### Answer to sTEm–at-Work Puzzle #46: Valve selection documentation

sTEm–at-Work Puzzle #46: Valve selection documentation

Analysis
Although these sTEm- at-work puzzles are intended to connect linear graphics to teaching technician
responsibilities, this puzzle can lead to a practical discussion of the simplest non-linear plots to real valve performance. In this situation the Tech reviewed the valve documentation with the knowledge that the actual value in service, Valve 34-a, (in the pipe) is a "Decreasing Sensitivity" valve type.

Another word for slope is sensitivity.  (High sensitivity means there is a large change in “y” as “x” changes (high slope value)). Valves with initial high sensitivity are also called "Quick Action" valves.  In a "Decreasing Sensitivity" type of valve, the change in the “y” value is high at low values of “x”, (the valve is just opening). When the valve is almost open, “x” is large , the change in the “y” is not as great. For Valve 34-a, the slope value of the plot is not changing much (if at all).  Thus, the chemical processing tech understands that for "Decreasing Sensitivity valves the change in flow rate compared to the change in the valve position (stem motion) decreases as the valve becomes closer to being wide open. The tech also knows that Valve 34-b is a Linear Response type.

A comparison of "y" for the linear response, y = mx +b, and the "y" for the decreasing sensitivity response, y = k(x)1/2 +b, with b= 0 in both models, emphasizes the sharp increase in slope in the red part of Valve 34-a flow response as compared to the small fraction, green abscissa value, in the value opening. The largest slope change (the red part) of the curve occurs before the valve is open (green part of abscissa) 20%.

Question
The Tech decided that the valve installed in the flow stream is correctly labeled as Valve 34-a. Yes or No