Assuming this is a pressurized chamber with hydro-static force acting on a semi circle stuck in a surface:
To find the resultant force, I would first divide the semicircle into half. Pressure on curve surface is equivalent to pressure on projected surface form the curve. Therefore, I can find the resultant force (F1) from multiplying water pressure (P) with radius of the circle (R):
Where $F_1 = P \times R$
Considering the other half of the semicircle, my free body diagram should look like this also:
Where $F_2 = P \times (R-r)$
Therefore, my resultant force should equals to $F_1 - F_2$.
I would like to know if this is the correct way of calculating the resultant force for such scenario.