Plant Oil Sdn. Bhd. used a storage tank (1.71-m long) to temporarily store refined palm oil (p = 892.5 kg/m3) before the packaging process. To automate discharging process, a 1.71-m long quarter-circular gate (AB) of radius 1.76 m and of negligible weight is hinged at the upper edge point B. The gate regulates the flow of palm oil over an inclined ledge at A, where the gate is pressed by a spring at 15. The palm oil is continuously supplied from a production line, hence constantly accumulate in the storage tank. When the depth from free surface to the imaginary boundary of submerged curved surface reaches 5.26 m, the gate opens by turning about the ledge at point A. For this complex submerged curved surface, the imaginary boundary is drawn as blue colour dotted line to ease the analysis of fluid statics. Storage tank Palm oil 5.26 m 1.76-m y radius FH FRCs Curved surface O Width F. sp Fy Spring 150 W (a) Calculate the volume and weight of the palm oil within the imaginary boundary. (3 Marks) (b) Compute the area of the vertical projection of the curved surface, the vertical distance from the free surface to the centroid of the vertical projection of curved surface, and the average hydrostatic pressure as well as the hydrostatic force acting on the vertical projection of curved surface. (5 Marks) (c) Compute the area of the horizontal projection of curved surface, the vertical distance from the free surface to the centroid of the horizontal projection of curved surface, and the average hydrostatic pressure as well as hydrostatic force acting on the horizontal projection of curved surface. (5 Marks) CONFIDENTIAL (d) By performing force balances, determine the hydrostatic force exerted by the palm oil on the quarter-circular gate and its line of action when the gate opens. Draw the force diagram for resultant hydrostatic force exerted by the palm oil on the quarter-circular gate. (7 Marks) (e) Sketch a free body diagram for the fluid body inside the imaginary boundary and label all the relevant forces. By perform moment balance at appropriate point, calculate the magnitude of spring force. (Hint: It is easier to solve by using resolved components) (5 Marks) Length