# Plant Oil Sdn. Bhd. used a storage tank (1.71-m long)

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
В
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