Dry air at a constant temperature of \(T\) passes through a valve into a rigid spherical container (Figure 7.44). The pressure at the inlet is \(p_{\mathrm{i}}\), and the one at the outlet is \(p_{\mathrm{a}}\). The linear resistances of the two valves at the inlet and the outlet are \(R_{1}\) and \(R_{2}\), respectively. Assume that the process is isothermal. Develop a mathematical model of the pressure \(p\) in the container.

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