The flow of water from a reservoir is controlled by a 3.5-m-wide L-shaped gate hinged at...

 

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The flow of water from a reservoir is controlled by a 3.5-m-wide L-shaped gate hinged at the point B. To close the gate, a mass with unknown weight W at the point A and a fixed ridge at the point C are used to exert some external forces on the gate. It is known that the gate will open when the water level in the reservoir reaches a height of 5.87 m. 2.75 m L-shaped gate 7.63 m 5.87 m FR Ridge FRidge FRidge (a) Calculate the submerged area of L-shaped gate that in contact with the water (treating it as a flat plate). [1 marks] (b) Calculate the hydrostatic pressure acting on the centroid and the centre of pressure of the gate. [4 marks] (c) Calculate the magnitude and define the location of resultant hydrostatic force that acting on the gate surface. [5 marks] (d) By performing the moment balance at two possible points, calculate required weight W to shut the gate if the force exerted by the ridge is 10 kN. (Hint: you will obtain either 1 or 2 [6 marks] values for W here) (e) Based on the answer of weight in the part (d), the selection of which point (out of the two possible points) provides sensible answer? Does it make any sense from the perspective of [2 marks] physics? Justify your answer. (f) Based on the answer in the part (d), try to comment on the feasibility of the design of such system. Does the design fail from the perspective of physics and mathematics? Justify your [2 marks] answer. The flow of water from a reservoir is controlled by a 3.5-m-wide L-shaped gate hinged at the point B. To close the gate, a mass with unknown weight W at the point A and a fixed ridge at the point C are used to exert some external forces on the gate. It is known that the gate will open when the water level in the reservoir reaches a height of 5.87 m. 2.75 m L-shaped gate 7.63 m 5.87 m FR Ridge FRidge FRidge (a) Calculate the submerged area of L-shaped gate that in contact with the water (treating it as a flat plate). [1 marks] (b) Calculate the hydrostatic pressure acting on the centroid and the centre of pressure of the gate. [4 marks] (c) Calculate the magnitude and define the location of resultant hydrostatic force that acting on the gate surface. [5 marks] (d) By performing the moment balance at two possible points, calculate required weight W to shut the gate if the force exerted by the ridge is 10 kN. (Hint: you will obtain either 1 or 2 [6 marks] values for W here) (e) Based on the answer of weight in the part (d), the selection of which point (out of the two possible points) provides sensible answer? Does it make any sense from the perspective of [2 marks] physics? Justify your answer. (f) Based on the answer in the part (d), try to comment on the feasibility of the design of such system. Does the design fail from the perspective of physics and mathematics? Justify your [2 marks] answer.