Problem $4(25$ points$)$: Methanol at $20C$ flows through a $4$ in diameter pipe. It is metered by a modern Venturi nozzle with a diameter of $2$ inches. The measured pressure drop is $1000lb\frac{f}{f}{t}^2.$

${}_{\text{m}\text{e}\text{t}\text{h}\text{a}\text{n}\text{o}\text{l}}=1\mathrm{.}53$slu$\frac{g}{f}{t}^3$;${}_{\text{m}\text{e}\text{t}\text{h}\text{a}\text{n}\text{o}\text{l}}=1\mathrm{.}25{10}^{-5}$ slug $\frac{?}{ft}-s.$

Estimate the volume flow rate $Q.$