# statics problem, help needed

#### dbag

Hello

Problem description: determine the lenght of h with respect to b so that the water flows. ive gotten as far as come up with an equation for the sum of moments and it goes as follows: $$\displaystyle bh*1/2b-1/2hb*1/3b=0$$ the answer is wrong and i dont know why. moment arm on the b is 1/2b and the moment arm on h is 1/3h because of the way water pressure works , meaning its a uniform load in the shape od triangle. the answer to this problem is supposed to be $$\displaystyle sqrt3 *b$$. Any help appreciated.

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#### oz93666

force acting on face length b .....= dencity x b x width x gravity x h , this acts at center of face so the turning torque is... dencity x 1/2 x b x b x width x gravity x h

Force acting on face h is ....= 1/2 dencity x h x width x gravity x h
This force acts 1/3 of the way up (www.youtube.com/watch?v=WkM1tCZDM2c)
so torque is ..... = 1/3 h x 1/2 dencity x h x width x gravity x h

tipping occurs when two torques are equal

so b x b = 1/3 x h x h so 3 b squared = h squared .... h = root 3 b

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#### dbag

thank you very much