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?