The GATE Grind

GATE 2026 CH – Question 44

Instrumentation and Process Control · Controller modes, control valves and tuning · 2 marks · Multiple choice

A control valve with hyperbolic characteristics has a turndown ratio (ratio of maximum flow to minimum controllable flow) of 50. The flow rate through the valve at 70% open is 5 m$^3$ s$^{-1}$. Assuming constant fluid density and pressure drop across the valve, which one of the following is the flow rate (in m$^3$ s$^{-1}$) through the valve at 30% open?

  1. 1.1
  2. 2.2
  3. 3.3
  4. 4.4

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 2.2

Explanation

For a hyperbolic valve with turndown $R$, the flow fraction is $f = \frac{1}{R - (R - 1)x}$ where $x$ is the fraction open. With $R = 50$: at $x = 0.7$, $f = \frac{1}{50 - 34.3} = 0.0637$ and at $x = 0.3$, $f = \frac{1}{50 - 14.7} = 0.0283$. The flow at 30% is $5 \times \frac{0.0283}{0.0637} = 2.22$ m$^3$ s$^{-1}$.