Question

Solve the following chemical dosage problems. Be sure to account for the differences in chemical percent concentrations. A water treatment operator adjusted the amount of \(20 \%\) Alum dosage from \(85 \mathrm{mg} / \mathrm{L}\) to \(70 \mathrm{mg} / \mathrm{L}\). Based on a treatment flow of \(10 \mathrm{MGD}\), what is the cost savings if \(20 \%\) Alum costs \(\$ 2.50\) per pound?

Short answer

The cost savings is $3152.50.

Step-by-step solution

Determine the Initial and Final Dosage Rates in pounds per gallon

Convert the initial and final dosage rates from mg/L to pounds per million gallons (MGD).1 mg/L = 8.34 pounds per MGDInitial dosage: 85 mg/L = 85 * 8.34 pounds per MGDFinal dosage: 70 mg/L = 70 * 8.34 pounds per MGDInitial dosage = 85 * 8.34 = 709.9 pounds per MGDFinal dosage = 70 * 8.34 = 583.8 pounds per MGD

Calculate the Difference in Chemical Dosage

Find the difference in pounds per MGD between the initial and final dosages.Difference = Initial dosage - Final dosage = 709.9 pounds per MGD - 583.8 pounds per MGD = 126.1 pounds per MGD

Determine the Daily Savings in Pounds

Multiply the difference by the treatment flow (10 MGD).Daily savings in pounds = Difference * Flow = 126.1 pounds per MGD * 10 MGD = 1261 pounds

Compute the Cost Savings

Calculate the cost savings by multiplying the daily saved pounds by the cost per pound of Alum.Cost savings = Daily savings in pounds * Cost per pound = 1261 pounds * 2.50 dollars per pound = 3152.50 dollars

Key concepts

Alum dosage adjustment

Adjusting the Alum dosage in water treatment is an important task to ensure effective and efficient water purification. When changing the Alum dosage, it means the concentration of alumine compound added to the system is modified. This helps achieve the desired water quality and can offer cost savings.

The problem deals with reducing the Alum dosage from 85 mg/L to 70 mg/L. **Why is this adjustment necessary?** It could be due to achieving the desired purification level or reducing chemical costs. Here, it targets reducing costs while maintaining efficiency.

An important conversion factor in these calculations is the conversion of mg/L to pounds per MGD (million gallons per day). Since 1 mg/L equals 8.34 pounds per MGD, understanding this conversion is crucial for dosage adjustment computations.

- Initial dosage: 85 mg/L = 85 * 8.34 = 709.9 pounds per MGD
- Final dosage: 70 mg/L = 70 * 8.34 = 583.8 pounds per MGD

By adjusting the dosage, you can calculate the difference per MGD, which in this scenario is 126.1 pounds. This figure is essential for determining daily chemical usage and associated costs.

chemical percent concentration

Chemical percent concentration refers to the proportion of a specific chemical present within a solution. This is significant when calculating dosages and ensuring accurate application in processes such as water treatment.

If a treatment operator uses 20% Alum, it implies that 20% of the solution's mass is Alum. This concentration impacts the amount needed to achieve the desired treatment results. Understanding percent concentration helps adjust the quantity to refine operations and manage costs efficiently.

For precise dosage calculations, we need to convert this 20% concentration into relevant units such as pounds per MGD. Given that the solution's concentration is a key factor:

• High concentration means fewer pounds needed per gallon for the same chemical effect.
• Lower concentration requires more solution to maintain the same efficacy.

Accurate calculations of chemical percent concentration ensure optimal application and cost management in water treatment processes.

cost savings calculation

Calculating cost savings is critical to evaluating the financial benefits of adjusting chemical dosages. By reducing the amount of Alum used from 85 mg/L to 70 mg/L, the operator can achieve considerable cost savings.

The sequence follows:

1. Determine the initial and final dosages in pounds per MGD.
2. Find the difference in pounds per MGD between initial and final dosages.
3. Multiply this difference by the daily flow rate (10 MGD) to find the daily savings in pounds.
4. Finally, compute the cost savings by multiplying the daily savings by the cost per pound of Alum.

Following through:

• Initial dosage: 85 * 8.34 = 709.9 pounds per MGD
• Final dosage: 70 * 8.34 = 583.8 pounds per MGD
• Difference: 126.1 pounds per MGD
• Daily Savings = 126.1 pounds * 10 MGD = 1261 pounds
• Cost Savings = 1261 pounds * \(2.50 = \)3152.50

This methodical calculation shows substantial daily cost savings, demonstrating how careful dosage adjustment can lead to significant financial benefits without compromising water quality.