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 = γ Ay sin θ = pA , where γ 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 = ∫ xy dA (see Sec. 9.8). Show also that the difference of ordinates yp−y is equal to kx2′x /y and thus depends upon the depth at which the area is submerged.
Step by Step Answer:
The pressure p at an arbitrary depth y sin is p yysine so that the hydrostatic force d...View the full answer
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