Answer:
If the square end is under water: 312271.92 N
If the round end is under water: 262976.67 N
Step-by-step explanation:
We have to:
P = ρ·g·d
where:
P is hydrostatic pressure, g is gravitational acceleration, d is depth, ρ is fluid density
Force = hydrostatic pressure x submerged area
F = PA
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If the square end is under water:
F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy .... from 0 to 2
F = 19620 ∫ (2-y)√(64 - y²) dy .... from 0 to 2
The result of the solution of the integral is 15.916
Thus:
F = 15.916*19620 = 312271.92 N
If the round end is under water:
F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy .... from 3 to 5
F = 19620 ∫ (y - 3) √(25 - y²) dy .... from 3 to 5
The result of the solution of the integral is 13.403
Thus:
= 13.403*19620 = 262976.67 N
The hydrostatic force against one side of the plate:
If the square end is under water is 312271.92 N
If the round end is under water is 262976.67 N
This is the resultant force caused by the pressure loading of a liquid acting on submerged surfaces.
Hydrostatic pressure (P) = ρ·g·d where ρ is fluid density , g is gravitational acceleration, d is depth.
Force = hydrostatic pressure x submerged area
F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy .. from 0 to 2
F = 19620 ∫ (2-y)√(64 - y²) dy .... from 0 to 2
= 15.916
F = 15.916× 19620 = 312271.92 N
F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy ... from 3 to 5
F = 19620 ∫ (y - 3) √(25 - y²) dy ...from 3 to 5
= 13.403
F = 13.403*19620 = 262976.67 N.
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