Answer:
Hydrostatic Force = 35.28KN
Step-by-step explanation:
To solve this question, let's consider integrating the hydrostatic force from the top of the triangle to the bottom.
Formula for a thin horizontal slice of the triangle the force is;
δF=ρgxwδx
Where w is width of triangle; ρ is density of water and g is acceleration due to gravity
At depth x, the width of the triangle is w=2/3x.
Thus, F = (3,0)∫)ρgxwδx
=(2/3)ρg[(3,0)∫)x²δx]
= integrating, we have;
F = (2/3)ρg[(3³/3) - (0³/3)]
F = (2/5)ρg [27/3] = (2/5)(1000)(9.8)(9) = 35280 N = 35.28 KN
