$6\mathrm{.}53$ A flow nozzle is a device for measuring the flow rate in a pipe. This particular nozzle is to be used to measure low$-$speed air flow for which compressibility may be neglected. During operation, the pressures $p_1$ and $p_2$ are recorded, as well as upstream temperature, $T_1.$ Find the mass flow rate in terms of $p=p_2-p_1$ and $T_1,$ the gas constant for air, and device diameters $D_1$ and $D_2.$ Assume the flow is frictionless. Will the actual flow be more or less than this predicted flow? Why?