Urban vehicular tunnels generally have a branched structure and complex nonlinear aerodynamics, the study of which is crucial for tunnel ventilation design and air quality control. In this study we aim to establish the aerodynamic equations describing the 1D airflow distribution in such bifurcate tunnel systems. A novel piecewise-affine (PWA) approximation is proposed for the flow-dependent local pressure-loss coefficients at tunnel junctions. This enables us to model the system via first-order ODEs with piecewise-quadratic polynomials. Based on this model, we derive the sufficient condition for the uniqueness and stability of the steady-state solution of each ODE piece. This condition is easily verifiable given the tunnel parameters. We will also show via numerical examples that there may exist multiple stable steady-state solutions for the entire system. Our model provides a theoretical foundation for ventilation design and air quality control in complex tunnels as well as for analysis of other hydraulic network systems with similar structures.