Question

A utility uses a 4-20 mA signal to determine the level in a well based on pressures. The set points are based on pressures in psi below ground surface (bgs). The 20 mA signal is set at 182 psi bgs and the 4 mA signal at 10 psi bgs. If the reading is 9 mA, what is the water level in feet?

Short answer

The water level is 147.26 feet.

Step-by-step solution

- Understand The Problem

The signal range of 4-20 mA is used to determine the pressures in psi bgs. A conversion needs to be performed from the 9 mA reading to the corresponding psi value using the given set points.

- Signal Conversion Formula

The general formula to convert a 4-20 mA signal to the corresponding measured range is: \( P = P_{\text{min}} + \frac{(P_{\text{max}} - P_{\text{min}})}{16} \times (\text{mA reading} - 4) \)

- Plug in Values

Here, the minimum value is 10 psi bgs and the maximum value is 182 psi bgs, and the reading is 9 mA. Plug in these values into the formula: \( P = 10 + \frac{(182 - 10)}{16} \times (9 - 4) \)

- Simplify the Formula

First calculate the range: \( 182 - 10 = 172 \) Then divide by 16: \( \frac{172}{16} = 10.75 \) Next, multiply by the difference in the mA reading and add the minimum pressure: \( P = 10 + 10.75 (9 - 4) \) \( P = 10 + 10.75 \times 5 \) \( P = 10 + 53.75 \) \( P = 63.75 \) psi

- Convert Psi to Feet

Assume that 1 psi is equivalent to 2.31 feet of water. Convert the pressure in psi to feet: \( \text{Water Level} = 63.75 \times 2.31 \) \( \text{Water Level} \text{ in feet} = 147.26 \)

Key concepts

Signal Conversion in Water Level Measurement

To measure water levels using a 4-20 mA signal is a common practice in industries such as utilities. This method employs a current signal range to communicate the pressure values in psi below ground surface (bgs). The endpoints in this setup are critical:
The 4 mA signal corresponds to the minimum pressure set point, and 20 mA corresponds to the maximum. For our exercise, the set points were:

• 10 psi for 4 mA (low end)
• 182 psi for 20 mA (high end)

Understanding this concept allows us to convert any mA reading within this range to its respective pressure, reflecting the water level inside a well.

Pressure Conversion in Psi

With the signal values understood, the next step is converting the 4-20 mA reading to pressure in psi. The process uses a linear interpolation formula:
\( P = P_{\text{min}} + \frac{(P_{\text{max}} - P_{\text{min}})}{16} \times (\text{mA reading} - 4) \)
This formula effectively breaks down the current range into 16 equal parts and uses it to pinpoint the exact pressure within the given range. Applying the formula to our example with:

• Minimum pressure: 10 psi
• Maximum pressure: 182 psi
• mA reading: 9 mA

We substitute these into the formula:
\( P = 10 + \frac{(182 - 10)}{16} \times (9 - 4) \)
Simplify and solve to find the pressure:
\( P = 10 + \frac{172}{16} \times 5 \)
\( P = 10 + 10.75 \times 5 \)
\( P = 10 + 53.75 \)
\( P = 63.75 \) psi.

Water Level Calculation in Feet

Finally, converting the calculated pressure in psi to the actual water level in feet is straightforward.
We use the conversion factor where 1 psi equals approximately 2.31 feet of water. Given our calculated pressure of 63.75 psi:
\( \text{Water Level} = 63.75 \times 2.31 \)
This leads to:
\( \text{Water Level} = 147.26 \) feet
This simple multiplication gives the direct water level measurement from our psi reading, making it incredibly practical for real-world applications where water levels need constant monitoring.