Question

A water tank is \(45 \mathrm{ft}\) tall and has \(32 \mathrm{ft}\) of water in it. If the \(4-20 \mathrm{~mA}\) set points are at \(2 \mathrm{ft}\) and \(42 \mathrm{ft}\) respectively, what is the mA reading?

Short answer

The mA reading is 16 mA.

Step-by-step solution

- Determine the range of the water levels

The given set points for the 4-20 mA signal are at 2 ft and 42 ft. Therefore, the range of the water levels is from 2 ft (minimum) to 42 ft (maximum).

- Calculate the current water level above the minimum set point

The current water level is 32 ft. Subtract the minimum set point (2 ft) from this value to determine how much above the minimum set point the current water level is. 32 ft - 2 ft = 30 ft.

- Calculate the total range of the set points

Subtract the minimum set point (2 ft) from the maximum set point (42 ft) to determine the total range. 42 ft - 2 ft = 40 ft.

- Determine the proportional position of the current water level

Divide the distance above the minimum set point (30 ft) by the total range of the set points (40 ft) to find the proportional position. \( \frac{30 \text{ ft}}{40 \text{ ft}} = 0.75 \)

- Apply the proportional position to the mA range

The mA signal ranges from 4 mA to 20 mA, so the total range is 16 mA (20 mA - 4 mA). Multiply the proportional position (0.75) by the total mA range (16 mA) and add the minimum mA value (4 mA). \( 0.75 \times 16 \text{ mA} = 12 \text{ mA} \) \( 12 \text{ mA} + 4 \text{ mA} = 16 \text{ mA} \)

Key concepts

Water Level Measurement

Water level measurement is an essential task in many industries. This measurement ensures that facilities like water tanks function correctly and safely. To measure the water level, various sensors and systems can be used. Understanding the water level in a tank is crucial for optimizing operations and maintaining safety.
One common method is using a signal that changes according to the water level. Technologies like ultrasonic, float-based, and pressure transducers are some of the popular approaches. These devices give readings that can be converted into understandable units, like feet or meters.
In this exercise, a 4-20 mA signal is used to measure and communicate the water level. This range represents the water level between two defined points – in this case, 2 ft and 42 ft. The conversion involves knowing the current level and translating it into the corresponding mA reading.

Proportional Positioning

Proportional positioning helps in expressing measurements relative to a known range. In our exercise, we use proportional positioning to translate the current water level into the corresponding mA value. This involves simple math to calculate relative distance within a given range.
To start, you find the current water level above a minimum reference point. For our tank, the current water level is 32 ft, and the minimum reference point is 2 ft. So, 32 ft - 2 ft = 30 ft above the minimum point.
Next, determine the total range of interest, which is from 2 ft to 42 ft. Thus, the total range is 42 ft - 2 ft = 40 ft. Now, by dividing the distance above the reference point by the total range, we get the proportional position: 30 ft / 40 ft = 0.75. This ratio shows us how much of the total range is covered by the current water level. We will use this number to find the corresponding mA in the last step.

4-20 mA Signal

The 4-20 mA signal is widely used in industrial and instrumentation control systems to represent various measurements. This current signal ranges from 4 mA (indicating the minimum measured value) to 20 mA (indicating the maximum measured value).
The 4-20 mA signal is preferred because it is less susceptible to signal loss over long distances and electrical noise. It ensures reliable transmission of readings, regardless of external disturbances.
In this exercise, we calculate the mA reading corresponding to a specific water level using proportional positioning. After determining the water level's proportional position (0.75), we apply this to the mA range. The total mA range is 16 mA (20 mA - 4 mA). Multiply 0.75 by 16 mA to get 12 mA. Finally, add this to the minimum signal: 12 mA + 4 mA = 16 mA.
Therefore, the mA reading for 32 ft of water in the tank is 16 mA, clearly showing how water level, proportional positioning, and the 4-20 mA signal interconnect to provide precise and reliable measurements.