A Venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at speed through a

horizontal section of pipe whose cross$-$sectional area is A$2=0\mathrm{.}0589$ m$2.$ The gas has a density of p $=1\mathrm{.}30$ kg$/$m$3.$ The Venturi meter has

a cross$-$sectional area of Al $=0\mathrm{.}0347$ m$2$ and has been substituted for a section of the larger pipe. The pressure difference between the

two sections is P$2-$ PI $=103$ Pa$.$ Find $($a$)$ the speed $1/2$ of the gas in the larger original pipe and $($b$)$ the volume flow rate Q of the gas.

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Venturi meter