I want someone to prove to me that the equation 3.26 / 3.27 is valid in terms of symbols.

How integral of ydA becomes y bar times A

P = -Az = yy sin a (3.25) 2 Combine Eqs. (3.24) and (3.25) to give First moment > ghet F - / paa - ( vy sin pd A = yy sin a dA = y sin ayda af yda (3.26) Hydro count Hy on state force Because the integral on the right side of Eq. (3.26) is the first moment of the area, replace the integral by its equivalent, yA. Therefore How? 9.55 y = 5 F = yy A sin a = (yy sin a)A (3.27) Apply the hydrostatic equation to show that the variables within the parentheses on the right side of Eq. (3.27) are the pressure at the centroid of the area. Thus, Ep = A (3.28)