Water The fluid(water) will exert a force on the wall due to pressure. Pressure in general will be a function of position over the surface(i.e., a function of x and y). For the picture shown it will simply be a function of y in specified coordinate system. For the selected element, the contribution to the overall force will be dF = - p dA n = p dA k (n -a unit vector, ┴ to dA in H2O) If you were to choose another element at a different location, the pressure might be different and its contribution to the overall force higher or lower depending upon its depth. x y Water dA n Wall of width W and height H To find the total force on the wall, we must integrate because pressure is not constant. In this coordinate system dA = dx dy. H W FR =  dF = -   p dA =   p dx dy k   A   0 0 The pressure must be found in terms of x and y to do the math: p(y) = Po + gy From the hydrostatic equation, we know p = p(y), so it is treated as a constant when we integrate w.r.t. x: H H FR = W  p dy k = W  [Po + gy] dy k   0 0 We carry out the integration. Hence, FR = {PoWH+ gWH2/2} k