Figure 4: Transport law for a curved medium with 16 metric perturbations (amplitude a0 = 0.1, width r0 = 4). | Scientific Reports

Figure 4: Transport law for a curved medium with 16 metric perturbations (amplitude a0 = 0.1, width r0 = 4).

From: Energy dissipation in flows through curved spaces

Figure 4

The solid line in the main plot represents a fit with respect to the non-linear transport law, |∇P| = αvΦ + βΦ2 for α = (5.8 ± 0.2) × 10−5 and β = (6.6 ± 0.3) × 10−5. Upper inset: Flux Φ as function of viscosity v at constant pressure drop |∇P| = 2.9 × 10−7. The solid line represents a fit using Eq. (3), obtaining α = (6.01 ± 0.06)10−5 and β = (6.7 ± 0.3) × 10−5, in agreement with the fitting values found above. Lower inset: Friction factor f = |∇P|/Φ2d as function of the Reynolds number Re = Φd/μ. We observe a linear power law, f = α/Re, for small Reynolds numbers, Re ≲ 2, where the flow is dominated by viscous shear forces, while for higher Reynolds numbers, Re ≳ 2 the departure from the linear law is visible.

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