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Fluid mechanics

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Angle between AB and the horizontal = arc-tan(1.5/2) degrees = 36.87 degrees Lenth of AB = square-root[1.5^2 + 2^2] m = 2.5 m The centroid of AB is at its mid-point, hence depth of centroid below water surface = (2 + 1.5/2) m = 2.75 m Pressure at centroid = 1025 x 9.81 x 2.75 N/m^2 Fluid force per metre width of the gate = (1025 x 9.81 x 2.75) x 2.5 N = 69 130 N Area moment of inertia of the gate about its centroid = 1 x 2.5^3/ 12 m ^4 = 1.302 m ^4 Distance of centroid below water surafce measured along diraction of the gate = 2.75/sin(36.87) m = 4.583 m Hence, distance of point of action of fluid force below water surface, measured along direction of gate = [4.583 + 1.302/(4.583 x 2.5 x 1)] m = 4.697 m Distance of action point of fluid force from B, measured along the gate = [3.5/sin(36.87) - 4.697] m = 1.136 m Take moment about B, 69130 x 1.136 = P x (2.5sin(36.87) P= 52 354 N

其他解答:A215E4A2B88AAE64
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