In this paper, we present the results of a statistical study of Pc3 velocity fluctuations in the Earth's dayside magnetosheath. There exists a notable dawn-dusk asymmetry, such that velocity fluctuations generally exhibit enhanced spectral power in the magnetosheath downstream of the quasi-parallel shock. The fluctuations in the central magnetosheath and close to bow shock tend to dampen with increasing tail-ward distance while the opposite trend is observed close to the magnetopause. This strongly suggests that velocity shear driven processes such as the Kelvin-Helmholtz instability drive Pc3 flow variations close to the magnetopause as the velocity shear increases with increasing tail-ward distance. We also show strong evidence that Pc3 velocity fluctuations are significantly enhanced during intervals of faster solar wind speeds. We see negligible differences between data collected during northward and southward IMF orientations, but in general, a dawn-favoured asymmetry persists.