Submerged Gate: Moment at Hinge

What would be the Hc( centroid height) if theres water on both sides at different pevers for example. 7.5 m water on on side and 3 m on the other

Can you explain why the center of force is 2/3 from the surface? This is glossed over.

Perfect! Thank you!

Exactly what I was looking for. Thanks!

All my doubts are clear now.

This is wrong at all perspectives don't use it. For a surface pressure on a side wall, you drew a rectangle which the center of the force should be 2/3 * a away from the top right corner rather than half way. The hc and yc of this question not only equal with each other but also equal to 2a/3. Too bad thousands of people got a question or two if not a whole concept wrong thanks to you guys!

Sir,what value of hc should we take if water level and total height of gate are different

How would this related if the hinge was off the bottom and the gate to be opened is below the hinge.

I had a PhD qualifier exam where we had a similar question but the gate height and length was given by a sinusoidal function. I was so lost, I ended up integrating but I don’t think I was correct