F&B Sdn. Bhd. designed a storage tank (0.003-km long) to temporarily store carbonated 8- up soft...

 

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F&B Sdn. Bhd. designed a storage tank (0.003-km long) to temporarily store carbonated 8- up" soft drink (SG 0.97) before the canning process. To automate the discharging process, a %3D 300-cm long quarter-circular gate (AB) of diameter 2.64 m and of negligible weight is hinged at the upper edge point B. The gate regulates the flow of "8-up" soft drink over the vertical ledge at A. where the gate is pressed by a spring. The "8-up" soft drink is continuously supplied from a production line, hence constantly accumulate in the storage tank. When the depth from the free surface to the imaginary boundary of submerged curved surface reaches 275 cm, the gate opens by turning about the ledge at point A. For this complex submerged curved surface, the imaginary boundary is provided as blue colour dotted line to ease the analysis of fluid statics. statics. to ease the analysis of fluid Storage tank "8-up" soft drink 275 cm F C Quarter- circular gate -FH Fx Length Width X. Spring F FR.Curved surface (FR.eS) Fy sp Table: Centroid and area of simple geometry OHeight (3 Marks) (c) Weight is a force component that exerted on the fluid body due to the gravity. It is well- known that the weight always acts downwards through the centroid point of the fluid body. Determine the centroid point (x and y) by using the point A as the reference point. (3 Marks) (d) Compute the area of vertical projection of curved surface, and the average hydrostatic pressure as well as hydrostatic force acting on the vertical projection of curved surface. (6 Marks) (e) Compute the area of the horizontal projection of curved surface, and average hydrostatic pressure as well as hydrostatic force acting on horizontal projection of curved surface. (6 Marks) (f) Determine the hydrostatic force exerted by the 8-up" soft drink on the quarter-circular gate and its line of action when the gate opens. Sketch the completely resolved force diagrams for resultant hydrostatic force exerted by the "8-up" soft drink on the quarter- circular gate and the reaction force acting on "8-up" soft drink by the quarter-circular gate (10 Marks) (g) Sketch a free body diagram for the fluid body inside the imaginary boundary and label all the relevant forces. Calculate the magnitude of spring force. (5 Marks) F&B Sdn. Bhd. designed a storage tank (0.003-km long) to temporarily store carbonated 8- up" soft drink (SG 0.97) before the canning process. To automate the discharging process, a %3D 300-cm long quarter-circular gate (AB) of diameter 2.64 m and of negligible weight is hinged at the upper edge point B. The gate regulates the flow of "8-up" soft drink over the vertical ledge at A. where the gate is pressed by a spring. The "8-up" soft drink is continuously supplied from a production line, hence constantly accumulate in the storage tank. When the depth from the free surface to the imaginary boundary of submerged curved surface reaches 275 cm, the gate opens by turning about the ledge at point A. For this complex submerged curved surface, the imaginary boundary is provided as blue colour dotted line to ease the analysis of fluid statics. statics. to ease the analysis of fluid Storage tank "8-up" soft drink 275 cm F C Quarter- circular gate -FH Fx Length Width X. Spring F FR.Curved surface (FR.eS) Fy sp Table: Centroid and area of simple geometry OHeight (3 Marks) (c) Weight is a force component that exerted on the fluid body due to the gravity. It is well- known that the weight always acts downwards through the centroid point of the fluid body. Determine the centroid point (x and y) by using the point A as the reference point. (3 Marks) (d) Compute the area of vertical projection of curved surface, and the average hydrostatic pressure as well as hydrostatic force acting on the vertical projection of curved surface. (6 Marks) (e) Compute the area of the horizontal projection of curved surface, and average hydrostatic pressure as well as hydrostatic force acting on horizontal projection of curved surface. (6 Marks) (f) Determine the hydrostatic force exerted by the 8-up" soft drink on the quarter-circular gate and its line of action when the gate opens. Sketch the completely resolved force diagrams for resultant hydrostatic force exerted by the "8-up" soft drink on the quarter- circular gate and the reaction force acting on "8-up" soft drink by the quarter-circular gate (10 Marks) (g) Sketch a free body diagram for the fluid body inside the imaginary boundary and label all the relevant forces. Calculate the magnitude of spring force. (5 Marks)