A pitot tube (the figure) is used to determine the airspeed of an airplane. It c

Question

A pitot tube (the figure) 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 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 VA = 0, At B, however, the speed of the air presumably equals the airspeed B of the plane. Use Bernoulli's equation to derive a formula giving the air speed in terms of the difference h in the liquid levels in that tube, the density of the liquid in the U-tube, and the density of air Pair. Suppose that the tube contains alcohol and the level difference h is 34.0 cm. What is the plane's speed relative to the air? The density of the air is 1.14 kg/m3 and that of alcohol is 810 kg/m3. Air Hole A Liquid Number Units

Explanation / Answer

from Bernaulli's eqn we know that

P1 + h rho g + 1/2 rho(a) v1^2 = P2 + h rho g + 1/2 rho v2^2

P is same ; v2 = 0 ;

1/2 rho(a) v1^2 = h rho g

v1 = sqrt [(2 h rho g)/ rho(a)]

Given, h = 34 cm = 0.34 m ; rho = 810 kg/m^3 ; rho(a) = 1.14 kg/m^3 ;

v1 = v = sqrt [2 x 0.34 x 810 x 9.81/1.14] = 68.85 m/s

Hence, v = 60.85 m/s

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