Weir Flow Calculations for Field Inlets in Sag Locations

Before we jump into specific guidelines, let’s understand the standard equations.

In the context of weir flow into a grate inlet, it's crucial to understand the differences between the weir coefficient and the discharge coefficient, as they represent distinct aspects of the flow behaviour.

Weir Discharge

Q ?????????? Discharge (m3/s)

C???????????? Weir coefficient

L????????????? Weir crest length (m)

H??????????? Energy head over weir crest (m)

The weir coefficient, as depicted in the weir equation above, is a composite parameter encompassing several components, including the discharge coefficient, the gravitational constant, and geometric constants.

Weir Coefficient

Cd?????????? Discharge coefficient

g????????????? Gravitational constant ≈ 9.81m/s2

Cd is typically 0.56 as used for field inlet calculations. This results in a weir coefficient of:

You may see weir coefficients Cw of 1.66, 1.67, 1.7 etc. depending on the guidelines used, which correspond to the above discharge coefficient (Cd = 0.56).

The discharge coefficient remains dimensionless, ensuring consistency across both English (U.S. Customary) Units and SI Units. However, the weir coefficient varies with unit systems due to its dependence on the gravitational constant, rendering it dimensioned. Therefore, it assumes distinct values depending on the unit system employed. It's imperative to exercise caution when distinguishing between C and Cd (weir vs. discharge coefficients), as they are distinct parameters often erroneously interchanged.

HEC-22

The Hydraulic Engineering Circular No. 22 (HEC-22) is a document published by the Federal Highway Administration (FHWA) in the United States. It provides comprehensive guidance on the design of highway drainage systems. HEC-22 covers various aspects of hydraulic design related to highway drainage, including the analysis and design of culverts, stormwater management, erosion control, and hydraulic modelling.

The document is widely used by engineers, designers, and professionals involved in the planning, design, construction, and maintenance of highway infrastructure. It offers detailed information, methodologies, and procedures for effectively managing stormwater runoff, preventing flooding, and ensuring the integrity and longevity of highway drainage systems.

Many Australian guidelines, standards and practices adopt HEC-22 as a trusted resource by civil engineering professionals. The current 4th Edition was published February 2024.

HEC-22 Weir Flow Equations

Field Inlet – Weir Flow Conditions (HEC-22 3rd Ed. 2009)

Qi ?????????? Inflow (m3/s)

Cw?????????? Weir coefficient ≈ 1.66

P???????????? Perimeter of grate (m)

d???????????? Average depth across the grate (m)

Field Inlet – Weir Flow Conditions (HEC-22 4th Ed. 2024)

Qi ?????????? Inflow (m3/s)

Cw?????????? Weir coefficient (typically equal to 0.37)

g????????????? Gravitational constant ≈ 9.81m/s2

P???????????? Perimeter of grate (m)

d???????????? Average depth across the grate (m)

Wait a moment… this differs from the HEC-22 3rd Ed. equation. Has the equation changed? Or is there an error in this publication?

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