Fluid Mechanics- Pressure on a gate

[giacomh]

Homework Statement

http://imgur.com/vXkg0

Homework Equations

Fw=γAH

Ycp=bh³/(12)(h/2)b + (h/2)

The Attempt at a Solution

I found the angle of the gate from the horizontal to be 53.1 degrees. Using this, I found y to be 2.5m and H (vertical distance to centroid) to be 6 m (2.5sin(53.1)+4).

I then found Fw=9810*6*(4*5)=1177200N, and Ycp=(4*5³)/(12*20*2.5) +2.5=3.33m.

By taking the moment at the ground, I found Fw*(5-3.33)-5P=0, so P= 393kN. My book says the answer should be 523 kN. Help please.

 

[rude man]

The picture does not show the angle P makes with the horizontal or vertical, so the question looks unanswerable to me. P could be an angle perpendicular to the 5m line or at some angle away from perpendicularity.

 

[giacomh]

I believe that P is supposed to be perpendicular surface (opposing Fw)