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Homework Statement
A inverted isosceles triangle gate with height a=3ft and base b=2ft is 6ft under the water (top of the inverted triangle). Find the Force on the gate and hp (the depth of the) center of pressure.
Homework Equations
hc= depth to gate + depth to centroid= 6+(1/3)•3= 6+1 = 7
Force = γ hc A = 62.4 • 7 • (0.5•2•3) = 1310 lb
Area Moment of Inertia of Triangle = Ic =ba³/36
So hp = hc + Ic/(hc•A) = 7 + [2*3³/36/(7*0.5*2*3)] = 7.07 ft
The Attempt at a Solution
What I don't understand is why Ic does not depends on whether the triangle is inverted or not. I looked >10 sites and always the triangle is "base down" and ALL of the other figures are symmetric so I cannot compare. (Sorry cannot put in sample link from wikipedia.)
I am a mathematician trying to help my son (studying engineering). I cannot find an integral for this to test how the "area of moment of inertia" is calculated (and I don't really understand what it is as I do with the centroid).
Thanks for any help. Linda