Problem 13.10 - A * and p zero. For: M 1 = 0.512 M 2 = 1.68...

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Problem 13.10 [Difficulty: 3] Given: Data on flow in a nozzle Find: Mass flow rate; Throat area; Mach numbers Solution: The given or available data is: R = 286.9 J/kg · K k = 1.4 T 0 = 523 K p 1 = 200 kPa p 2 = 50 kPa A = 1 cm 2 Equations and Computations: We don't know the two Mach numbers. We do know for each that Eq. 13.7a applies: Hence we can write two equations, but have three unknowns ( M 1 , M 2 , and p 0 )! We also know that states 1 and 2 have the same area. Hence we can write Eq. 13.7d twice: We now have four equations for four unknowns ( A *, M 1 , M 2 , and p 0 )! We make guesses (using Solver) for M 1 and M 2 , and make the errors in computed
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Unformatted text preview: A * and p zero. For: M 1 = 0.512 M 2 = 1.68 Errors from Eq. 13.7a: p = 239 kPa p = 239 kPa 0.00% and from Eq. 13.7d: A* = 0.759 cm 2 A* = 0.759 cm 2 0.00% Note that the throat area is the critical area Sum 0.00% The stagnation density is then obtained from the ideal gas equation = 1.59 kg/m 3 The density at critical state is obtained from Eq. 13.7a (or 12.22c) * = 1.01 kg/m 3 The velocity at critical state can be obtained from Eq. 12.23) V* = 418 m/s The mass flow rate is * V * A * m rate = 0.0321 kg/s...
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This note was uploaded on 01/20/2012 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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