In microfluidics and other low-Reynolds-number systems, hydraulic conductivity often exhibits a continuous spatial gradation due to structural or external field effects; however, the lack of a predictive theory for such graded regions has forced hydrodynamic metamaterial design to rely on piecewise-constant approximations, which introduce parasitic perturbations at layer interfaces. Here, we introduce a continuous-gradient paradigm and establish a predictive forward-design theory. We derive exact analytical expressions for the effective hydraulic conductivity ($H_{\mathrm{eff}}$) of cylindrical graded regions with two canonical radial profiles—power law and linear—and rigorously validate them against finite-element simulations. Armed with these closed-form solutions, we demonstrate the on-demand forward design of devices with prescribed macroscopic responses, including hydrodynamic cloaks realized through two distinct continuous profiles. By inherently suppressing the interface-induced perturbations endemic to stratified designs while precisely replicating the target far-field behavior, our approach offers a pathway toward devices that are both physically robust and fabrication friendly. This work shifts the paradigm from numerical imitation of discrete, layered structures to the rational engineering of continuously tunable effective properties, opening a vast design space for applications in microfluidics, particle manipulation, and engineered porous media.

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• Cloaking
• Flow control
• Hele-shaw flows
• Low Reynolds number flows
• Metamaterials
• Hydrodynamics