Dry air at a constant temperature of \(25^{\circ} \mathrm{C}\) passes through a valve out of a rigid cubic container of \(1.5 \mathrm{~m}\) on each side (Figure 7.42). The pressure \(p_{\mathrm{o}}\) at the outlet of the valve is constant, and it is less than \(p\). The valve resistance is approximately linear, and \(R=1000 \mathrm{~Pa} \cdot \mathrm{s} / \mathrm{kg}\). Assume that the process is isothermal.

a. Develop a mathematical model of the pressure \(p\) in the container.

b. Construct a Simulink block diagram to find the output \(p(t)\) of the pneumatic system if the pressure inside the container is initially 2 atm and the pressure at the outlet is \(1 \mathrm{~atm}\).

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Pip FIGURE 7.42 Problem 1. V R 90 Po