Calculate the flow velocity at the throat.

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?


 

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