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 $5 \mathrm{~m}^{3} \mathrm{~s}^{-1}$. Assuming constant fluid density and pressure drop across the valve, which one of the following is the flow rate (in $\mathrm{m}^{3} \mathrm{~s}^{-1}$) through the valve at $30 \%$ open?
- $1.1$
- $2.2$
- $3.3$
- $4.4$
