Question 3.P.22: An oil tank of elliptical section of major axis 3 m and mino......
An oil tank of elliptical section of major axis 3 m and minor axis 2 m is completely filled with oil of specific gravity 0.9. The tank is 6 m long and has flat vertical ends. Determine the forces and their direction of action on the two sides and the ends.
Considering the surface of the left half of the tank, horizontal force = γ \bar{h} A
= 9810 × 0.9 × 1 × 2 × 6 = 105948 N to the left
Line of action = 1 + (6 × 2³/12) (1/1) (1/6 × 2) = 1.333 m from top. Similar force acts on the right half of the tank to the right, at the same level.
Vertical force on the left half = Weight of displaced liquid
= 9810 × 0.9 × (π × 3 × 2/4 × 2) = 20803 \mathrm{N}
downward and the location is 4h/3π = 4 × 1.5/3π = 0.63662 \mathrm{m}, from centre line
Resultant = (105948^{2} + 20803^{2})^{0.5} = 107971 \mathrm{N}
Direction (with vertical) = \tan^{– 1} (105948/20803) = 78.89°. Similar force acts on the other half.
Ends: Elliptical surfaces : F = γ \bar{h} A = 9810 × 0.9 × 1 × π × 3 × 2/4 = 41606 \mathrm{N}
Line of action = 1 + (π × 3 × 2³/64) (1/1) (4/π × 3 × 2)
= 1.25 m from top.