A pitot tube is used to determine the airspeed of an airplane. It consists of an

Question

A pitot tube 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; as shown in the figure, that tube in connected to one arm of a U-tube. The other arm of the U-tube is connected to 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. Suppose that the tube contains alcohol and the level difference h is 22.5 cm. What is the plane s speed relative to the air The density of the air is 1.03 kg/m^3 and that of alcohol is 810 kg/m^3

Explanation / Answer

using bernoulli equation

Pa = Pb + rho_air*v^2/2

Pa-Pb = rho*g*h ( for balance the pressure in the two arms of U-tube)

rho*g*h = rho_air*v^2/2

v = sqrt(2*rho*g*h/rho_air)

rho = alcohol density = 810 kg/m^3

rho_air = 1.03 kg/m^3

h = 22.5 cm = 0.225 m

v = 58.89 m/s

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