Answer:
Hydrostatic Force = 14952.35N
Step-by-step explanation:
From the question, we are given;
Diameter of hemispherical plate = 6 ft
Height of submergence = 2ft
Weight density of water = 62.5 lb/ft³
Now, if we assume that the hemispherical plate is residing on x and y axis, then bottom of the plate is on x-axis while the left side of the plate touches the y-axis
Now, the plate is defined by the upper half of the circle as;
(x - 3)² + (y-0)² = 3²
(x - 3)² + y² = 9
Thus, y² = 9 - (x - 3)²
y = √(9 - (x - 3)²)
To solve this, hydro static force on one side of plate is given as;
F = ∫ ρgd•xw(x)δx =
2∫ρgx√(9 - (x - 3)²)δx at boundary of 3 and 0
F = 62.5•9.8•2∫x√(9 - (x - 3)²)δx at boundary of 3 and 0
F = 1225[(27π/4) - 9]
F = 1225 x 12.206 = 14952.35N
