Consider the flow of air through a convergent-divergent  duct, such as the  tube described in Prob. 4.4. The inlet, throat, and exit areas are 3, 1.5, and 2m2, respectively. The inlet and exit pressures are 1.02 x 105 and 1.00 x  N/m2, respectively. Calculate the flow velocity at the throat. Assume incompressible flow with standard sea-level density.

Prob. 4.4.

An instrument used to \ii.Ce the airspeed on many early low-speed airplanes, principally during 1919 to 1930, was the  tube. This simple device is a convergent-divergent duct. (The front section's cross-sectional area A decreases in the flow direction, and the back section's cross-sectional area increases in the flow direction. Somewhere between the inlet and exit of the duct, there is a minimum area called the throat.) See figure below. Let A₁ andA₂ denote the inlet and throat areas, respectively. Let p₁ and p₂ be the pressures at the inlet and throat, respectively. The  tube is mounted at a specific location on the airplane (generally on the wing or near the front of the fuselage) where the inlet velocity V₁ is essentially the same as the free-stream velocity- that is, the velocity of the airplane through the air. With a knowledge of the area ratio A:z/A1 (a fixed design feature) and a measurement of the pressure difference p₁ - P₂• we can determine the airplane's velocity. For example, assume  If the airplane is flying at standard sea level, what is its velocity?