Guest Column | November 30, 2016

Math Solutions: Hydraulic Loading Calculations

Wastewater Dan Theobald

By Daniel Theobald, "Wastewater Dan"

Water Online’s “Math Solutions” series, presented by wastewater consultant and trainer Dan Theobald (“Wastewater Dan”), instructs operators on hydraulic loading calculations.

Hydraulic loading is defined in a wastewater treatment process unit as the volume of wastewater applied to the surface of the process unit per time period. It is often expressed in gallons per day per square foot (gpd/ft2).

Hydraulic loading design criteria are often expressed as maximum days to optimize water clarity resulting from actual square feet surface area per incoming flow rate.

Water clarity is often improved by either increasing surface area or decreasing incoming  flow rate.

This tool for operators, represented through video tutorials, offers mathematical templates to master the hydraulic loading gallons per day per square foot by evaluating the incoming flow and surface area.

The tool also provides definitions, explanations, and alternative applications for the calculations beyond the specific examples presented. In addition to operators, it may also serve educators, engineers, regulators, and others.

A representative hydraulic loading math word problem followed by exact step-by-step solutions is presented  below.

Determine the number of the four (4) large, idle clarifiers ‘out of service’ that are needed to put ‘in service’ in the wastewater treatment plant. Assume flow of 2,000 gpm from 7:00 a.m. to 5:00 p.m. and 511.9048 gpm from 5:00 p.m. to 7:00 a.m. Seven (7) small clarifiers in service have a diameter of 213.2968387 feet and the four large clarifiers in service have a diameter of 282.166324 feet; the design-required gpd per square foot must not exceed 2.75.

Hydraulic Loading Calculation Solutions

Flow Calculation Solutions:

Flow – Daytime (10 hours):

Flow – Nighttime (14 hours):

Flow – gpd (24 hours):


Surface Area Calculation Solutions:

Surface area – One small clarifier:

Surface area – One large clarifier:

Surface area – All clarifiers in service:

Resulting Hydraulic Loading Calculation Solutions:

Gallons per day per square foot (gpd/ft2):

Combined required surface area (ft2):

Number of idle large clarifiers to put in service:

Playlist of 45-plus process control calculations (including hydraulic loading)

Playlist of 35-plus ‘conversions’ wastewater math calculations

Playlist of 20-plus ‘volume’ wastewater math calculations

Playlist of all 160-plus Math Solutions

This is the Hydraulic Loading Calculations presentation in my series of “Math Solutions.” If you have specific wastewater math queries, please submit a question

About Dan Theobald:

Known in the industry as “Wastewater Dan,” Daniel L. Theobald, proprietor of Environmental Services (, is a professional wastewater and safety consultant/trainer. He has more than 24 years of hands-on industry experience operating many variants of wastewater treatment processing units and is eager to share with others his knowledge about water conservation.

Theobald serves as an active consultant for industries looking to achieve and maintain improved wastewater treatment at reduced cost. He is a Lifetime Member of the Who’s Who Registry of Professionals and holds numerous certifications from wastewater management regulatory boards and professional organizations. Theobald contributed one chapter to the Water Environment Federation’s ( Manual of Practice # 37 (MOP-37), a technical manual resource guide for biological nutrient removal, published in 2013.