A liquid of density $750$ kg m$^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from $A_{1} = 1.2 \times 10^{-2}$ m$^{2}$ to $A_{2} = \frac{A_{1}}{2}$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is \_\_\_\_ $\times 10^{-3}$ m$^{3}$ s$^{-1}$.