Question

A well (A) has shown quarterly arsenic levels above the MCL over the last year, of 14 \(\mathrm{ug} / \mathrm{L}, 20 \mathrm{ug} / \mathrm{L}, 18 \mathrm{ug} / \mathrm{L}\) and \(16 \mathrm{ug} / \mathrm{L} .\) A utility wants to blend this well to a level of \(8.0 \mathrm{ug} / \mathrm{L}\) with a well (B) that has a level of \(4.5 \mathrm{ug} / \mathrm{L}\). The total production needed from both of these wells is 3,575 gpm. How much can each well produce?

Short answer

Well A: 1000 gpm, Well B: 2575 gpm.

Step-by-step solution

- Determine the average arsenic level for well A

To find the average arsenic level in well A, sum up the arsenic levels measured over the last year and divide by the number of measurements.\[ \text{Average for Well A} = \frac{14 + 20 + 18 + 16}{4} \]

- Calculate average

Compute the sum and then the average.\[ \text{Sum} = 14 + 20 + 18 + 16 = 68 \]\[ \text{Average for Well A} = \frac{68}{4} = 17 \mathrm{ug}/\mathrm{L} \]

- Set up the blending equation

Let \( x \) be the flow rate from well A in gpm and \( y \) be the flow rate from well B in gpm. We know that the total production needed is 3,575 gpm. We also know the final blended concentration should be 8.0 \( \mathrm{ug}/\mathrm{L} \).\[ 17x + 4.5y = 8 (x + y) \]

- Write the equation for total flow

Express the sum of the flow rates from both wells.\[ x + y = 3575 \]

- Substitute and solve

Using the total flow equation, substitute \( y \) with \( 3575 - x \) into the blending equation.\[ 17x + 4.5(3575 - x) = 8(3575) \]

- Simplify the equation

Expand and simplify the equation:\[ 17x + 16087.5 - 4.5x = 28600 \]\[ 12.5x + 16087.5 = 28600 \]

- Solve for x

Isolate the variable \( x \).\[ 12.5x = 28600 - 16087.5 \]\[ 12.5x = 12512.5 \]\[ x = 1000 \mathrm{gpm} \]

- Calculate y

Substitute \( x \) back into the total flow rate equation to find \( y \).\[ y = 3575 - 1000 \]\[ y = 2575 \mathrm{gpm} \]

Key concepts

arsenic concentration calculation

Understanding how to calculate arsenic concentration is critical when dealing with environmental engineering.
In this exercise, we're first asked to find the average arsenic level in a well by summing quarterly measurements and then dividing by the number of measurements.
This is a straightforward arithmetic mean calculation.
Summing the values: \[ 14 + 20 + 18 + 16 = 68 \]
Dividing by the number of measurements (4): \[ \frac{68}{4} = 17 \text{ ug/L} \]

This average gives us an understanding of the consistent contamination level in the well, which is essential in formulating a strategy for safe drinking water. Calculations in environmental contexts like this are important to ensure public health is protected.

water well flow rates

Flow rates are essential in managing water supply systems, particularly when blending is necessary.
In the given problem, the total production needed is 3,575 gallons per minute (gpm). To calculate how much each well can produce, we use the following relationship:

\[ x + y = 3575 \]
Where \( x \) is the flow rate from well A, and \( y \) is the flow rate from well B.

Understanding flow rates aids not only in making sure we meet the water demand but also in ensuring the mixing rates for contaminants like arsenic are properly set.
This step ensures that our blend meets the intended safety guidelines.

blending equations in environmental engineering

Blending equations are used to mix water from different sources to achieve a desired contaminant concentration.
Here, the blending equation is used to mix water from wells with different arsenic concentrations.

The blending equation given in the exercise is:

\[ 17x + 4.5y = 8(x + y) \]

Where:

• 17 ug/L is the average arsenic concentration from well A
• 4.5 ug/L is the arsenic concentration from well B
• 8 ug/L is the desired final blend concentration

By substituting and solving the equations, well engineers ensure the final blended water meets regulatory standards.
Mastering blending equations aids in performing complex environmental assessments in various contexts, contributing to safer water for communities.

MCL for arsenic in drinking water

The Maximum Contaminant Level (MCL) for arsenic in drinking water is a critical guideline.
According to the U.S. Environmental Protection Agency, the MCL for arsenic in drinking water is set at 10 ug/L.
This means that for water to be considered safe for consumption, arsenic levels should not exceed this limit.

In our exercise, despite well A's concentrations being above the MCL, through blending with well B, we aim to achieve a level of 8 ug/L, which is below the MCL.
This demonstrates how actual environmental engineering practices align with regulatory requirements to ensure public safety.
Understanding and adhering to MCLs is essential for anyone involved in managing water quality.