Modern urban vehicular tunnels generally have a branched structure and complex nonlinear aerodynamics. We established and analyzed the 1-D aerodynamic equations and pollutant dispersion model in such bifurcate hydraulic networks. To design a tractable model that captures system complexity, we proposed a novel piecewise-affine (PWA) approximation for the flow-dependent local pressure-loss coefficients at tunnel junctions. This enables us to model the flow system via first-order ordinary differential equations (ODEs) with piecewise-quadratic polynomials. We proved a fundamental and easily verifiable sufficient condition for the uniqueness and stability of the steady-state solution of each ODE piece. We also demonstrated via a numerical study that for the entire system (across different ODE pieces) there may exist multiple stable steady-state solutions, which can lead to different CO concentration distributions in the system. Our study provides a systematic modeling tool and a theoretical foundation for air quality management in complex tunnels.