# Fluid mechanics problem: Hydrostatic forces acting on a gate

• civil_eng_student
In summary, fluid mechanics is a branch of physics that studies the behavior of fluids and the forces acting on them. Hydrostatic forces, which are caused by the weight of a fluid at rest, can be calculated by multiplying the density of the fluid, gravitational acceleration, and height of the fluid above the surface. These forces can affect the stability of a gate, making proper design and placement important for withstanding them. The equation for calculating hydrostatic forces is F = ρghA.

#### civil_eng_student

Homework Statement
hydrostatic forces acting on gate,need to find the force at point X in order to have equilibrium
Relevant Equations
I posted this because i used two methods in order to find the force acting at point X but i get different results...
my thoughts:
in order to find the force at X i just need to ΣΜ(B)=0 so i just need to find the forces acting on ABD.
first on AB i found the hydrostatic force =(1/2)*2,25*γ*2,25*length and the distance from b is 0,75m.
secondly we have a uniformly load acting on BD=2,25*γ*2*length and distance 1 from b.
under ABD we have a quarter of a circle so i know that the forces acts on B(the center) so they dont give any moments...
then i sum the moments and find the force.
now using the second method is finding the forces acting on the quarter and not putting them acting on the center.
for the horizontal force i find F1=2,25*γ*R*lenght and F2=(1/2)*2*γ*R*length. F1 is acting 1 from b and F2 4/3.
then the vertical acts on the centroid and the distance is 4*R/3*PI=0,848.
then i sum the moments and find a different result for the force a X.
hope i was clear.

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can anyone check if i am right? thanks a lot