Accurate modeling of acoustic propagation in tubes of varying cross-section in musical acoustics must include the effect of viscous and thermal boundary layers. Models of viscothermal losses are classically written in the frequency domain. An approximate time-domain model is proposed, where all the physical parameters of the instrument as the bore shape or the wave celerity are explicit coefficients. The model depends on absolute tabulated constants which only reflect that the pipe is axisymmetric. It can be seen as a telegrapher’s equations augmented by an adjustable number of auxiliary unknowns. A global energy is dissipated. A time discretization based on variational approximation is proposed along with numerical experiments and comparisons with other models