A 40-foot-diameter gravity thickener is used to thicken 80 gallons per minute of primary sludge. The primary sludge is applied to the thickener at an initial sludge solids concentration of 4 percent. Find the solids loading rate applied to the gravity thickener in pounds per square foot per day. Round to the nearest whole number.

To find the **solids loading rate** applied to the gravity thickener in pounds per square foot per day, we can break the problem down into the following steps:

### Step 1: Convert the flow rate to gallons per day
We are given the flow rate of 80 gallons per minute. To convert this to gallons per day:

\[
80 \, \text{gallons per minute} \times 60 \, \text{minutes per hour} \times 24 \, \text{hours per day} = 115,200 \, \text{gallons per day}
\]

### Step 2: Convert the concentration to a decimal
The concentration of solids in the sludge is given as 4%. To work with this, we need to convert it to decimal form:

\[
4\% = \frac{4}{100} = 0.04
\]

### Step 3: Calculate the amount of solids in pounds
The amount of solids in the sludge is 4% of the total flow rate. First, we need to convert the gallons of sludge to pounds of sludge. The weight of water is approximately 8.34 pounds per gallon. Thus, the total pounds of sludge per day is:

\[
115,200 \, \text{gallons per day} \times 0.04 \, \text{(concentration of solids)} \times 8.34 \, \text{pounds per gallon} = 38,438.4 \, \text{pounds of solids per day}
\]

### Step 4: Calculate the surface area of the thickener
The thickener has a diameter of 40 feet, so its radius is:

\[
\frac{40}{2} = 20 \, \text{feet}
\]

The surface area \(A\) of the thickener is the area of a circle, which can be calculated using the formula:

\[
A = \pi r^2 = \pi (20)^2 = 1,256.64 \, \text{square feet}
\]

### Step 5: Calculate the solids loading rate
Now, we can calculate the solids loading rate by dividing the total pounds of solids by the surface area of the thickener:

\[
\text{Solids loading rate} = \frac{38,438.4 \, \text{pounds per day}}{1,256.64 \, \text{square feet}} = 30.6 \, \text{pounds per square foot per day}
\]

### Final Answer:
The solids loading rate applied to the gravity thickener is approximately **31 pounds per square foot per day** (rounded to the nearest whole number).

---

Would you like any additional clarification on the steps involved?

Here are 5 related questions to expand on this topic:
1. How does the initial sludge concentration affect the solids loading rate?
2. What would happen if the diameter of the thickener was reduced to 30 feet?
3. How would increasing the sludge flow rate affect the performance of the thickener?
4. What role does gravity play in the thickening process?
5. How can the efficiency of a gravity thickener be improved?

**Tip:** Always ensure that units are consistent throughout your calculations to avoid errors.

Learn how to calculate the solids loading rate for a 40-foot-diameter gravity thickener with an 80 gallons per minute primary sludge flow and a 4% solids concentration. This step-by-step solution covers key concepts such as unit conversions, surface area calculations, and solids loading rate. Ideal for environmental engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation