$3\mathrm{.}2-2.$ Gas Flow Rate Using a Pitot Tube. The flow rate of air at $37\mathrm{.}8C$ is being measured at the center of a duct having a diameter of $800$ mm by a pitot tube. The pressure difference reading on the manometer is $12\mathrm{.}4$ mm of water. At the pitot tube position, the static pressure reading is $275$ mm of water above one atmosphere absolute$.$ The pitot tube coefficient is $0\mathrm{.}97.$ Calculate the velocity at the center and the volumetric flow rate of the air.