You witnessed the failure of a nylon rim which exploded injuring the person filling the tire with air. Develop a documented mathematical model that predicts the time required to reach a specific pressure. Your results are to be tabulated and plotted. Specifically predict the time to change from 100 kPa to 800 kPa. Assume the process is adiabatic and that the tire volume may be represented by a Torus (doughnut). In order work this problem you have to solve for pressure by iterating forwards in time.
Given:
Tire size 25 cm x 8 cm (outside diameter x width)
Rim diameter 11 cm
Air line pressure 1380 kPa
Initial tire pressure 100 kPa
Airline pipe area 32 mm2
Valve orifice area 6 mm2
Initial tire temp 16°C
The volume of torus is pi^2/4 D x d, where D is 19 cm while d is 8 cm. V therefore is 375 cm3.
What math model should I use to start my iteration? Which formula will harmonize all the variables?