Clarifier Slope

Clarifier Slope Calculations

There are two reasons I’ve had a need to consider the slope in the bottom of a secondary clarifier:

    1. To more accurately compute the volume of the clarifier, and

    2. When using the outstanding GPS-X wastewater modeling program to compute the depth of the clarifier at its center point.

Let’s explore both of these reasons in more detail.

The slope in a conically shaped secondary clarifier is typically described as either being “shallow” or “steep” as shown in the graphic below. For shallow clarifiers the slope is 1-foot for every 50 feet of radius. A steeply sloped clarifier will drop 1-foot for every 12 feet of radius.

clarifier-slope-visio-sketch
volume-cylinder-and-cone

The volume of a cylinder is computed easily enough using the formulas provided below.

Volume of a Cylinder (Diameter)

Volume of a cylinder
volume-of-a-cylinder-full-equation

Volume of a Cylinder (Radius)

Volume of a cylinder

The conical section of a clarifier is calculated as shown below. Using the example of a 100-ft diameter (D) clarifier with a 14-ft sidewall depth (H), the calculations for both a shallow cone and a steep cone are provided.

volume-of-a-cone

The secondary clarifier model in GPS-X requires various inputs including the dimensions of the clarifier found by right-clicking on the clarifier and going to “Input Parameters” and then to “Physical.”.

gpsx-clarifier-2
gpsx-clarifier-3
gpsx-clarifier-4
gpsx-clarifier-5

You can download a simple Excel spreadsheet, shown below, to calculate clarifier surface area, cylinder volume, cone volume, total volume, and depth at the center of the clarifier for both shallow and steep clarifier bottoms by clicking here or on the graphic below.

Excel slope calculations