High-temperature superconductors are strongly coupled systems which present a complicated phase diagram with many coexisting phases. This makes it difficult to understand the mechanism which generates their singular transport properties. Hydrodynamics, which mostly relies on the symmetries of the system without referring to any specific microscopic mechanism, constitutes a promising framework to analyze these materials. In this paper we show that, in the strange metal phase of the cuprates, a whole set of transport coefficients are described by a universal hydrodynamic framework once one accounts for the effects of quantum critical charge-density waves. We corroborate our theoretical prediction by measuring the DC transport properties of Bi-2201 close to optimal doping, proving the validity of our approach. Our argument can be used as a consistency check to understand the universality class governing the behavior of high-temperature cuprate superconductors.