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Constant head permeability tests were performed on two soil specimens, $S1$ and $S$. The ratio of height of the two specimens $(L_{S1}: L_{S2})$ is $1.5$, the ratio of the diameter of specimens $(D_{S1}: D_{S2})$ is $0.5$, and the ratio of the constant head $(h_{S1}: h_{S2})$ applied on the specimens is $2.0$. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens $(k_{S1}: k_{S2})$ is _____
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