Show that the resultant of the hydrostatic forces acting on a submerged plane area A is a force P perpendicular to the area and of magnitude P Icirc sup3 Ay sin Icirc cedil pA, where Icirc sup3 is the specific weight of the liquid and p is the pressure at the centroid C of the area Show that P is a...

The pressure p at an arbitrary depth y sin is p yysine so that the hydrostatic force ...

Show that the resultant of the hydrostatic forces acting on a submerged plane area A is a

Question:

Show that the resultant of the hydrostatic forces acting on a submerged plane area A is a force P perpendicular to the area and of magnitude P = Î³Ay sin Î¸ = pA, where Î³ is the specific weight of the liquid and p is the pressure at the centroid C of the area. Show that P is applied at a point Cp, called the center of pressure, whose coordinates are xp = Ixy / Ay and yp = Ix/Ay, where Ixy = ˆ«xydA (see Sec. 9.8). Show also that the difference of ordinates yp ˆ’ y is equal to k2/x/y and thus depends upon the depth at which the area is submerged.