(Solved): Problem \#4: Tire dimensions and speed ratings are listed in the sidewall of passenger tires as sho ...

Problem \#4: Tire dimensions and speed ratings are listed in the sidewall of passenger tires as shown in Figure 1. In the figure below it is given that the tire width is $215\mathrm{mm}$ ( 8.465 inches), the sidewall height-to-width ratio is $65\%$, and the wheel rim diameter is 15 inches. The tire volume can be approximated as a short cylinder with a central hole. A typical passenger vehicle tire has an inflated gage pressure of 35 psig and is effectively 'flat' when the gage pressure is less than 10 psig. Consider a scenario in which the tire temperature and pressure are initially $100^{?}\mathrm{F}$ and 35 psig, respectively. The tire is then punctured by a nail resulting in a small round hole having a diameter of 0.025 inches. Assuming ideal (incompressible) flow through this hole, determine: a) the initial mass flow rate of air through the hole when the tire is first punctured $\left({\mathrm{lb}}_{\mathrm{m}}/\mathrm{hr}\right)$, b) the mass flow rate of air through the hole when the tire pressure has fallen to $10\mathrm{psig}(\mathrm{lb}/\mathrm{hr})$, c) Bonus question $(+1\mathrm{pt})$ : how long it will take for the tire to become 'flat' at 10 psig (minutes: seconds)?