Chapter 17, Problem 18RQ

A pilot tube is a device that measures the velocity of a fluid, typically the airspeed of an aircraft. The failure of the pilot tube was credited as the cause of Austral Lineas Aereas flight 2553’s crash in October 1997. The pilot tube had frozen, causing the instrument to give a false reading of slowing speed. As a result, the pilots thought the plane was slowing down, so they increased the speed and tried to maintain their altitude by lowering the wing slats. Actually, they were flying at such a high speed that one of the slats ripped off, causing the plane to nosedive; the plane crashed at a speed of 745 miles per hour [mph).

In the pilot tube, as the fluid moves, the velocity creates a pressure difference between the ends of a small tube. The tubes are calibrated to relate the pressure measured to a specific velocity, using the speed as function of the pressure difference (P, in units of pascals) and the density of the fluid (ρ, in units of kilograms per cubic meter).

     $\text{v}=(2\text{ρ)0}\text{.5Pm}$

1. a. Create a proper plot of the velocity (v, ordinate) versus the pressure (P) assuming the data are experimental.
2. b. Use polyfit to determine the power relationships for the data sets and graph the resulting trend lines along with the experimental data.