Weir Overflow Rate Formula: Clarifier Calculation

What Is the Weir Overflow Rate Formula?

The weir overflow rate formula divides flow by weir length: Weir Overflow Rate (gpd/ft) = Flow (gpd) / Weir Length (ft). Also called weir loading rate, this calculation tells you how much flow passes over each foot of the effluent weir in your clarifier.

That's it. Flow divided by weir length. The result is in gallons per day per foot (gpd/ft), and it tells you whether your clarifier's weir is handling flow evenly or getting slammed with too much water per foot of edge.

Why Does the Weir Overflow Rate Matter?

Here's the practical side. If your weir overflow rate is too high, the velocity of water approaching the weir increases. That pulls settled solids up and carries them right over the weir and into your effluent. You'll see higher TSS in your final effluent, and your permit numbers start looking ugly.

Typical design values for secondary clarifiers generally fall in the range of 10,000 to 20,000 gpd/ft, though specific criteria vary by state standards and design manual. Primary clarifiers can handle higher rates since the solids are heavier and settle faster. If your plant's weir loading rate creeps above design, it might be time to look at adding weir length - which is why you'll sometimes see finger weirs, double-sided launders, or inboard launders. They all increase the total weir length to bring that gpd/ft number down. V-notch weirs are also common, though their primary purpose is to improve even flow distribution across the weir.

How Do You Calculate Weir Overflow Rate Step by Step?

Let's walk through a typical exam problem using the weir rate calculation.

That's well within a typical design range for a secondary clarifier. On the exam, you'd pick the closest answer choice.

What's the Difference Between Weir Overflow Rate and Surface Overflow Rate?

This is where people get burned on the exam. The names sound almost identical, but they're completely different calculations with different units.

The surface overflow rate formula uses the clarifier's surface area (π x r²), while the weir overflow rate uses the weir's linear length (usually the circumference, π x d). If you grab the wrong measurement, you'll get the wrong answer even if your math is perfect.

What About Rectangular Clarifiers?

Rectangular clarifiers are simpler. The weir is usually a straight line across the end of the tank (the effluent end). Sometimes there are multiple weir troughs running the length of the tank.

That's a high weir loading rate. In practice, a designer would add finger weirs or double-sided launders to increase the total weir length and bring that number down. On the exam, don't second-guess the answer just because the number seems high - plug and chug, then pick the match.

What If There Are Multiple Weirs or Double-Sided Weirs?

Some exam questions throw a curveball by specifying an inboard weir trough or double-sided weir. If flow spills over both sides of a weir trough, you count both sides.

For example, if a circular clarifier has an inboard launder trough that's 150 ft long and flow goes over both sides, the effective weir length is:

150 ft x 2 = 300 ft

Always read the problem statement carefully. If it says "double-sided" or "both sides," multiply the trough length by two. If it just says "the weir runs around the circumference," use the circumference as-is.

Common Weir Overflow Rate Exam Traps and Mistakes

Forgetting to convert MGD to gpd. The formula needs gallons per day, not million gallons per day. If your flow is 2.0 MGD, that's 2,000,000 gpd. If you plug 2.0 directly into a formula that expects gallons per day, your answer will be off by a factor of one million.

Using area instead of length. If you catch yourself calculating π x r², stop. That's for surface overflow rate. Weir overflow rate uses the weir's linear length - circumference for a circular tank, width (or total weir trough length) for rectangular.

Using diameter instead of circumference. The weir goes around the tank, not across it. For circular clarifiers, weir length = π x diameter, not just the diameter.

Ignoring the question's weir description. If the problem says the weir is only along 75% of the circumference, don't use the full circumference. Calculate the full circumference, then multiply by 0.75.

Calculator errors from not clearing. This is a general exam trap, but it bites hard on these problems. Clear your calculator between steps, especially when you're switching from a circumference calculation to the division step.

When Do Operators Use the Weir Overflow Rate?

You'll calculate weir overflow rate when:

• Evaluating clarifier performance. If your effluent TSS is climbing, a high weir overflow rate might be part of the problem.
• Reviewing plant design. When your facility is looking at upgrades or capacity increases, weir loading rate is one of the design checks.
• Completing monthly operating reports. Some states and permits require reporting hydraulic loading parameters, including weir overflow rate.

It also ties directly into detention time calculations and overall clarifier hydraulics. A clarifier might have plenty of surface area but still perform poorly if all that flow is funneling over a short weir.

For more on how these clarifier formulas connect, the Sacramento State OWP manuals cover clarifier design criteria in detail, and the EPA's NPDES resources provide regulatory context for permit compliance.