Problem 4. (20) A constant area tube is filled with air, treated as an inviscid perfect...

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Problem 4. (20) A constant area tube is filled with air, treated as an inviscid perfect gas, undergoing a one-dimensional unsteady process. At a given instant in time, the conditions along the length of the tube (x) are known. Two nearby points, 1 and 2, have the following state: Point 1: T=300K, u-30 m/s (positive u is rightward) Point 2: T=280K, u=40 m/s a) Treating point 1 as the reference state, determine the U and A values at states 1 and 2. b) Use the method of characteristics to determine the state (U and A) at a point 3 at a later dimensionless time Z. c) Points 1 and 2 are separated by 0.1 of the tube length L, which is the reference length, so X2-X1=0.1 Determine the X location of point 3. Also determine the elapsed time (in seconds) between the initial state (1 and 3) and state 3. d) Show on an X-Z diagram the region influenced by states 1 and 2. State in a few words how you would estimate the state of an arbitrary point within that region. Problem 4. (20) A constant area tube is filled with air, treated as an inviscid perfect gas, undergoing a one-dimensional unsteady process. At a given instant in time, the conditions along the length of the tube (x) are known. Two nearby points, 1 and 2, have the following state: Point 1: T=300K, u-30 m/s (positive u is rightward) Point 2: T=280K, u=40 m/s a) Treating point 1 as the reference state, determine the U and A values at states 1 and 2. b) Use the method of characteristics to determine the state (U and A) at a point 3 at a later dimensionless time Z. c) Points 1 and 2 are separated by 0.1 of the tube length L, which is the reference length, so X2-X1=0.1 Determine the X location of point 3. Also determine the elapsed time (in seconds) between the initial state (1 and 3) and state 3. d) Show on an X-Z diagram the region influenced by states 1 and 2. State in a few words how you would estimate the state of an arbitrary point within that region.