Example 5

In the side wall of the tank, which is under pressure \( p_n = 4905 Pa \), there is a hole. The hole is closed by a flat flap with a width of L using a float in the shape of a cone with a height of d connected to a half of a sphere with a radius of r. The flap can rotate relative to point O. The float has a mass m. The elevation of the vertex of the float above the axis of rotation of the flap is b. The vertex of the float is submerged at a depth of a. What volume V must the float have to ensure the closure of the hole as shown in the picture?
Data: \( a=0.25m, b=0.75m, d=0.5m, m=10kg, \rho_{H_2O} = 1000 kg/m^3, L=0.5m, p_n=4905Pa \)

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