A Venturi meter is a device for measuring the speed of a fluid within of a pipe. The drawing shows a gas flowing at speed v$2$ through a horizontal section of pipe whose cross$-$sectional area is A$2=0\mathrm{.}0779$ m$2.$ The gas has a density of p$=1\mathrm{.}30$ kg$/$m$3.$ The Venturi meter has a cross$-$sectional area of A$1=0\mathrm{.}0187$ m$2$ and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P$2-$P$1=57\mathrm{.}2$ Pa$.$ Find $($a$)$ the speed v$2$ of the gas in the larger original pipe and $($b$)$ the volume flow rate Q of the gas.