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Question: 1 3 points consider flow a mach 6 ludwieg tube...

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1. [3 points] Consider flow a Mach 6 Ludwieg tube. Gas in the upstream driver tube is initially at a pressure of 2 atm and a temperature of 650 R. When the wind tunnel is started, gas under stagnation conditions upstream is expanded through a converging-diverging nozzle to the test section.

(a) If the working fluid is air with constant specific heats and g = 1.4, determine the following conditions in the test section (with the units indicated):

(i) The static temperature, Te [R],

(ii) The static pressure, Pe [lb/ft2],

(iii) The static density, re [slugs/ft3],

(iv) The velocity, ue [ft/s],

(v) The stagnation pressure, P0e [lb/ft2].

Assume there is no model in the test section and, therefore, no shock waves. Use the tables in the appendices of the text to help you solve this problem.

(b) Redo the problem in part (a); however, now assume the working gas is Helium. The value of the ratio of specific heats is g = 5/3, and the value of the specific gas constant for Helium is R = 12,419 ft . lb/(slug . R). Because the gas has a different value of g than in part (a), the same nozzle will give a different Mach number in the test section. Using methods we will learn later in the semester, we find the Mach number with Helium in the wind tunnel is 9.26. Assume the stagnation pressure and temperature are the same as used in part (a). Use the equations in the text to solve for the quantities (i)-(v). As you are working the problem, be sure to make it clear what equations from the text you are using. Check the assumptions to be sure the equations are valid for the situation in which you are using them.

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