to its design eliminating end contractions.