Preferably in MATLAB:

Problem Statement In hydrogen powered fuel cell cars, hydrogen gas is often stored at rest in a tank at 300K and 900 atm. Now consider a tiny hole instantly forms in the tank. Your task is to determine what initial shock strength is to be expected during the subsequent release of hydrogen gas into ambient air. Since there will initially be a discontinuity in pressure, your task is to develop a solution to the well-known "shock-tube" or Riemann problem in order to solve the task at hand. It is also of interest to show how the release shock strength varies with storage pressure. Storage pressures of interest are in the range of 1 atm to 1000 atm To accomplish this goal, it will be necessary to apply the relevant gas dynamic relations through each component: the shock wave (zones 1 to 2) and expansion fan (zones 5 to 3), and match the pressure and velocity across the contact surface accordingly (zones 2 to 3). Since the shock Mach number is unknown, an iterative solution will be required (Newton iteration works well). Solutions should be obtained by writing a computer script or prograim in any language of choice shock tube driver gas High P, P test gas Low P, Xi diaphragm contact surface expansion waves zone 3 shock wave zone 2 zone 4 zone 1 zone 5 Gas A Gas B particle path> -particle path x-0 Schematic of the Shock Tube Problem Problem Statement In hydrogen powered fuel cell cars, hydrogen gas is often stored at rest in a tank at 300K and 900 atm. Now consider a tiny hole instantly forms in the tank. Your task is to determine what initial shock strength is to be expected during the subsequent release of hydrogen gas into ambient air. Since there will initially be a discontinuity in pressure, your task is to develop a solution to the well-known "shock-tube" or Riemann problem in order to solve the task at hand. It is also of interest to show how the release shock strength varies with storage pressure. Storage pressures of interest are in the range of 1 atm to 1000 atm To accomplish this goal, it will be necessary to apply the relevant gas dynamic relations through each component: the shock wave (zones 1 to 2) and expansion fan (zones 5 to 3), and match the pressure and velocity across the contact surface accordingly (zones 2 to 3). Since the shock Mach number is unknown, an iterative solution will be required (Newton iteration works well). Solutions should be obtained by writing a computer script or prograim in any language of choice shock tube driver gas High P, P test gas Low P, Xi diaphragm contact surface expansion waves zone 3 shock wave zone 2 zone 4 zone 1 zone 5 Gas A Gas B particle path> -particle path x-0 Schematic of the Shock Tube