Many different types of animals use appendages bearing rows of hairs to capture food or molecules from the surrounding fluid, to locomote or to move fluids past themselves. The performance of these appendages, whose hairs operate at Reynolds numbers (Re) of 10(-5) to 10, depends on how much of the fluid that they encounter flows through the gaps between the hairs rather than around the perimeter of the whole array. We have employed mathematical modeling, microcinematography of hairy appendages on small aquatic animals and flow visualizations around dynamically scaled physical models to elucidate the factors that determine the leakiness of arrays of hairs. We found that rows of hairs operating at very low Re function as paddles, whereas those at Re near 1 operate like leaky sieves. The Re range through which the transition in leakiness occurs depends on the geometry of the appendage. We have discovered that different aspects of morphology and behavior are important in determining the leakiness of a hair-bearing appendage at different Re. Our study has revealed conditions under which morphological diversity of hairy appendages has little consequence for performance and other conditions under which simple changes in speed, size or mesh coarseness can lead to novel physical mechanisms of operation.