$[1$ point$]$ A liquid with volumetric flow rate $Q$ and density $$ flows through a pipe of cross$-$sectional area A and passes through the Venturi "meter" with cross$-$sectional area $a.$ A manometer containing mercury $({}_m)$ is connected between an upstream joint $($station $1)$ and the throat $($station $2),$ and registers a pressure difference of $10$ psig $.$ If the diameter of the pipe is $6$ in $.$ and the throat of the Venturi is $3$ in $.,$ calculate the upstream velocity of the fluid $(=38\mathrm{.}75l\frac{b_m}{f}{t}^3).$