Question

Solve the following chemical dosage problems. Be sure to account for the differences in chemical percent concentrations. A water utility produced 11,275 AF of water last year. The entire amount was dosed at an average rate of \(1.5 \mathrm{ppm}\). If the chemical of choice was \(65 \% \mathrm{HTH}\) at a per pound cost of \(\$ 1.85\), what was the annual budget?

Short answer

The annual budget for the chemical is $15,688.08.

Step-by-step solution

Convert Acre-Feet to Gallons

First, convert the total volume of water produced from acre-feet (AF) to gallons. Use the conversion factor: 1 AF = 325,851 gallons. So, 11,275 AF x 325,851 gallons/AF = 3,674,685,025 gallons.

Calculate Total Pounds of Chemical Needed

Next, determine the total amount of chemical in pounds needed to dose the water at 1.5 ppm (parts per million). Since 1 ppm is 1 pound per million gallons: 1.5 pounds per million gallons x 3,674.685 million gallons = 5,512.0275 pounds.

Adjust for Chemical Concentration

Adjust the total pounds needed based on the chemical's concentration. The chemical used is 65% HTH, so the required pure chemical is diluted. Pure chemical pounds = 5,512.0275 pounds / 0.65 = 8,480.0423 pounds of 65% chemical.

Calculate the Total Cost

Multiply the total pounds of chemical needed by the cost per pound to find the annual budget. Total cost = 8,480.0423 pounds x \(1.85 per pound = \)15,688.0783.

Key concepts

Water Utility

Water utilities are essential services that provide communities with safe and clean drinking water. They manage the collection, treatment, and distribution of water to meet public demand. These utilities ensure compliance with safety standards and regulations. They also handle various operational tasks, such as chemical dosing, to maintain water quality. In this context, chemical dosage is critical to eliminate harmful contaminants and ensure safe water for consumption. Without proper dosing, the water delivered may not meet health standards.

Chemical Percent Concentration

Chemical percent concentration indicates the purity of a chemical solution. In this exercise, the chemical used is 65% HTH (High Test Hypochlorite), which means that 65% of the substance is active chlorine. The remaining 35% is inert material.

When calculating the required amount of a chemical, it is essential to adjust based on its concentration. For instance, if you need a particular quantity of pure chlorine, you must account for the percent concentration to determine the actual volume needed. In this problem:

• Total pounds of pure HTH required = 5,512.0275 pounds
• After adjusting for 65% concentration: 5,512.0275 pounds / 0.65 = 8,480.0423 pounds

This calculation ensures the correct amount of the chemical is applied to achieve the desired effect.

Acre-Feet to Gallons Conversion

When dealing with large volumes of water, such as those managed by water utilities, measurements like acre-feet are used. One acre-foot (AF) is the volume of water that would cover one acre to a depth of one foot. To convert acre-feet to gallons, use the conversion factor: 1 AF = 325,851 gallons.

• For 11,275 AF of water: 11,275 AF x 325,851 gallons/AF = 3,674,685,025 gallons

Understanding this conversion is crucial for accurately determining the amount of chemical needed for treatment as it establishes the basis for further calculations.

Parts per Million (ppm)

Parts per million (ppm) is a unit of measurement for chemical concentration, especially in water treatment. It denotes the amount of a substance in one million parts of water. When dosing water at 1.5 ppm: it means 1.5 pounds of chemical per million gallons of water. With the calculated water volume of 3,674.685 million gallons, the required chemical weight can be determined as:

• 1.5 pounds/million gallons x 3,674.685 million gallons = 5,512.0275 pounds

Using ppm helps ensure precise chemical dosing, crucial for maintaining water safety.

Chemical Cost Calculation

Cost calculation is a vital aspect of budgeting for water utilities. After determining the total pounds of chemical needed and adjusting for concentration, the next step is to find the total cost by multiplying the total weight by the chemical's per pound price. In this case:

• Total weight of 65% HTH required = 8,480.0423 pounds
• Cost per pound = \(1.85
• Total annual budget = 8,480.0423 pounds x \)1.85/pound = $15,688.0783

Understanding these steps ensures proper financial planning and resource allocation for effective water treatment processes.