In the following practice problem, we’ll learn how to calculate detention time. Simply put, it’s the amount of time the wastewater spends inside of a basin, such as a primary clarifier or a secondary clarifier. For example, if an influent spends three hours inside of a basin to get from the point of entry to the outflow pipe, then its detention time is three hours. It’s a fairly simple concept.
Here’s a video that demonstrates how to calculate detention time.
[latexpage]
If you finished watching the video, let’s go through a different sample problem for more practice.
Practice Problem:
A circular clarifier with a diameter of 52 feet and a depth of 9 feet has a flowrate of 1.7 MGD. Find the detention time in hours.
Known:
Diameter = 52 feet
Depth = 9 feet
Flowrate = 1.7 MGD
Solve for:
Detention = ? hours
Step 1: Calculate the Volume
In order to calculate the detention time, we need the volume of the clarifier and the flowrate. Since we don’t have the volume, we’ll need to calculate it before we can use the detention time formula. Note that the volume of a circular clarifier is the volume of a cylinder.
Detention time (hr) = $latex \frac{tank\;volume\;(gal)}{flowrate\;(gal/hour)}&s=2$
Volume of Cylinder = Area of Circle x Depth
Area of Circle = 0.785 x Diameter x Diameter
Area of Circle = 0.785 x 52 feet x 52 feet = 2,122.64 $latex ft^{2}$
Volume = 2, 122.64 $latex ft^{2}$ x 9 ft = 19,103.76 $latex ft^{3}$
Convert from $latex ft^{3}$ to gallons.
19103.76 $latex ft^{3}$ x $latex \frac{7.48 gallons}{ft^{3}}&s=2$ = 142,896.12 gallons
Step 2: Convert Flowrate from MGD to Gallons/Hour
We need to convert the flowrate from MGD to gallons/hour so that the gallons will cancel out in the Detention Time formula, and the answer will be in hours.
1.7 MGD = 1,700,000 gallons/day
1,700,000 $latex \frac{gallons}{day}$ x $latex \frac{1 \;day}{24\;hours}&s=2$ = 70,833.33 gallons/hour
Step 3: Calculate Detention Time
Detention time (hr) = $latex \frac{clarifier\;volume\;(gal)}{flowrate\;(gal/hour)}&s=2$
Detention time (hr) = $latex \frac{142,896.12}{ 70,833.33}&s=2$ = 2 hours
HELPFUL RESOURCES
Practice Tests for Wastewater Treatment Operator Certification
Questions on detention time are common on the operator certification exam, so make sure to solve many practice problems until you feel confident with your knowledge. Tackling wastewater math involves repetition. Do as many problems as you can to improve your problem-solving skills.
For more practice problems, click here.