Question:

Based on the diagram shown below, what should the mA output of the transmitter be? 

Note – There are many ways to setup DP level applications. In each of them, you get an increasing DP with decreasing level and this must be factored in by either reversing the ports and using negative DP values, or by inverting the calibration curve (which this problem utilizes). It is important for instrument techs and control engineers to be able to work with reversed calibration ranges (which is why this problem uses this approach).

Learning Tip - I sometimes see 'easy' formulas and other cheat-sheets or excel tables for these problems and if you understand the concepts, those can be useful - but if the concepts don't really make sense, the user inevitably enters errant data and the answer is misleading. Take the time to actually understand the concepts of this problem and then you likely won't need a cheat-sheet, and/or it will make it so that you enter the values correctly if you do and you will be able to logic check the answers. 

The answer is provided below the diagram. 

Solution:

Step 1 - determine the DP by finding the total pressure on each port.

Notes: The 17psig vessel pressure is applied to both legs – so it cancels out. Head height is actual distances measured in inches. Pressures are measured in inches water column (IWC) and should factor in Specific Gravity. 

HP port: Head height x Specific Gravity

(140" x 0.934) = 130.76 IWC

LP port: Head height x Specific Gravity

[(10+50) x 0.82) = 49.2 IWC

Find DP: The DP is simply the difference between the HP and LP pressures. So; (HP IWC - LP IWC) = DP IWC

130.76 IWC - 49.2 IWC = 81.56 IWC

Step 2 - Once you know the actual DP, Determine the percent of scale based on the calibration values. Be sure to factor in any reverse scales such as on this problem.  

It is a good idea to sketch or mentally picture the scale and approximate the value before doing the calculations. This not only helps ensure you go the right direction, but it is also very helpful for locking in the concepts and solidifying your understanding of the problem. This is especially helpful when scale values are reversed such as in many wet-leg DP level scenarios. 

For those fluent with linear algebra, you can simply use the standard mX+b scaling formula. For those who prefer to keep it intuitive or don't enjoy algebra so much, you can break it down into the following steps (based on the 'Scale Box' diagram above)

Determine how much of the span the input has traveled. In this case the level has gone from 100 IWC to 81.56 IWC (100-81.56) = 18.44 IWC

Then, determine what percentage of the total span that travel is. In this case the total span is Max-Min (100-20) = 80 IWC

Divide the span input value 'travel' (18.44 IWC), by the total span (80 IWC) to determine the fractional (decimal value) traveled. In this case; 18.44 / 80 = 0.2305. This would equate to 23.05% on a bar graph and matches up easily with the estimate sketch we drew above.  

Now that we know the travel fraction, we can simply reverse the process to determine the mA output, by multiplying the 'travel fraction' by the output span of 16mA, AND THEN adding in the 4mA offset. 

Determine output travel:     

(0.2305 x 16mA) = 3.688 mA 

Determine final output value = output travel + offset start point

(3.688mA + 4mA) = 7.688 mA

Tips on Learning & Understanding this and other related problems: 

If you sketch a diagram on graph paper or roughly to scale, you can picture that the actual level is about 25% up from the low end which would approximate to around 8mA (so we know where the ball park is). Thought of another way; Since it is a wet-leg instrument, the max DP occurs when level is lowest and the DP decreases as the level rises and it has risen about 1/4 of the way upwards from the bottom of the scale - so again, about 8mA.

Creating sketches of a problem is a huge benefit to any tech or engineer because it helps one fully visualize and understand the problem - but it also helps lock the solution and concepts into the brain long term and that pays off huge over time... 

During assessments and interviews, I have noticed that techs and engineers who sketch a problem out and who take the effort to actually visualize the problem and details nearly always perform way better than those who do not in terms of speed and accuracy.

Get in the habit of visualizing any problem you run into as you solve it and then go back to reaffirm and make sure you fully understand the concepts once you find the solution. This single habit is one of the best ways to continuously learn and grow and to become the best possible tech or engineer you can be.