Mercury is 13× denser than water yet flows just as easily; honey is barely denser than water yet far more viscous.
Density is about mass per volume; viscosity is about internal friction resisting flow — a fluid can be heavy and thin, or light and thick, with no contradiction.
They stop being independent the moment flow is involved. What governs pipe behaviour is kinematic viscosity, ν = µ/ρ, which couples the two: mercury flows freely because its ν is tiny (0.11 mm²/s), not because density and viscosity are unrelated in the Reynolds number.
Estimate with the rule, then check it against the calculator that models it properly.
Open Fluid Properties →Mercury is 13× denser than water yet flows just as easily; honey is barely denser than water yet far more viscous. Density is about mass per volume; viscosity is about internal friction resisting flow — a fluid can be heavy and thin, or light and thick, with no contradiction.