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A mathematical model of the problem of pulse propagation in a semi-infinite gas pipeline was developed by expressing the pressure drop by the quadratic law of resistance and the local component of the gas inertia force by the law of conservation of momentum, using the law of conservation of mass in a one-dimensional statement. The model repeats the Riemann problem but takes into account the frictional resistance force. Using an auxiliary function in the form of the natural logarithm of the reduced density, and gauge functions, and certain simplifications, an equation for the reference solution of the problem in terms of gas velocity was derived and solved. For the analytical solution of the problem on gas velocity, the Riemann solution was used, and a refined analytical solution was obtained considering the quadratic law of resistance for the calculation of the perturbed and non-perturbed subdomains.

Generalization of the Riemann method for the trunk gas pipelines considering the quadratic law of resistance