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MAT136H1 Lecture Notes - Riemann Sum

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UTSG
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Mathematics
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MAT136H1
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Question #3 (medium): hydrostatic force on a partially submerged vertical plate. The hydrostatic force is given by the depth below the surface, the area of the thin th strip. A vertical plate that is partially submerged in water has the shape shown by the diagram. Express the hydrostatic force against one side of the place by a riemann sum as well as an integral, and then evaluate it. [a upside down trapezoid with top side of and bottom side of , height h with emerged in water] The units are given in variables, therefore is kept as it is. , the depth be determined based on the similar triangle ratio:

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Related Questions

A trapezoidal plate with bases 2 m and 4 m is partially submerged vertically in water so that the top is 1 m above the surface and the bottom is 1 m below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)

A trapezoidal plate with bases 4 m and 8 m is partially submerged vertically in water so that the top is 2 m above the surface and the bottom is 2 m below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)

A trapezoidal plate with bases 2 m and 4 m is partially submerged vertically in water so that the top is 1 m above the surface and the bottom is 1 m below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)