We present an analytical solution of flow through disordered porous media with inertia effects at a finite Reynolds number ($\mathrm{Re}$), and consequently a truncated quadratic formula for easy use without any fitting parameters. The derivation is based on an effective capillary model in which the effective radius of capillaries varies with $\mathrm{Re}$. Inspired by the asymptotic solution of flow in curved capillaries [S. Murata, Y. Miyake, and T. Inaba, J. Fluid Mech. 73, 735 (1976)], the Oseen-form equation is derived to capture the flow behavior in each capillary. The analytical formula has been validated by comparisons with numerous available experimental data.

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• Flows in porous media
• Laminar flows
• Low Reynolds number flows
• Porous media
• Functional analytical methods