An aircraft is flying horizontally. A Pitot tube is mounted on the aircraft to measure its speed. The pressure difference between the stagnation point (where air is brought to rest) and the static port is measured using a U-tube manometer filled with a liquid of density _L . If the density of air is _a , the height difference in the manometer liquid column is h , and the acceleration due to gravity is g , the speed o

Step-by-step solution

The pressure difference P measured by the manometer is given by the hydrostatic pressure of the liquid column: P = _L g h According to Bernoulli's principle, the pressure difference between the stagnation point (where velocity is zero) and the static port (where velocity is v ) is equal to the dynamic pressure of the air: P = 1 2 _a v^2 Equating the two expressions for P : _L g h = 1 2 _a v^2 Solving for the speed of the aircraft v : v^2 = 2 _L g h _a v = 2 _L g h _a Answer: 2 _L g h _a