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The effect of compaction and fiber volume fraction on the transverse permeability of a fluid flowing through stacked layers of fiber mats has been experimentally studied. A Unifilo-101 random mat of continuous glass strands, held together with a binder soluble in styrene was used. The stacked layers were compacted using a Wabash instrumented press. Changing the maximum load, resulted in different fiber volume fractions. Mixtures of glycerol and water with viscosities between 85 and 100 mPa-s were used. This fluid is passed in a rectangular cell, through the fibers arranged transverse to the direction of flow. The pressure drop across the mat and the flow rate were monitored. The study was carried out at different flow rates of the fluid and was repeated for other fiber volume fractions. A power-law relation was observed between the permeability and the fiber volume fraction.