Question

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 \(\text{m}^3\,\text{s}^{-1}\). Assuming constant fluid density and pressure drop across the valve, which one of the following is the flow rate (in \(\text{m}^3\,\text{s}^{-1}\)) through the valve at 30% open?

• A. 1.1
• B. 2.2
• C. 3.3
• D. 4.4

Hint:

Use $f(l)=1/[1+R(1-l)]$ for the hyperbolic valve; find $Q_{max}$ from the 70% open data point, then apply it at 30% open.

Answer 1

The Correct Option is B

Taking the ratio directly, since Q_max cancels: \[ \frac{Q(0.3)}{Q(0.7)} = \frac{1+15}{1+35} = \frac{16}{36} = 0.4444 \] So $Q(0.3) = 0.4444 \times 5 = 2.222 \approx 2.2\ \text{m}^3\,\text{s}^{-1}$.\[ \boxed{Q(30\%) \approx 2.2\ \text{m}^3\,\text{s}^{-1}} \]