Problem 5–3. Freely Settling Hinge. A plate of density pm, thickness d, and width W (you may consider the third dimension to be infinite – it is a 2D problem – and d/W « 1) is hinged at one edge in contact with the bottom of a tank filled with a viscous liquid. The angle separating the plate and the plane is given by æ. If we release the plate it will settle toward the plane (e.g., a will decrease in time). In the limit a « 1, develop an equation governing a as a function of time. d W Pm a Ps

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Fluid Mechanics

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Problem 5–3. Freely Settling Hinge. A plate of density pm, thickness d, and width W (you may consider the third dimension to be infinite – it is a 2D problem – and d/W « 1) is hinged at one edge in contact with the bottom of a tank filled with a viscous liquid. The angle separating the plate and the plane is given by æ. If we release the plate it will settle toward the plane (e.g., a will decrease in time). In the limit a « 1, develop an equation governing a as a function of time. d W Pm a Ps