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GATE 2024 IN – Question 12

Sensors and Industrial Instrumentation · Flow and level measurement · 1 mark · Multiple choice

The pressure drop across a control valve is constant. Its inherent characteristic has decreasing sensitivity. If $x$ is the fraction of maximum stem position, the fraction of maximum flow $f(x)$ is

  1. $\alpha^{x-1}$, where $\alpha$ is constant
  2. $\sqrt x$
  3. $x$
  4. $x^2$

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Correct answer: (B) $\sqrt x$

Explanation

Sensitivity is $df/dx$. For $f(x)=\sqrt x$, $df/dx=1/(2\sqrt x)$ decreases as $x$ increases. The linear characteristic has constant sensitivity; $x^2$ has increasing sensitivity.

Therefore **B** is the decreasing-sensitivity characteristic at constant pressure drop.