  The strongly correlated electron fluids in high temperature cuprate
superconductors demonstrate an anomalous linear temperature ($T$) dependent
resistivity behavior, which persists to a wide temperature range without
exhibiting saturation. As cooling down, those electron fluids lose the
resistivity and condense into the superfluid. However, the origin of the
linear-$T$ resistivity behavior and its relationship to the strongly correlated
superconductivity remain a mystery. Here we report a universal relation
$d\rho/dT=(\mu_0k_B/\hbar)\lambda^2_L$, which bridges the slope of the
linear-$T$-dependent resistivity ($d\rho/dT$) to the London penetration depth
$\lambda_L$ at zero temperature among cuprate superconductor
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and heavy fermion superconductors
CeCoIn$_5$, where $\mu_0$ is vacuum permeability, $k_B$ is the Boltzmann
constant and $\hbar$ is the reduced Planck constant. We extend this scaling
relation to different systems and found that it holds for other cuprate,
pnictide and heavy fermion superconductors as well, regardless of the
significant differences in the strength of electronic correlations, transport
directions, and doping levels. Our analysis suggests that the scaling relation
in strongly correlated superconductors could be described as a hydrodynamic
diffusive transport, with the diffusion coefficient ($D$) approaching the
quantum limit $D\sim\hbar/m^*$, where $m^*$ is the quasi-particle effective
mass.
