Question

A thin, SQUARE plate of mass M, side length D is rigidly and centrally connected to a small rigid rod on its top edge. The plate-rod assembly is hung in a stream of air which blows horizontally at a constant speed V, and the assembly pivots about a hinge at the rod’s upper end, as shown. The plate-rod assembly is well balanced, such that the plate’s top edge is always horizontal. The whole arrangement is at sea level in standard conditions. Under the effect of the wind, the plate-rod assembly is deflected by an angle α with respect to the vertical, as shown. the middle of the plate is at a distance L from the hinge. Neglect the mass of the rod, and assuming steady flow and negligible drag on the rod, determine the air speed V for the following data: D = 200 mm, L = 220 mm, M = 200 g, α = 20°

L Small Rod Plate

Answer 1

Solution Given DE 200Ymm o. 2 Y = 220mm = 0.22m M = 20명 =02y Cc 20 level At sea density of air I2 Nomal force activg giren by cn the plate is F PA V2 E 2 X 0 04 XVCOS 20 COSO y2 Fn .0451 hinge Taking moment about Mg x L sinor Fn x L Ma sin o 0. 2X 9.8xsin20 O.671 Equating aud (2) we 2 O. 045 V O.671 V 3.857 mys