Fourier analysis is usually employed for the computation of blood flow in arteries. Although the orthogonality of Fourier eigenfunctions guarantees the accurate mathematical modeling of the blood pressure and flow waveforms, the physics behind this objective function is frequently missing. We propose a new method to account for the blood pressure and flow, single-cycle (systole-diastole) waveforms. It is based on the one dimensional hydrodynamic mass and momentum conservation equations for viscous flow. The similarity of the linear problem, under discussion, with related transmission line theory in electromagnetic wave propagation, permits expansion in anharmonic, non-separable eigenfunctions. In some cases one term in the expansion is adequate to fit the main peak of the observed waveforms. Analytical formulas are derived for the dependence of the pressure and flow main peaks on whole blood viscosity and distance from the heart, which interpret observations related to hypertension.