Abstract
We develop a unified viscous hydrodynamics for charge and valley transport in gapped graphene in the quantum Hall regime. We redefine Hall viscosity as a response to static electric-field gradients instead of strain, establishing a derivative hierarchy that fundamentally links it to nonlocal Hall conductivity. The theory predicts quantized Hall viscosity for charge and valley, including a ground-state contribution. Crucially, the valley current is unaffected by the Lorentz force and is directly accessible via the local pressure, namely the electrostatic potential that tracks fluid vorticity.