Chapter 14, Problem 62P

A pitot tube (Fig. 14-48) is used to determine the airspeed of an airplane. It consists of an outer tube with a number of small holes B (four are shown) that allow air into the tube; that tube is connected to one arm of a U-tube. The other arm of the U-tube is connected lo hole A at the front end of the device, which points in the direction the plane is headed. At A the air becomes stagnant so that v_A = 0. At B, however, the speed of the air presumably equals the airspeed v of the plane. (a) Use Bernoulli’s equation to show that

$v=\sqrt{\frac{2\rho gh}{{\rho }_{{}_{air}}}},$

where ρ is the density of the liquid in the U-tube and h is the difference in the liquid levels in that tube. (b) Suppose that the tube contains alcohol and the level difference h is 26.0 cm. What is the plane's speed relative to the air? The density of the air is 1.03 kg/m³ and that of alcohol is 810 kg/m³.

Figure 14-48 problems 62 and 63