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In earlier papers (Bagnold 1936, 1937a) a description was given of experiments made in a wind tunnel 1 ft. sq. in cross-section to examine the conditions of wind and ground surface governing the mass flow q of sand across open country. It was found that: (a) The sand movement over a loose sand surface profoundly modifies the vertical velocity distribution of the wind, and that Prandtl's expression for the velocity distribution over a roughly surface of immobile grains v = 5.75 V log 30z/k (1) (where the drag velocity V = √(T/p), z is the height of measurement above the surface, k is the height above the surface at which v is zero―a height of the order of 1/30 of the dimension of the surface irregularity, i. e. the grain diameter, T is the surface drag and p the air density)
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R. A. Bagnold (1938) studied this question.
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