Below is a running shock tube illustration. 0.1 0.0 | 0.0 4 4 Diaphragm 1 0.5 Image: Shock tube Initial setup 1 3 2 1 Expansion Head Expansion Tail Slip Shock Surface Image: Running Shock Tube Density 0.125 0.300 0.475 0.650 0.825 1.000 Image: Shock C Image: Density distribution in Shock Tube The following are nomenclatures in a shock tube: y: Gas constant =1.4 for air shock tube Ms :Mach number of the shock Ms>1 a1 Sonic Speed downstream of the shock 1.0 a4 Sonic Speed in the driver section P1: Pressure (absolute) of the downstream of the shock P2: Pressure (absolute) of the upstream of the shock P3 Pressure (absolute) of the upstream of the expansion wave P4: Pressure (absolute) of the downstream of the expansion wave T1 Temperature of the downstream of the shock T Temperature of the upstream of the shock P1 Density of the downstream of the shock P2 Density of the upstream of the shock V Flow velocity of the downstream of the shock V2 Flow velocity of the upstream of the shock Shock Relation: = P 2y Py+1 -M 7-1 =1+ 2Y (M 1) y+1 7+1 27 P Expansion relation: PA 2 a Velocity in Region 2 & 3, 3 = = 2 (M.M.) y+1 B-||-7-10 (M-1) P3 This leads to : -=[1 P 7 +1 2y M Contact Surface (Slip Surface) Relation: P2=P3 Overall Relation from Driver and Driven Sections: PPP = = PA P P3 P P P P 2y Or: =(- -M - -)[1 P 7+1 7+1 y-1 (Ms 7 +1 2y 1 y-1 M. So Based on given P4/P ratio, you need to use Matlab to calculate the corresponding M, then calculate a few more parameters in the same program using the following relations: P2_ M P 1+ - (M 1) 7+1 (2_M () }+1 a 2 1 -(Ms a y+1 M y+1 y-1 )(1+ -M) 2 +1 M 2 Use your program to solve initial driver section pressures at: P4=40psi, 60psi, and 80psi respectively. Use input(prompt) function to allow users to enter the P4 pressure manually for calculations, so you don't need to change your program for different P4 values. You will need to submit the matlab code .m file and a brief report in word file explaining your algorithm used in the code and add results of your calculations for above pressures P4.